1. In the equation above, x =

2. Triangle ABC is an equilateral triangle with an altitude of 6. What is its area?

3. In the equation above, x =

The second one throws in a little geometry. You may want to review the properties of the 30-60-90 Triangle and the Equilateral Triangle if those are unfamiliar. The first one is just straightforward arithmetic. The third is quite hard. For any of these, it may well be that, even if you did all your multiplication and division correctly, you wound up with an answers of the form — something divided by the square root of something — and you are left wondering: why doesn’t this answer even appear among the answer choices? If this has you befuddled, you have found exactly the right post.

When we first met fractions, in our tender prepubescence, both the numerators and denominators were nice easy positive integers. As we now understand, any kind of real number, any number on the entire number line, can appear in the numerator or denominator of a fraction. Among other things, radicals —- that is, square-root expressions —- can appear in either the numerator or denominator. There’s no particular issue if we have the square-root in a numerator. For example,

is a perfectly good fraction. In fact, those of you who ever took trigonometry might even recognize this special fraction. Suppose, though, we have a square root in the denominator: what then? Let’s take the reciprocal of this fraction.

This is no longer a perfectly good fraction. Mathematically, this is a fraction “in poor taste”, because we are dividing by a square-root. This fraction is crying out for some kind of simplification. How do we simplify this?

By standard mathematical convention, a convention the GMAT follows, we don’t leave square-roots in the denominator of a fraction. If a square-root appears in the denominator of a fraction, we follow a procedure called **rationalizing the denominator**.

We know that any square root times itself equals a positive integer. Thus, if we multiplied a denominator of the square root of 3 by itself, it would be 3, no longer a radical. The trouble is —- we can’t go around multiplying the denominator of fractions by something, leaving the numerator alone, and expect the fraction to maintain its value. BUT, remember the time-honored fraction trick — we can always multiply a fraction by A/A, by something over itself, because the new fraction would equal 1, and multiplying by 1 does not change the value of anything.

Thus, to simplify a fraction with the square root of 3 in the denominator, we multiply by the square root of 3 over the square root of 3!

That last expression is numerically equal to the first expression, but unlike the first, it is now in mathematical “good taste”, because there’s no square root in the denominator. The denominator has been rationalized (that is to say, the fraction is now a rational number).

Sometimes, some canceling occurs between the number in the original numerator and the whole number that results from rationalizing the denominator. Consider the following example:

That pattern of canceling in the simplification process may give you some insight into practice problem #1 above.

This is the next level of complexity when it comes to dividing by square roots. Suppose we are dividing a number by an expression that involves adding or subtracting a square root. For example, consider this fraction:

This is a fraction in need of rationalization. BUT, if we just multiply the denominator by itself, that WILL NOT eliminate the square root — rather, it will simply create a more complicated expression involving a square root. Instead, we use the difference of two squares formula, = (a + b)(a – b). Factors of the form (a + b) and (a – b) are called **conjugates** of one another. When we have (number + square root) in the denominator, we create the conjugate of the denominator by changing the addition sign to a subtraction sign, and then multiply both the numerator and the denominator *by the conjugate of the denominator*. In the example above, the denominator is three minus the square root of two. The conjugate of the denominator would be three ** plus** the square root of two. In order to rationalize the denominator, we multiply both the numerator and denominator by this conjugate.

Notice that the multiplication in the denominator resulted in a “differences of two squares” simplification that cleared the square roots from the denominator. That final term is a fully rationalized and fully simplified version of the original.

Having read these posts about dividing by square roots, you may want to give the three practice questions at the top of this article another try, before reading the explanations below. If you have any questions on dividing by square roots or the explanations below, please ask them in the comments sections! And good luck conquering these during your GMAT!

1) To solve for x, we will begin by cross-multiplying. Notice that

because, in general, we can multiply and divide through radicals.

Cross-multiplying, we get

You may well have found this and wondered why it’s not listed as an answer. This is numerically equal to the correct answer, but of course, as this post explains, this form is not rationalized. We need to rationalize the denominator.

Answer = **(D)**

2) We know the height of ABC and we need to find the base. Well, altitude BD divides triangle ABC into two 30-60-90 triangles. From the proportions in a 30-60-90 triangle, we know:

Now, my predilection would be to rationalize the denominator right away.

Now, AB is simplified. We know AB = AC, because the ABC is equilateral, so we have our base.

Answer = **(C)**

3) We start by dividing by the expression in parentheses to isolate x.

Of course, this form does not appear among the answer choices. Again, we need to rationalize the denominator, and this case is a little trickier because we have addition in the denominator along with the square root. Here we need to find the conjugate of the denominator —- changing the plus sign to a minus sign — and then multiply the numerator and denominator by this conjugate. This will result in —-

Answer = **(A)**

The post GMAT Math: How to Divide by a Square Root appeared first on Magoosh GMAT Blog.

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1) Let abcd be a general four-digit number and all the digits are non-zero. How many four-digits numbers abcd exist such that the four digits are all distinct and such that a + b + c = d?

(A) 6

(B) 7

(C) 24

(D) 36

(E) 42

2) Let abcd be a general four-digit number. How many odd four-digits numbers abcd exist such that the four digits are all distinct, no digit is zero, and the product of a and b is the two digit number cd?

(A) 4

(B) 6

(C) 12

(D) 24

(E) 36

3) There are 500 cars on a sales lot, all of which have either two doors or four doors. There are 165 two-door cars on the lot. There are 120 four-door cars that have a back-up camera. Eighteen percent of all the cars with back-up cameras have standard transmission. If 40% of all the cars with both back-up cameras and standard transmission are two-door cars, how many four-door cars have both back-up cameras and standard transmission?

