A complete breakdown of GMAT Math question types and its history Updated on Aug 20th, 2020 What should you study more? Arithmetic? Geometry? Probability? All? When preparing for the GMAT, test-takers often ask about which math concepts are covered on the GMAT and about the most common question types that appear in the actual test. Therefore, in this article, I will not only delve into past trends but also the current trend of the GMAT Math test. Also, I will discuss the types of questions that appear on the test every month. You can also find our observations regarding the hardest question types that appear on the test here: The Ultimate Q51 Guide The scope of Math Tested on the GMAT 1. Topics that appear frequently on the GMAT - This is what you need to study and know: Integer: Questions in this section involve dividing an integer n by 5 or 10, solving the units digit for an integer n , finding the remainder of an integer n after dividing it by 3 or 9, and solving for factors and prime factors. Geometry: Questions in this section involve Pythagorean Theorem, special angles (1:1: \sqrt{2} , 1: \sqrt{3} :2), and solving for the area of different figures. Statistics: Questions in this section involve finding the average, standard deviation, median, and range. Speed Rate: Questions in this section involve solving average speed rate problems. Inequality: Questions in this section involve inequality questions that ignore squares and DS questions related to the inclusion relation. Equation: Questions in this section involve calculations using (a − b)(a + b) = a^2 − b^2. DS questions: Common Mistake Type questions that are determined and categorized by Math Revoluition NOTE: Please refer to the table below for additional types of questions that appear on the test. However, remember that the types mentioned above are the most common types of questions. Quant Topics and Types of Questions Tested on the GMAT Today Topics Questions that frequently appear Questions that appear occasionally Questions that infrequently appear Integer Remainders Factors multiples Evens and odds Prime factors GCD and LCM Remainder questions after dividing the number by 4 or 8 Consecutive integers Estimated integers Modula questions Gaussian integers Perfect numbers Numbers, Fractions, Decimals Decimal digits Rounding numbers Mixed and compound fractions Number lines Terminating decimals Reciprocals Undefined functions Non-real numbers Ratios, Rates, Proportions, and Percentages Properties of ratios Properties of work rates Percent changes Average speed Round trips Matching ratios Inverse proportions Equations Basics of factoring Polynomial equations Algebraic expressions Discount problems Profit problems Duplicated square roots Mixture problems Data interpretation problems Indeterminate and impossible equations Exponents Properties of exponents Comparison of exponents Operations of numbers with exponents Inequalities Five fundamental concepts 3 properties Relationship between a question and the conditions (DS) 1 is standard Maximum and minimum ranges The effect of negative numbers Positive numbers Non-zero numbers Non-negative numbers Absolute Value 4 properties 7 frequent cases Distance between x and y on a number line Relationship between the nth root and absolute value Two types of absolute value inequalities Counting Methods Factorials Combinations Permutations with the same letters Permutations Circular permutations At least (counting methods) Permutations with restrictions on the order Probability Events and probability Relationship between numbers and ratios At least (probability) The rule of addition in probability Binomial Theorem Independent and exclusive events Statistics Means Medians Ranges Standard deviations Harmonic means Modes Sets with the same elements Normal distributions Modes Relationships among mean, median, range, and standard deviation Geometry Pythagorean Theorem Circles Lines Properties of triangle sides Special angle problems Areas of geometric diagrams Cubes Rectangular solids Circular cylinders Spheres Regular n-polygons (DS) Quadrilaterals Number of diagonals in n-polygons Diagonal Theory Heron’s Theory Area of parallelograms and trapezoids Coordinate Geometry Quadrants Line equations x- and y-intercepts Parabolas Symmetric axis Discriminant Equation of a circle Distance between points and a line Functions Functions with repeated intervals Additional graphs Reflections Binary operations Domains Codomains Ranges Equation of an ellipse Sets Venn Diagrams Intersections Unions Complements Addition rule 3 sets Subsets Start with the intersection Disjoint or mutually exclusive sets Difference between two sets Sequences Arithmetic and geometric sequences Counting consecutive integers Simple and compound interest rates Sum of arithmetic and geometric sequences Other sequences Counting consecutive multiples Adding the reciprocals of consecutive integers Note: Max Lee, founder of Math Revolution has been analyzing these types of questions for decades. 2. Mathematical concepts that are partially covered In the case of sequences, only fundamental concepts such as arithmetic and geometric sequences are included within the scope of the test. This means more complex concepts like difference sequences will not be tested. There are also questions regarding probability and statistics, but these questions tend to be fairly simple. In other words, concepts like combinations with repetition, conditional probability, discriminating distributions, and average deviations will not be on the test. In the end, test-takers are not trying to go to a graduate program in mathematics! 3. Questions/Topics that Never Appear The level of GMAT Math is generally what people learn in high school. This means that the scope of GMAT Math does not include difficult concepts like trigonometrical functions, logarithms, differentiation, integration, or limits. Also, even though basic concepts such as calculating volume and areas of geometric figures and finding diagonal length appear in the test, more difficult concepts such as vectors or inner products do not appear. During decades of experience in teaching GMAT Math, I have encountered only 2 matrix questions. Due to its infrequency, we can say matrixes are not included within the scope of GMAT Math. Additionally, questions regarding imaginary numbers - a complex number ( \sqrt{-1} = i ) - also are not included in GMAT Math. NOTE: During my extensive experience teaching GMAT Math, I found some patterns on the GMAT test. It was that some questions, which were on the test in 2001, have reappeared recently. Even though I cannot give any assurance as to whether GMAC - the question bank of GMAT Math – reutilizes its questions, I believe that it occasionally uses some questions that appeared on previous exams along with new questions it creates every year. History and Evolution of GMAT Math In this part, I will analyze GMAT Math trends beginning from 2001, the year when I started teaching. Evolution of Topics Tested Since 2001 Topics 2001 - 2005 2006 - 2011 2011 - Today NOTE Arithmetic 40% 40% 30% Consistent Algebra 35% 30% 30% Consistent Geometry 10% 10% 15% The number of questions is increasing, and the questions are becoming more difficult. Word Problems 5% 5% 5% The number of work rate questions is increasing. Data Interpretation 5% 5% 10% The number of questions is increasing, and the questions have characteristics related to daily life. Common Mistake Types 3 and 4(A or B) 5% 5% 10% The number of questions is increasing, and the questions are becoming more difficult. Note: This table is based on my decades of experience. Conclusion I want to emphasize that it would be especially helpful for those preparing for the GMAT Math to focus on mastering the integer and statistics sections. In fact, I have seen students who get every integer and statistics question right in prep tests (mock tests distributed freely by GMAC) and achieve late 40’s. Additionally, I want to advise test-takers to focus on studying questions that appear every month. As explained earlier, integer questions are the most common type of questions (not only the number of questions but the number of different types of integer questions are numerous). Hence, spending more time learning these areas than on other concepts would be an effective and time-efficient way to tackle GMAT Math. Also, the recent trend of GMAT Math is that questions contain characteristics of daily life. Thus, it would be helpful for test-takers to have a general understanding of the culture of the United States. Additionally, questions involving geometric figures are increasing in number. I want to advise test-takers to spend some time learning this concept. As mentioned earlier, questions are becoming wordier. So, while studying the Official Guide, please spend some time observing the trend and styles of the questions. It is vital for test-takers to regularly exercise generating equations after reading difficult and wordy questions. As many test-takers are already aware, solving 31 questions in just 62 minutes is very challenging. Therefore, it is important to have strategies for time management. Many people can solve simple questions in approximately 1 minute with no problems. However, those who solve questions using the conventional method of approach take approximately 5 minutes to solve just one difficult question. Thus, it is very helpful to learn various techniques and tips that can guide test-takers to solve difficult questions in approximately 2 minutes. The average GMAT score is 38 (it is 33 for the United States alone). However, I firmly believe that if test-takers clearly understand about GMAT Math trends and the history of the test, they will not only be able to exceed the average score but will be able to score at least 45 or even get a score of 49 to 51. Thank you so much for reading this article, and I wish you the best of luck. *** We are math experts, and if you find any grammatical issues – that is because we spend all of our time focusing on math, sorry grammar. Note that the information herein is based on the knowledge and experience of Max Lee, Founder of Math Revolution who has taught 30,000+ students and solved 100,000+ problems over the last few decades. He discovered and analyzed types of GMAT Math questions after continuous and numerous interviews with students who wrote the GMAT exam. Thus, please note that the information herein is based solely on the experience of Max Lee. Due to the nature of the test and lack of transparency regarding the algorithm used in preparing the questions, this guide is a best-effort attempt based on the best information available. If you have any questions or other information to share, please feel free to post it here for the benefit of the community.