(A) 18

(B) 27

(C) 36

(D) 45

(E) 54

4) At Mnemosyne Middle School, there are 700 students: all the students are boys or girls in the 4^{th} or 5^{th} grade. There are 320 students in the 4^{th} grade, and there are 210 girls in the 5^{th} grade. Fifty percent of the 5^{th} graders and 40% of the 4^{th} graders take Mandarin Chinese. Ninety 5^{th} grade boys do not take Mandarin Chinese. The number of 4^{th} grade girls taking Mandarin Chinese is less than half of the number of 5^{th} grade girls taking Mandarin Chinese. Which of the following could be the number of 5^{th} grade boys in Mandarin Chinese?

(A) 10

(B) 40

(C) 70

(D) 100

(E) 130

5) A hundred identical cubic boxes are currently arranged in four cubes: a single cubic box, a 2 x 2 x 2 cube, a 3 x 3 x 3 cube, and a 4 x 4 x 4 cube. These four are not touching each other. All outward faces are painted and all inward faces are not painted. These four cubes are going to be dismantled and reassembled as a flat 10 x 10 square. The top and all the edges of this 10 x 10 square must be painted, but there is no requirement for paint on the bottom. How many individual faces will have to be painted to accommodate the requirements of this new design?

(A) 0

(B) 5

(C) 9

(D) 16

(E) 27

6) Twelve points are spaced evenly around a circle, lettered from A to L. Let N be the total number of isosceles triangles, including equilateral triangles, that can be constructed from three of these points. A different orientation of the same lengths counts as a different triangle, because a different combination of points form the vertices. What is the value of N?

(A) 48

(B) 52

(C) 60

(D) 72

(E) 120

7) Theresa is a basketball player practicing her free throws. On her first free throw, she has a 60% chance of making the basket. If she has just made a basket on her previous throw, she has a 80% of making the next basket. If she has just failed to make a basket on her previous throw, she has a 40% of making the next basket. What is the probability that, in five throws, she will make at least four baskets?

8) Suppose a “Secret Pair” number is a four-digit number in which two adjacent digits are equal and the other two digits are not equal to either one of that pair or each other. For example, 2209 and 1600 are “Secret Pair” numbers, but 1333 or 2552 are not. How many “Secret Pair” numbers are there?

(A) 720

(B) 1440

(C) 1800

(D) 1948

(E) 2160

9) In the coordinate plane, a circle with its center on the negative x-axis has a radius of 12 units, and passes through (0, 6) and (0, – 6). What is the area of the part of this circle in the first quadrant?

10) In the coordinate plane, line L passes above the points (50, 70) and (100, 89) but below the point (80, 84). Which of the following could be the slope of line L?

(A) 0

(B) 1/2

(C) 1/4

(D) 2/5

(E) 6/7

11) At the beginning of the year, an item had a price of A. At the end of January, the price was increased by 60%. At the end of February, the new price was decreased by 60%. At the end of March, the new price was increased by 60%. At the end of April, the new price was decreased by 60%. On May 1^{st}, the final price was approximately what percent of A?

(A) 41%

(B) 64%

(C) 100%

(D) 136%

(E) 159%

12) Suppose that, at current exchange rates, $1 (US) is equivalent to Q euros, and 1 euro is equivalent to 7Q Chinese Yuan. Suppose that K kilograms of Chinese steel, worth F Chinese Yuan per kilogram, sold to a German company that paid in euros, can be fashioned into N metal frames for chairs. These then are sold to an American company, where plastic seats & backs will be affixed to these frames. If the German company made a total net profit of P euros on this entire transaction, how much did the US company pay in dollars for each frame?

13) At the Zamenhof Language School, at least 70% of the students take English each year, at least 40% take German each year, and between 30% and 60% take Italian each year. Every student must take at least one of these three languages, and no student is allowed to take more than two languages in the same year. What is the possible percentage range for students taking both English and German in the same year?

(A) 0% to 70%

(B) 0% to 100%

(C) 10% to 70%

(D) 10% to 100%

(E) 40% to 70%

14) On any given day, the probability that Bob will have breakfast is more than 0.6. The probability that Bob will have breakfast **and** will have a sandwich for lunch is less than 0.5. The probability that Bob will have breakfast **or** will have a sandwich for lunch equals 0.7. Let P = the probability that, on any given day, Bob will have a sandwich for lunch. If all the statements are true, what possible range can be established for P?

(A) 0 < P < 0.6

(B) 0 ≤ P < 0.6

(C) 0 ≤ P ≤ 0.6

(D) 0 < P < 0.7

(E) 0 ≤ P < 0.7

(A) – 64

(B) – 7

(C) 38

(D) 88

(E) 128

Explanations for this problem are at the end of this article.

Here are twenty-eight other articles on this blog with free GMAT Quant practice questions. Some have easy questions, some have medium, and few have quite challenging questions.

1) GMAT Geometry: Is It a Square?

2) GMAT Shortcut: Adding to the Numerator and Denominator

3) GMAT Quant: Difficult Units Digits Questions

4) GMAT Quant: Coordinate Geometry Practice Questions

5) GMAT Data Sufficiency Practice Questions on Probability

6) GMAT Quant: Practice Problems with Percents

7) GMAT Quant: Arithmetic with Inequalities

8) Difficult GMAT Counting Problems

9) Difficult Numerical Reasoning Questions

10) Challenging Coordinate Geometry Practice Questions

11) GMAT Geometry Practice Problems

12) GMAT Practice Questions with Fractions and Decimals

13) Practice Problems on Powers and Roots

14) GMAT Practice Word Problems

15) GMAT Practice Problems: Sets

16) GMAT Practice Problems: Sequences

17) GMAT Practice Problems on Motion

18) Challenging GMAT Problems with Exponents and Roots

19) GMAT Practice Problems on Coordinate Geometry

20) GMAT Practice Problems: Similar Geometry Figures

20) GMAT Practice Problems: Variables in the Answer Choices

21) Counting Practice Problems for the GMAT

22) GMAT Math: Weighted Averages

23) GMAT Data Sufficiency: More Practice Questions

24) Intro to GMAT Word Problems, Part I

25) GMAT Data Sufficiency Geometry Practice Questions

26) GMAT Data Sufficiency Logic: Tautological Questions

27) GMAT Quant: Rates and Ratios

28) Absolute Value Inequalities

These are hard problems. When you read the solutions, don’t merely read them passively. Study the strategies used, and do what you can to retain them. Learn from your mistakes!

1) We need sets of three distinct integers {a, b, c} that have a sum of one-digit number d. There are seven possibilities:

- a) {1, 2, 3}, sum = 6
- b) {1, 2, 4}, sum = 7
- c) {1, 2, 5}, sum = 8
- d) {1, 3, 4}, sum = 8
- e) {1, 2, 6}, sum = 9
- f) {1, 3, 5}, sum = 9
- g) {2, 3, 4}, sum = 9

For each set, the sum-digit has to be in the one’s place, but the other three digits can be permutated in 3! = 6 ways in the other three digits. Thus, for each item on that list, there are six different possible four-digit numbers. The total number of possible four-digit numbers would be 7*6 = 42. Answer =** (E)**

2) The fact that abcd is odd means that cd must be an odd number and that a & b both must be odd. That limits the choices significantly. We know that neither a nor b can equal 1, because any single digit number times 1 is another single digit number, and we need a two-digit product—there are no zeros in abcd. We also know that neither a nor b can equal 5, because any odd multiple of 5 ends in 5, and we would have a repeated digit: the requirement is that all four digits be distinct.

Therefore, for possible values for a & b, we are limited to three odd digits {3, 7, 9}. We can take three different pairs, and in each pair, we can swap the order of a & b. Possibilities:

- use {3, 7}, product = 21, abcd could be 3721 or 7321
- use {3, 9}, product = 27, abcd could be 3927 or 9327
- use {7, 9}, product = 63, abcd could be 7963 or 9763

Those six are the only possibilities for abcd.

Answer = **(B)**

3) Total number of cars = 500

2D cars total = 165, so

4D cars total = 335

120 4D cars have BUC

“*Eighteen percent of all the cars with back-up cameras have standard transmission*.”

18% = 18/100 = 9/50

This means that the number of cars with BUC must be a multiple of 50.

How many 2D cars can we add to 120 4D cars to get a multiple of 50? We could add 30, or 80, or 130, but after that, we would run out of 2D cars. These leaves three possibilities for the total number with BUC:

If a total of 150 have BUC, then 18% or 27 of them also have ST.

If a total of 200 have BUC, then 18% or 36 of them also have ST.

If a total of 250 have BUC, then 18% or 45 of them also have ST.

Then we are told: “*40% of all the cars with both back-up cameras and standard transmission are two-door car*.”

40% = 40/100 = 2/5

This means that number of cars with both back-up cameras and standard transmission must be divisible by 5. Of the three possibilities we have, only the third words.

Total cars with BUC cams = 250 (120 with 4D and 130 with 2D)

18% or 45 of these also have ST.

40% of that is 18, the number of 2D cars with both BUC and ST.

Thus, the number of 4D cars with both BUC and ST would be

45 – 18 = 27

Answer = **(B)**

4) 700 student total

4G = total number of fourth graders

5G = total number of fifth graders

We are told 4G = 320, so 5G = 700 – 320 = 380

5GM, 5GF = fifth grade boys and girls, respectively

We are told 5GF = 210, so 5GM = 380 – 210 = 170

4GC, 5GC = total number of 4^{th} or 5^{th} graders, respectively taking Chinese

We are told

5GC = 0.5(5G) = 0.5(380) = 190

4GC = 0.4(4G) = 0.4(320) = 128

4GFM, 4GMC, 5GFC, 5GMC = 4^{th}/5^{th} grade boys & girls taking Chinese

We are told that, of the 170 fifth grade boys, 90 do not take Chinese, so 170 = 90 = 80 do. Thus 5GMC = 80.

5GMC + 5GFC = 5GC

80 + 5GFC = 190

5GFC = 110

We are told:

4GFM < (0.5)(5GFC)

4GFM < (0.5)(100)

4GFM < 55

Thus, 4GFM could be as low as zero or as high as 54.

4GMC = 4GC – 4GFM

If 4GFM = 0, then 4GMC = 128 – 0 = 128

If 4GFM = 54, then 4GMC = 128 – 54 = 74

Thus, fourth grade boys taking Mandarin Chinese could take on any value N, such that 74 ≤ N ≤ 128. Of the answer choices listed, the only one that works is 100.

Answer = **(D)**

5) The single cube has paint on all six sides. Each of the eight boxes in the 2 x 2 x 2 cube has paint on three sides (8 corner pieces). In the 3 x 3 x 3 cube, there are 8 corner pieces, 12 edge pieces (paint on two sides), 6 face pieces (paint on one side), and one interior piece (no paint). In the 4 x 4 x 4 cube, there are 8 corner pieces, 24 edge pieces, 24 face pieces, and 8 interior pieces. This chart summarizes what we have:

For the 10 x 10 flat square, we will need 4 corner pieces that have paint on three sides, 32 edge pieces that have paint on two sides (top & side), and 64 middle pieces that have paint on one side (the top).

We could use either the single total box or any of the 24 corner boxes for the four corners of the square. That leaves 21 of these, and 35 edge boxes, more than enough to cover the 32 edges of the square. The remaining ones, as well as all 30 face boxes, can be turned paint-side-up to fill in the center. The only boxes that will need to be painted, one side each, are the 9 interior boxes. Thus, we have 9 sides to paint.

Answer = **(C)**

6) Here’s a diagram.

First, let’s count the equilateral triangles. They are {AEI, BFJ, CGK, DHL}. There are only four of them.