(Function) The function f(x) is defined as x - 10 . ( is the greatest integer less than or equal to x). What is f(7) + f(7^2) + f(7^3) +…+ f(7^2020)? A. 10036 B. 10039 C. 10040 D. 10100 E. 10107 => f(x) = x – 10 means the remainder of x when x is divided by 10. For example, f(1234) = 1234 – 10* = 1234 – 10* = 1234 – 10*123 = 1234 – 1230 = 4. Units digit of Powers of base 7 repeats as follows. f(7^1) = 7 ~ 7^5 ~ 7^9 ~ … f(7^2) = f(49) = 9 ~ 7^6 ~ 7^10 ~ … f(7^3) = f(343) = 3 ~ 7^7 ~ 7^11 ~ … f(7^4) = f(2401) = 1 ~ 7^8 ~ 7^12 ~ … f(7) + f(7^2) + f(7^3) +…+ f(7^2020) = f(7) + f(7^2) + f(7^3) + f(7^4) + f(7^5) +…+ f(7^2017) + f(7^2018) + f(7^2019) + f(7^2020) = (7 + 9 + 3 + 1) + (7 + 9 + 3 + 1) +…+ (7 + 9 + 3 + 1) = 20 * 2020/4 = 20*505 = 10100 Therefore, D is the answer. Answer: D