Now, consider all possible isosceles triangles, excluding equilateral triangles, with point A as the vertex. We could have BAL, CAK, DAJ, and FAH. All four of those have a line of symmetry that is vertical (through A and G). Thus, we could make those same four triangles with any other point as the vertex, and we would never repeat the same triangle in the same orientation. That’s 4*12 = 48 of these triangles, plus the 4 equilaterals, is 52 total triangles.

Answer = **(B)**

7) There are five basic scenarios for this:

__Case I__: (make)(make)(make)(make)(any)

If she makes the first four, then it doesn’t matter if she makes or misses the fifth!

__Case II__: (miss)(make)(make)(make)(make)

__Case III__: (make)(miss)(make)(make)(make)

__Case IV__: (make)(make)(miss)(make)(make)

__Case V__: (make)(make)(make)(miss)(make)

Put in the probabilities:

__Case I__: (0.6)(0.8)(0.8)(0.8)

__Case II__: (0.4)(0.4)(0.8)(0.8)(0.8)

__Case III__: (0.6)(0.2)(0.4)(0.8)(0.8)

__Case IV__: (0.6)(0.8)(0.2)(0.4)(0.8)

__Case V__: (0.6)(0.8)(0.8)(0.2)(0.4)

Since all the answers are fractions, change all of those to fractions. Multiply the first by (5/5) so it has the same denominator as the other products.

__Case I__: (3/5)(4/5)(4/5)(4/5)(5/5) = 960/5^5

__Case II__: (2/5)(2/5)(4/5)(4/5)(4/5) = 256/5^5

__Case III__: (3/5)(1/5)(2/5)(4/5)(4/5) = 96/5^5

__Case IV__: (3/5)(4/5)(1/5)(2/5)(4/5) = 96/5^5

__Case V__: (3/5)(4/5)(4/5)(1/5)(2/5) = 96/5^5

Add the numerators. Since 96 = 100 – 4, 3*96 = 3(100 – 4) = 300 – 12 = 288.

288 + 256 + 960 = 1504

P = 1504/5^5

Answer = **(E)**

8) There are three cases: AABC, ABBC, and ABCC.

In case I, AABC, there are nine choices for A (because A can’t be zero), then 9 for B, then 8 for C. 9*9*8 = 81*8 = 648.

In case II, ABBC, there are 9 choices for A, 9 for B, and 8 for C. Again, 648.

In case III, ABCC, there are 9 choices for A, 9 for B, and 8 for C. Again, 648.

48*3 = (50 – 2)*3 = 150 – 6 = 144

3*648 = 3(600 + 48) = 1800 + 144 = 1948

Answer = **(D)**

9)

We know that the distance from A (0,6) to B (0, – 6) is 12, so triangle ABO is equilateral. This means that angle AOB is 60°. The entire circle has an area of

A 60° angle is 1/6 of the circle, so the area of sector AOB (the “slice of pizza” shape) is

The area of an equilateral triangle with side s is

Equilateral triangle AOB has s = 12, so the area is

If we subtract the equilateral triangle from the sector, we get everything to the right of the x-axis.

Again, that’s everything to the right of the x-axis, the parts of the circle that lie in Quadrants I & IV. We just want the part in Quadrant I, which would be exactly half of this.

Answer = **(C)**

10) One point is (50, 70) and one is (100, 89): the line has to pass above both of those. Well, round the second up to (100, 90)—if the line goes above (100, 90), then it definitely goes about (100, 89)!

What is the slope from (50, 70) to (100, 90)? Well, the rise is 90 – 70 = 20, and the run is 100 – 50 = 50, so the slope is rise/run = 20/50 = 2/5. A line with a slope of 2/5 could pass just above these points.

Now, what about the third point? For the sake of argument, let’s say that the line has a slope of 2/5 and goes through the point (50, 71), so it will pass above both of the first two points. Now, move over 5, up 2: it would go through (55, 73), then (60, 75), then (65, 77), then (70, 79), then (75, 81), then (80, 83). This means it would pass under the third point, (80, 84). A slope of 2/5 works for all three points.

We don’t have to do all the calculations, but none of the other slope values works.

Answer = **(D)**

11) The trap answer is 100%: a percent increase and percent decrease by the same percent do not cancel out.

Let’s say that the A = $100 at the beginning of the year.

End of January, 60% increase. New price = $160

End of February, 60% decrease: that’s a decrease of 60% of $160, so that only 40% of $160 is left.

10% of $160 = $16

40% of $160 = 4(16) = $64

That’s the price at the end of February.

End of March, a 60% increase: that’s a increase of 60% of $64.

10% of $64 = $6.40

60% of $64 = 6(6 + .40) = 36 + 2.4 = $38.40

Add that to the starting amount, $64:

New price = $64 + $38.40 = $102.40

End of April, 60% decrease: that’s a decrease of 60% of $102.40, so that only 40% of $102.40 is left.

At this point, we are going to approximate a bit. Approximate $102.40 as $100, so 40% of that would be $40. The final price will be slightly more than $40.

Well, what is slightly more than $40, as a percent of the beginning of the year price of $100? That would be slightly more than 40%.

Answer = **(A)**

12) The K kilograms, worth F Chinese Yuan per kilogram, are worth a total of KF Chinese Yuan. The German company must pay this amount.

Since 1 euro = (7Q) Chinese Yuan, then (1/(7Q)) euro = 1 Chinese Yuan, and (KF/7Q) euros = KF Chinese Yuan. That’s the amount that the Germans pay to the Chinese.

That is the German company’s outlay, in euros. Now, they make N metal chairs, and sell them, making a gross profit of P euros.

That must be the total revenue of the German company, in euros. This comes from the sale to the American company. Since $1 = Q euros, $(1/Q) = 1 euro, so we change that entire revenue expression to euros to dollars, we divide all terms by Q.

That must be the total dollar amount that leaves the American company and goes to the German company. This comes from the sale of N metal frames for chairs, so each one must have been 1/N of that amount.

Answer = **(A)**

13) First, we will focus on the least, the lowest value. Suppose the minimum of 70% take English, and the minimum of 40% take German. Even if all 30% of the people not taking English take German, that still leaves another 10% of people taking German who also have to be taking English. Thus, 10% is the minimum of this region.

Now, the maximum. Both the German and English percents are “at least” percents, so either could be cranked up to 100%. The trouble is, though, that both can’t be 100%, because some folks have to take Italian, and nobody can take three languages at once. The minimum taking Italian is 30%. Let’s assume all 100% take German, and that everyone not taking Italian is taking English: that’s 70% taking English, all of whom also would be taking German. Thus, 70% is the maximum of this region.

Answer = **(C)**

14) Let A = Bob eats breakfast, and B = Bob has a sandwich for lunch. The problem tells us that:

P(A) > 0.6

P(A and B) < 0.5

P(A or B) = 0.7

First, let’s establish the minimum value. If Bob never has a sandwich for lunch, P(B) = 0, then it could be that P(A and B) = 0, which is less than 0.5, and it could be that P(A) = 0.7, which is more than 0.6, so that P(A or B) = 0.7. All the requirements can be satisfied if P(B) = 0, so it’s possible to equal that minimum value.

Now, the maximum value. Since P(A or B) = 0.7, both P(A) and P(B) must be contained in this region. See the conceptual diagram.

The top line, 1, is the entire probability space. The second line, P(A or B) = 0.7, fixes the boundaries for A and B. P(A) is the purple arrow, extending from the right. P(B) is the green arrow extending from the left. The bottom line, P(A and B) < 0.5, is the constraint on their possible overlap.

Let’s say that P(A) is just slightly more than 0.6. That means the region outside of P(A), but inside of P(A or B) is slightly less than 1. That’s the part of P(B) that doesn’t overlap with P(A). Then, the overlap has to be less than 0.5. If we add something less than 1 to something less than 5, we get something less than 6. P(B) can’t equal 0.6, but it can any value arbitrarily close to 0.6.

Thus, 0 ≤ P(B) < 0.6.

Answer = **(B)**

15)

Answer = **(E)**

The post Challenging GMAT Math Practice Questions appeared first on Magoosh GMAT Blog.

]]>If you have a strong business school application, you likely won’t need a near-perfect GMAT score for admission into a top MBA program. But how do you know if your GMAT score is up to par with your dream school’s GMAT requirements? Have no fear; we’ve collected GMAT score data from the admissions offices of all the top business schools to bring you the most recent data in average GMAT scores by school.

** Special update:** We’ve collected the very most recent information for average GMAT scores by school for the top 10 business schools in the United States. See the section immediately below.

**Note:** This is the most up-to-date information on average GMAT scores by school, GMAT requirements by schools, and other important statistics. All data for Harvard GMAT scores, Stanford GMAT scores, and the rest (including school ranking), comes from U.S. News and Word Report.

Name of MBA Program/Business School | Average GMAT Score | Rank | Enrollment, 2016-2017 |
---|---|---|---|

Harvard Business School |
725 | 1 | 1,872 |

Stanford Graduate School of Business |
733 | 2 (tie) | 824 |

University of Chicago(Booth) |
726 | 2 (tie) | 1,180 |

University of Pennsylvania(Wharton) |
732 | 4 | 1,715 |

Northwestern University(Kellogg) |
724 | 5 (tie) | 1,272 |

Massachusetts Institute of Technology(Sloan) |
716 | 5 (tie) | 806 |

University of California-Berkeley(Haas) |
715 | 7 | 502 |

Yale School of Management |
761 | 8 (tie) | 668 |

Dartmouth(Tuck) |
717 | 8 (tie) | 563 |

Columbia Business School |
715 | 10 | 1,287 |

Of course, there’s a lot more out there than just the top 10. When it comes to finding your fit and researching MBA programs, the ranking numbers don’t tell the whole story.

Scroll down to see average GMAT scores for a wide range of reputable b-schools in the USA.

**Note:**** **This information is recent, but is not quite as up-to-date as the date in the table above. Still, these stats should give you a pretty good idea of these schools’ GMAT requirements and expectations. More updates will be coming soon. In the meantime, use this table to get a general idea of where you stand with each school.

(Click the image to open the infographic in a new page and zoom in/out!)

*Important to note: officially, the GMAT scale for verbal and quantitative goes up to 60, but in practice, the scale tops out at 51. Nowadays, a verbal subscore of 46 would get you in the 99th GMAT score percentile, while a 51 quant subscore would be in the 97th.*

To accurately assess your GMAT score, you must understand the big picture of GMAT admissions, and remember that your GMAT score is just one part of your application.

First, familiarize yourself with GMAT scoring. Then, compare your score to the average GMAT scores by school of admitted students at your target programs. Keep in mind that an average score for a top business school is not the bare minimum you need to get in–approximately half of applicants get into that school with less than that average score. (In other words, not all Wharton students attained a 732 score even though that’s the average Wharton GMAT score). That means you can think about it as just that–an average score.

If your GMAT is good enough for the programs you like (say, for example, you want to go to University of Chicago and your score is a 726, just as Booth’s GMAT score is a 726), then focus your energy on strengthening other aspects of your application. And if your score doesn’t quite make the cut, then consider retaking the GMAT only so you can distinguish yourself from other applicants with a similar application profile to yours.

Ultimately, you have to decide what is a good GMAT score for you. GMAT scores may be paramount to the application process, but even a 720 combined score won’t get you into the best business schools without a strong application to back it up. Your entire profile must honestly and effectively represent your successes, abilities, and potential.

Still … a 720 can’t hurt.