(Geometry) We have a right triangle ABC with ∠A = 90, AD = 6 and CD = 8. AD and BC are perpendicular to each other. If x = AC and y = BD, what is the value of xy? 4.6ps.png A. 40 B. 42 C. 45 D. 50 E. 56 => We have x^2 = 6^2 + 8^2 = 36 + 64 = 100 and x = 10. Since we have 6^2 = 8y or 8y = 36, we have y = 9/2. Thus, we have xy = 10*(9/2) = 45. Therefore, C is the answer. Answer: C

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Overview of GMAT Math Question Types and Patterns on the GMAT

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MathRevolution

This question is frequently on GMAT Math lately, which is 2 by 2 question.

Attachment:

GCDS overview of GMAT (20160118).jpg

On the above, suppose all the passengers 100p(if there is %, use 100 since it is per cent. p is an initial for passengers). Passengers who brought a round ticket and a laptop is 40% of the total passengers, which is 40p. However, what 20% means is that x=10 is derived from 40p:xp=80%:20%=4:1. That is, 40p+10p=50p, which means 50% of the passengers have round tickets. Therefore, the answer is C.

Yeah but this is still wrong. Your chart is wrong..
On a certain transatlantic crossing, 40 percent all passengers held round-trip tickets.
40 is the total of Round-trip laptop + non laptop. You diagram illustrates 40 = round trip and laptop only.

Additionally, they also took their laptops aboard the ships. If 20 percent of the passengers with round-trip tickets did not take their laptops aboard the ship, what percent of the ship’s passengers held round-trip tickets?
If 40 have round trip tickets, 20% of 40 is 8.
So 8 have round trip with no laptop.
40-8 = 32 with round trip and laptop.

32+8 = 40 percent of all passangers with round trip tickets.

Your explanation only works if we are given that 40% is the number of roundtrip tickets with laptops, not total round trip tickets..which is what the question asks for and is given in the question.

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[GMAT math practice question]

(Algebra) What is a/ab+a+1 + b/bc+b+1 + c/ca+c+1?

1) abc = 1
2) a, b, and c are integers

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Condition 1)
If we have abc = 1, then we have

a/ab+a+1 + ab/a(bc+b+1) + abc/ab(ca+c+1)
= a/ab+a+1 + ab/abc+ab+a + abc/abca+abc+ab
=a/ab+a+1 + ab/ab+a+1 + 1/ab+a+1 (substituting 1 for abc)
=ab+a+1/ab+a+1 = 1.
Since condition 1) yields a unique solution, it is sufficient.

Condition 2)
Since we don’t have any information about a, b and c, it is not sufficient.

Therefore, A is the answer.
Answer: A

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[GMAT math practice question]

(Function) The function f(x) is defined as x - 10[x/10]. ([x] is the greatest integer less than or equal to x). What is f(7) + f(7^2) + f(7^3) +…+ f(7^2020)?