If you’ve checked out an average GMAT score by school and think you need help getting there, then reach out about our Magoosh GMAT Prep! And while you’re at it, leave us a comment below with your thoughts about this infographic.

The post GMAT Scores for Top MBA Programs appeared first on Magoosh GMAT Blog.

]]>If you are planning to apply to full-time MBA programs next year to start classes in the next 12-18 months, this is the perfect time to start preparing for your GMAT test date. Even if you aren’t planning to apply for another few years, it’s not too early to take the test! GMAT scores are valid for five years so the sooner you can get this test out of the way, the more time you will have to focus on other aspects of your application, and the less stressed out you will be when deadlines start rolling around.

These timelines will help guide you as you start planning your preparation calendar for the next year. These timelines are based on the most common deadlines for rounds of applications at top MBA programs. Most top schools set MBA application deadlines three times a year, in three rounds. Check with specific schools for exact deadlines for Round 1, Round 2, and Round 3. And check out this article for help figuring out which round you should apply in.

December - February | March | April - May | June | July - August | September - October |
---|---|---|---|---|---|

Study | Take GMAT | Study | Retake GMAT | Essays, etc... | Round 1 due |

March - May | June | July - August | September | October-November | December - January |
---|---|---|---|---|---|

Study | Take GMAT | Study | Retake GMAT | Essays, etc... | Round 2 due |

June - August | September | October - November | December | January - February | March - April |
---|---|---|---|---|---|

Study | Take GMAT | Study | Retake GMAT | Essays, etc... | Round 3 due |

You can register to the test anywhere between six months to 24 hours in advance of your GMAT test date (or GMAT test dates if you are retaking the test; remember you need to allow for a 16-day window between test days!). Unlike the SAT, the GMAT is offered on an ongoing basis, but if you wait too late to register, spots may fill up and you may not get the dates/times you prefer.

Assuming…

- You will take 3 months to study
- You will retake the test if you are not happy with your score
- You will use 2 months to prepare other aspects of your application (writing essays, working with recommenders, doing research and visiting schools, soul-searching, etc.)

Keep in mind that the GMAC recommends that you take the test at least 21 days prior to your application deadline, so that there is ample time for your scores to be processed and sent to your school.

The amount of time you’ll need to study will depend on your strengths and weaknesses, but according to a GMAC survey in 2014, students who scored 700+ prepared for an average of 121 hours. Factoring in your full-time job and real life, this gives you about 3 months of study time. We have super-detailed study schedules that I would highly recommend you take a look at to help you plan for your GMAT date.

The post GMAT Test Dates | 2016, 2017, 2018 and Beyond! appeared first on Magoosh GMAT Blog.

]]>Getting into and going to graduate school is costly, and the GMAT cost is an added expense. The fee is a hefty one and is more expensive than many similar standardized exams (except the MCAT…). Further, the actual GMAT cost is not the only budget item you have to consider. Most students purchase some sort of practice materials, and a few students even take the exam more than once. Added together, there’s no question that taking the GMAT will hurt your wallet.

No matter what country you live in, the base cost of the GMAT is the same — $250. Depending on your country, you may also need to pay some taxes on top of this price, though. Paying this $250 fee entitles you to one sitting of the GMAT.

Note, however, that if you choose to pay by phone you will be charged an additional $10. So, if you have easy access to the internet, register online!

The $250 base fee gives you one administration of the exam. GMAC, however, will add to your GMAT cost if you choose to do something like reschedule your exam. A rescheduling costs $50 if you reschedule your exam more than 7 days before your scheduled test. You can also get a refund of $80 (from your initial $250).

If you decide to reschedule at the very last minute, you’re out of luck. You’ll be charged another full $250. You also will not be entitled to a refund of your initial payment. That makes your GMAT cost essentially double — $500 for one sitting.

You cannot reschedule within 24 hours. Your account history will instead register a “no-show.” Note that this will not be sent to schools in your score report, however.

Besides rescheduling fees, GMAC also charges for score reports. On test day, you are given five (5) free score reports. Any more will cost you $28 each.

Finally, if you cancel your scores and then later decide you want to un-cancel them, you’ll be charged a $50 reinstatement fee.

While most of the GMAT cost comes from GMAC directly, you’ll also want to buy some prep materials! Keep in mind that the range on these materials is enormous. A full, in-person course will run you thousands of dollars. Something more self-guided, like a book or online test prep (Magoosh!) could cost you less than $150. You can see some of our Magoosh plans here.

There are even some free resources (and they’re high-quality!):

Always remember to put your GMAT cost in perspective. The whole point of taking the GMAT is to get into graduate school, after all. And that’s very expensive! Since graduate school itself will be pricey, you might want to consider this when budgeting in your GMAT cost. If you’re concerned about expenses, you might consider planning to avoid a rescheduling fee or a retake. You might also be prepared to send in your score reports to maximize your five free ones. Any fee you can avoid will help!

The post How Much Does the GMAT Cost? appeared first on Magoosh GMAT Blog.

]]>Getting into and going to graduate school is costly, and the GMAT cost is an added expense. The fee is a hefty one and is more expensive than many similar standardized exams (except the MCAT…). Further, the actual GMAT cost is not the only budget item you have to consider. Most students purchase some sort of practice materials, and a few students even take the exam more than once. Added together, there’s no question that taking the GMAT will hurt your wallet.

No matter what country you live in, the base cost of the GMAT is the same — $250. Depending on your country, you may also need to pay some taxes on top of this price, though. Paying this $250 fee entitles you to one sitting of the GMAT.

Note, however, that if you choose to pay by phone you will be charged an additional $10. So, if you have easy access to the internet, register online!

The $250 base fee gives you one administration of the exam. GMAC, however, will add to your GMAT cost if you choose to do something like reschedule your exam. A rescheduling costs $50 if you reschedule your exam more than 7 days before your scheduled test. You can also get a refund of $80 (from your initial $250).

If you decide to reschedule at the very last minute, you’re out of luck. You’ll be charged another full $250. You also will not be entitled to a refund of your initial payment. That makes your GMAT cost essentially double — $500 for one sitting.

You cannot reschedule within 24 hours. Your account history will instead register a “no-show.” Note that this will not be sent to schools in your score report, however.

Besides rescheduling fees, GMAC also charges for score reports. On test day, you are given five (5) free score reports. Any more will cost you $28 each.

Finally, if you cancel your scores and then later decide you want to un-cancel them, you’ll be charged a $50 reinstatement fee.

While most of the GMAT cost comes from GMAC directly, you’ll also want to buy some prep materials! Keep in mind that the range on these materials is enormous. A full, in-person course will run you thousands of dollars. Something more self-guided, like a book or online test prep (Magoosh!) could cost you less than $150. You can see some of our Magoosh plans here.

There are even some free resources (and they’re high-quality!):

Always remember to put your GMAT cost in perspective. The whole point of taking the GMAT is to get into graduate school, after all. And that’s very expensive! Since graduate school itself will be pricey, you might want to consider this when budgeting in your GMAT cost. If you’re concerned about expenses, you might consider planning to avoid a rescheduling fee or a retake. You might also be prepared to send in your score reports to maximize your five free ones. Any fee you can avoid will help!

The post How Much Does the GMAT Cost? appeared first on Magoosh GMAT Blog.

]]>Yes, the GMAT is challenging. It’s supposed to be challenging. It’s supposed to be hard. In mythology, the hero, at the outset of her journey, encounters the “Guardian of the Threshold,” the initial challenge she must face in order to undertake her adventure—what the Tusken Raiders were to Luke Skywalker, or what the first Nazguls were to Frodo & friends at the Prancing Pony. This is precisely what the GMAT is for anyone keen to undertake the adventure of earning an MBA and pursuing a career in the business world. In any context, part of the role of the Guardian of the Threshold is to separate the daring from the lily-livered, the bold & adventurous from those who would prefer to be sheepish followers. The GMAT is hard—in preparing for it and taking it, you will take risks, experience pressure, and feel yourself stretched. If you are the sort of person who doesn’t like risks, doesn’t like pressure, and doesn’t like to feel stretched, then it’s an excellent question why you are pursuing an MBA and a career in management in the first place!

Simply in terms of showing up and taking the test, the GMAT is hard. From the moment you walk into the testing center and they relieve you of any indication of your individuality, until you finally emerge, it will be, at minimum, a little over four hours–four long difficult hours. Just to maintain concentration and focus during this, you need to be in good physical shape, well-rested, and well-nourished. I would recommend no alcohol for the week leading up to your GMAT. I would recommend not just one, but three or four consecutive nights of 8+ hours of sleep. I would recommend lots of water, healthy snacks, and some stretching on the breaks. During my own GMAT experience, I found myself running out of gas by the end of the test—this may have something to do with the fact that I am old enough to remember Nixon‘s Presidency! If you remember no Presidents before Clinton, then your youthful vigor will certain help you, but even then, do not underestimate the GMAT’s difficulty — both mentally and physically.

In many ways, this is really the question people are asking when they ask, “how hard is the GMAT?” Sure, any slob can waltz into the GMAT exam with no preparation, do shoddy work, and get an abysmal score without much effort. The GMAT is relatively easy if you simply don’t care how you do. But what if you do care? Then how hard is the GMAT? To answer that question, it helps to know how others score. Only 23% of GMAT takers score over 650, and only 10% cross that magical 700 threshold. Something above 700 is generally what folks have in mind when they consider a “good” GMAT score. The average score on the GMAT (the numerical mean of everyone who takes the test) is 547. That score won’t turn any heads for you. How hard is it to get a GMAT score of a higher caliber?

Well, this is the “*it depends* …” part. If you regularly score in the 99th percentile of standardized tests, then getting over a 700 on the GMAT shouldn’t be too difficult with moderate preparation. If you regularly flub standardized tests, then acing the GMAT will be that much more difficult. If you remember the percentile of any previous standardized test, the percentile of your SAT score for example, then imagine you score at the same percentile on the GMAT—you can use this official chart to gauge what an equivalent score on the GMAT might be. You could also take the Magoosh GMAT Diagnostic Test, to give yourself a rough idea of your starting point. Whatever you score cold, on a dry run before any preparation—assume it will not hard to score this much after preparation on the real test. The question is: how do you improve your score?

Pushing yourself beyond what you already have achieved, pushing yourself toward your own excellence—this is always hard. Improving on the GMAT takes focus, responsibility, dedication, determination, and commitment. Again, if these are qualities you don’t like to exercise, then the whole idea of management in the modern business world might not be for you. If you are ready to do the hard work of improving, then avail yourself of the best GMAT resources. How much you will improve depends very much on how disciplined and how thorough you are willing to be in your preparation. Many folks dream about a spectacular performance, but do only moderate preparation. Remember the Great Law of Mediocrity: if you do only what most people do, you will get only what most people get. If you want to stand out, you have to take outstanding action. If you are willing to do outstanding work in your preparation for the GMAT, that’s very hard, but with good material, the results will really pay off.

An ordinary soldier fears his enemy, but a samurai in kensho would experience no separation between self & other, friend & enemy, life & death. While that mindset might seem somewhat extreme, consider that what’s hard about the GMAT—the intellectual challenges, the time pressure, etc.—is not too different from what’s hard about being a manager charged with important decisions in the business world: in other word, what’s “hard” about the GMAT is, in many respects, the same as what’s “hard” about the life & career you are choosing for yourself by pursuing an MBA. If you pursue this life, that level of difficulty and challenge will become, as it were, your “new normal”—get used to this “new normal” now, and what’s had appeared “hard” about the GMAT will be simply normal. When you routinely expect challenge as a matter of course, nothing is “hard.” That perspective is exactly what I would wish for you as you prepare for the GMAT!