A. 10036
B. 10039
C. 10040
D. 10100
E. 10107

=>

f(x) = x – 10[x/10] means the remainder of x when x is divided by 10.
For example, f(1234) = 1234 – 10*[1234/10] = 1234 – 10*[123.4] = 1234 – 10*123 = 1234 – 1230 = 4.

Units digit of Powers of base 7 repeats as follows.
f(7^1) = 7 ~ 7^5 ~ 7^9 ~ …
f(7^2) = f(49) = 9 ~ 7^6 ~ 7^10 ~ …
f(7^3) = f(343) = 3 ~ 7^7 ~ 7^11 ~ …
f(7^4) = f(2401) = 1 ~ 7^8 ~ 7^12 ~ …
f(7) + f(7^2) + f(7^3) +…+ f(7^2020)
= f(7) + f(7^2) + f(7^3) + f(7^4) + f(7^5) +…+ f(7^2017) + f(7^2018) + f(7^2019) + f(7^2020)
= (7 + 9 + 3 + 1) + (7 + 9 + 3 + 1) +…+ (7 + 9 + 3 + 1)
= 20 * 2020/4 = 20*505 = 10100

Therefore, D is the answer.
Answer: D

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30 Mar 2020, 00:37

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[GMAT math practice question]

(Geometry) We have a square □ABCD, and △AEF is a triangle inscribed in □ABCD. What is the length of BE?

1) □ABCD is a square with AB = 10
2) △AEF is an equilateral triangle.

Attachment:

3.26(ds).png [ 5.63 KiB | Viewed 2988 times ]

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have a triangle and a square, we have 3 variables and 1 variable for the triangle and the square, respectively. Since we have 4 variables and 0 equations, E is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)

Attachment:

3.26ds(a).png [ 9.37 KiB | Viewed 3006 times ]

Assume BE = x (0 < x < 10).
Then we have BE = DF since the triangle AEF is equilateral.
AE^2 = 100 + x^2 = EF^2 = (10 - x)^2 + (10 - x)^2.
Then we have
100 + x^2 = (10 - x)^2 + (10 - x)^2
100 + x^2 = 2(10 – x)^2 (adding like terms)
100 + x^2 = 2(10 – x)(10 – x)
100 + x^2 = 2(100 – 10x – 10x + x^2) (foiling out the brackets)
100 + x^2 = 2x^2 – 40x + 200 (multiplying 2 through the bracket and combining like terms)
x^2 – 40x + 100 = 0 (bringing all terms to one side)
Thus, we have x = 20 ± 10√3. (using the quadratic formula)
But we have x = 20 - 10√3 since 0 < x < 10.

Since both conditions together yield a unique solution, they are sufficient.

Therefore, C is the answer.
Answer: C

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2) when taken together. Obviously, there may be occasions on which the answer is A, B, C, or D.

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[GMAT math practice question]

(Function) For a positive integer n, f(n) and g(n) are defined as follows

f(n)={0 ,(n is a multiple of 5) 1 , (n is not a multiple of 5)
g(n)={0 ,(n is a multiple of 7) 1 , (n is not a multiple of 7)

Moreover, h(n) is defined as (1 - f(n))(1 - g(n)).
What is the value of h(3) + h(6) + h(9) + … + h(2004) + h(2007)?

A. 13
B. 19
C. 38
D. 57
E. 152

=>

h(n) = 0 when f(n)=1 or g(n) = 1
h(n) = 1 when f(n)=0 and g(n)=0
Thus, we have h(n) = 1 when n is a multiple of both 5 and 7. It means we have h(n) = 1 when n is a multiple of 35.

3, 6, 9, … , 2016, 2019 are multiples of 3.
The function values of h for those numbers is 1 when they are multiples of 105 = 35*3.
2019 = 105*19 + 24
Thus, we have 19 multiples of 105 between 1 and 2007, inclusive.

Therefore, B is the answer.
Answer: B

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[GMAT math practice question]

(Function) What is the value of f(2019)?

1) f(3) = 5
2) f(x+2)=f(x - 1)/f(x + 1)

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Since we have many variables to determine the function f(x), E is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
Since f(3) = 5, we have:
f(5) = (f(3) - 1) / (f(3) + 1)
f(5) = (5 - 1) / (5 + 1)
f(5) = 4/6 = 2/3.

Then we have:
f(7) = (f(5) - 1) / (f(5) + 1)
f(7) = ((2/3) - 1) / ((2/3) + 1)
f(7) = -(1/3) / (5/3) = -(1/5).
We have:
f(9) = (f(7) - 1) / (f(7) + 1)
f(9) = (-(1/5) - 1)/(-(1/5) + 1)
f(9) = -(6/5) / (4/5) = -(3/2).

We have:
f(11) = (f(9) - 1) / (f(9) + 1)
f(11) = (-(3/2) - 1)) / (-(3/2) + 1)
f(11) = -(5/2) / -(1/2) = 5.

Since f(3) = f(11), we have f(8k - 5) = 5.

Then we have:
f(8k-3) = 2/3, f(8k-1) = -(1/5) and f(8k+1) = -(3/2).
f(2007) = f(8*251-1) = -(1/5).

Since both conditions together yield a unique solution, they are sufficient.

Therefore, C is the answer.
Answer: C

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[GMAT math practice question]

There are 1 card written ‘1’, 2 cards written ‘2’, …, and n cards written ‘n’. The average of all the numbers written on the cards is 17. How many cards are there? (Use the fact : 1 + 2 + … + n = n(n+1)/2, 1^2 + 2^2 + … + n^2 = n(n+1)(2n+1)/6)

A. 25 B. 125 C. 225 D. 325 E. 425

=>

( 1*1 + 2*2 + 3*3 + … +n*n ) / ( 1 + 2 + 3 + … + n ) = 17
[(1/6)n(n+1)(2n+1)] / [(1/2)n(n+1) ] = (2n+1)/3 = 17.
Thus, we have 2n+1 = 51 or n = 25.

Then the number of cards is
1 + 2 + 3 + … + 25 = (1/2)25*26 = 325

Therefore, D is the answer.
Answer: D

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[GMAT math practice question]

(Geometry) We have a right triangle ABC with ∠A = 90, AD = 6 and CD = 8. AD and BC are perpendicular to each other. If x = AC and y = BD, what is the value of xy?

Attachment:

4.6ps.png [ 8.7 KiB | Viewed 2896 times ]

A. 40
B. 42
C. 45
D. 50
E. 56

=>

We have x^2 = 6^2 + 8^2 = 36 + 64 = 100 and x = 10.
Since we have 6^2 = 8y or 8y = 36, we have y = 9/2.

Thus, we have xy = 10*(9/2) = 45.

Therefore, C is the answer.
Answer: C

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[GMAT math practice question]

(Statistics) s is the standard deviation of 3 real numbers x, y, and z, where a = x - y, b = y – z and c = z - x. What is the expression of s^2 in terms of a, b, and c?

A. a^3 + b^3 + c^3
B.(abc)^2
C. 0
D. a^2 + b^2 + c^2
E. 1/9(a^2 + b^2 + c^2)

=>

Assume m = (1/3)(x + y + z), which is the average of x, y, and z.
x – m = x – (1/3)(x + y + z) = (1/3)(3x – x – y - z) = (1/3)(2x – y - z) = (1/3)(x – y - (z - x)) = (1/3)(a - c).
We have y – m = (1/3)(b - a) and z – m = (1/3)(c - b) similarly.

Then, we have a + b + c = (x - y) + (y - z) + (z - x) = 0.

s^2 = (1/3)[(x - m)^2 + (y - m)^2 + (z - m)^2]
= (1/3)(1/3)[(a - c)^2 + (b - a)^2 + (c - b)^2]
= (1/27)[(a - c)^2 + (b - a)^2 + (c - b)^2]
= (1/27)[(a – c)(a – c) + (b – a)(b -a ) + (c – b)(c – b)]
= (1/27)(a^2 – 2ac + c^2 + b^2 – 2ab + a^2 + c^2 – 2bc + b^2)
= (1/27)[2(a^2 + b^2 + c^2) - 2(ab + bc + ca)]
= (1/27)[3(a^2 + b^2 + c^2) - (a + b + c)^2]
= (1/27)[3(a^2 + b^2 + c^2)], since a + b + c = 0
= (1/9)(a^2 + b^2 + c^2)

Therefore, E is the answer.
Answer: E

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[GMAT math practice question]

(Inequalities) What is the value of (x, y) satisfying √x^2+4y, with the integer portion equaling 5.

1) x and y are the numbers of eyes on two dice.
2) x and y are positive integers.