The post How Hard is the GMAT? appeared first on Magoosh GMAT Blog.

]]>Now is the time to get started! There is still a lot you can do between now and next year’s Round 1 deadlines to improve your chances of admission to b-school. By preparing now you’ll be able to apply to more programs earlier and change your Round 2 strategy if necessary. Also, when you apply early there are more seats and financial aid available. However, your application has to be of the highest quality whenever you apply, so don’t rush!

Here’s what you should be doing now to assure that you have the best possible app at the earliest possible date.

If you haven’t already taken the GMAT, this is the time to prep and take the test, preferably in the spring. Choosing schools without knowing your score leads to unnecessary stress. Taking the test early will give you time to evaluate your score and see if it’s in the range needed for the schools you want to get into. If not, you will still have time to retake the test, reevaluate your target schools, or both. Taking the GMAT early will allow you to focus on the rest of the application process.

Now is the best time to visit schools – when classes are in session. You’ll get to see the professors and students in action and get a feel for the campus. This will help determine your fit with each school. A school may be perfect for you on paper, but if you don’t hit that “fit” factor, then it’s not the best match. During this research phase, you’ll also want to make sure that you’re competitive at the program and that it supports your goals.

Review your record to look for potential weaknesses. Now is the time to take appropriate classes – and ACE them! This will show the adcom that you are able to excel academically.

If you don’t know who to ask, now is the time to consider your various options and possibly raise the subject with people who can write you a strong recommendation. Be sure they see you in positive situations to ensure an amazing letter.

Whether or not you have a formal leadership role in school or work, you can always find ways to become an informal leader. The more the better – you can never have too much leadership in an MBA app. If there’s not enough space to write about it in your essays, be sure to include it in your resume.

What can you say about your goals – your planned industry, company function – that is interesting? Now is the time to read books, journals, and company reports. Talk to people. In less than 10 minutes, with good questions, you can get informative, instructive information that will make your essay stand out from the others.

Now is the time to get 95% of your resume done. You can adjust it for new developments along the way. It’s good to have this ready if you have the opportunity to visit a school or meet with an adcom member earlier than you’d planned.

**Need more help determining where you are, where you’re going and how to stay on track? Download our free guide, MBA Action Plan: 6 Steps for the 6 Months Before You Apply.**

The post Timing is Everything: The Ideal Time to Apply to Business School appeared first on Magoosh GMAT Blog.

]]>It’s 2017. You have 12 new chapters and 360 fresh chances ahead of you. The year is yours…to squander or to make the most of. If you see business school in your future, let 2017 be the year you make it happen.

Our friends at Stacy Blackman Consulting, want to help you reach your most ambitious professional goals by giving you access to their entire library of online MBA prep guides, valued at over $470, for FREE, for the first 500 downloads.

Simply visit the SBC store, add All Guides Bundle to your cart, and use promo code BEST2017, by the end of January 2017.

Wishing you a happy and successful 2017. Let’s do this!

The post Special Offer: FREE Stacy Blackman MBA Prep Guides appeared first on Magoosh GMAT Blog.

]]>The GMAT is a tough exam, even for those who have been speaking English their entire lives. Another degree of difficulty is added for those who are non-native English speakers. Here at Magoosh, we’re proud to have helped many students from around the world who speak English as a second language. There’s no denying that this endeavor is challenging. Below we share a few study habits to help unlock the GMAT verbal section for non-native English speakers.

The most important thing you can do to improve your verbal performance on the GMAT is to **read English as much as possible**. Reading will not only boost your knowledge of vocabulary, but also your comprehension skills — your ability to digest meaning and decipher the author’s intent. This is a crucial skill for the GMAT verbal section’s critical reasoning questions.

But don’t just read anything: it’s important to read high-level materials that are similar to what you’ll see come test day. Consider such venerated publications as *The New York Times, The New Yorker, The Economist, *and* Arts & Letters Daily*. Take a look at our full list of recommended periodicals. Or, if you prefer books, check out our recommended fiction & non-fiction (this list is written for the GRE, but all the picks would suit the GMAT as well).

You should read for *at* *least* 30 minutes a day. If you can afford the time, make it one hour a day.

To master the GMAT verbal section, you need to ‘trick’ your brain into being alert and attentive at all times. In other words, you need to make it a priority to read actively.

Many students make the mistake of trying to rush through passages in the hopes that they can spend more time focusing on the questions. In the end, this approach only wastes time, as you’ll find yourself frequently returning to the passage to fish out details you can no longer remember.

So keep calm, slow down, and make it your goal to read the entire passage with determination and poise.

As you read, strive to understand the nuances and figurative connotations of the English language — this can be particularly difficult for non-native English speakers. Fortunately, we have a couple of free resources to aid you.

For on-the-go study, give our Idiom Flashcards a try. These decks cover 160 of the most common idioms you’ll encounter on the GMAT.

For a more methodical look at idioms, check out our GMAT Idioms eBook. This free eBook examines hundreds of idioms broken down into 27 different categories.

And when hitting the books becomes tedious, you can study more leisurely by consuming English-language video media, such as films, TV shows, and podcasts. These are often rife with idioms and important colloquialisms. As you encounter new idioms, be sure to look up their meaning in a resource such as The Free Dictionary’s idiom database.

It will be difficult to catch up with native speakers on an exam like the GMAT. Part of bridging this gap is to ask for help when you get stuck. For Premium members, Magoosh offers a ‘Help’ button in the corner of every screen, and we’re happy to answer any questions regarding our materials. We’ve helped thousands of non-native speakers with a range of concepts, from simply defining words or idioms to making sense of an author’s implied arguments on the critical reasoning section — so sign up today!

The post GMAT Verbal for Non-Native English Speakers appeared first on Magoosh GMAT Blog.

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