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Since the integer part of √x^2+4y, we have
5≤√x^2+4y < 6
=> 25 x^2 + 4y < 36
X = 1, y = 6 and x = 2, y = 6 are possible solutions.

Since both conditions together do not yield a unique solution, they are not sufficient.

Therefore, E is the answer.
Answer: E

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17 Apr 2020, 22:01

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[GMAT math practice question]

(Statistics) The average of x1, x2, x3, x4, x5 is m. What is the average of x1-a, x2-2a, x3-3a, x4-4a, x5-5a?

A. m
B. m - 1/2a
C. m - a
D. m - 3a
E. m - 3/2a

=>

Since m is the average of x1, x2, x3, x4, x5, we have m = (x1 + x2 + x3 + x4 + x5) / 5 or x1 + x2 + x3 + x4 + x5 = 5m.
Then the average of x1-a, x2-2a, x3-3a, x4-4a, x5-5a is
[(x1 - a) + (x2 - 2a) + (x3 - 3a) + (x4 - 4a) + (x5 - 5a)] / 5
= (x1 + x2 + x3 + x4 + x5 - 15a) / 5
= (x1 + x2 + x3 + x4 + x5) / 5 – 3a
= m – 3a

Therefore, D is the answer.
Answer: D

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20 Apr 2020, 23:07

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[GMAT math practice question]

(Algebra) a, b, and c are positive integers with abc + 2ab + 2bc + 2ca + 4a + 4b + 4c = 447. What is the value of a + b + c?

A. 17
B. 19
C. 21
D. 23
E. 25

=>

abc + 2ab + 2bc + 2ca + 4a + 4b + 4c + 8 = 455
a(bc + 2b + 2c + 4) + 2(bc + 2b + 2c + 4) = 455 (taking out a common fraction of a from the first 4 terms and a common factor of 2 from the last 4 terms)
= (a + 2)(bc + 2b + 2c + 4) = 455 (taking out a common factor of (bc + 2b + 2c +4))
(a + 2)[b(c + 2) + 2(c + 2)] = 455 (taking out common factors of b and 2)
= (a + 2)(b + 2)(c + 2) = 455 (taking out a common factor of (c + 2))
= 3*5*11.
a, b, and c are interchangeable since the equation (a + 2)(b + 2)(c + 2) = 5*7*13 is symmetric.
Then we have a + b + c = 3 + 5 + 11 = 19.

Therefore, B is the answer.
Answer: B

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23 Apr 2020, 21:17

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[GMAT math practice question]

(Algebra) If the decimal part of √5 is x, what is the decimal part of √45?

A. 3x - 2
B. 3x - 1
C. 3x
D. 3x + 1
E. 3x + 2

=>

Since 2 < √5 < 3, we have x = √5 - 2.
Since 6 < √45 < 7, the decimal part of √45 is √45 – 6 = 3√5 – 6 = 3(√5 - 2) = 3x.

Therefore, C is the answer.
Answer: C

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26 Apr 2020, 21:00

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[GMAT math practice question]

(Algebra) What is the value of x^2(x - y) + y^2(y - x)?

1) x + y = 3.
2) xy = 1.

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

The expression in the question x^2(x - y) + y^2(y - x) is equivalent to (x - y)^2(x + y) for the following reason:
x^2(x - y) + y^2(y - x)
= x^2(x - y) - y^2(x - y) (taking out a common factor of -1 from the second bracket)
= (x - y)(x^2 - y^2) (taking out a common factor of (x – y))
= (x - y)(x - y)(x + y) (factoring (x^2 – y^2) using a difference of squares)
= (x - y)^2(x + y) (putting like terms together)

(x - y)^2
= x^2 - 2xy + y^2 (foiling (x - y)(x – y))
= x^2 + 2xy + y^2 – 4xy (since 2xy – 4xy = -2xy in the previous equation)
= (x + y)^2 – 4xy (factoring x^2 + 2xy + y^2 using trinomial factoring)
= 3^2- 4*1 = 9 – 4 = 5 when we have x + y = 3 and xy = 1 from both conditions 1) & 2).

Then we have (x - y)^2(x + y) = 5*3 = 15.

Therefore, C is the answer.
Answer: C

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27 Apr 2020, 18:25

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[GMAT math practice question]

(Algebra) What is the coefficient of x^2 in the expression (-3x^2 + 2x + 1)(x - 1)^2?

A. -6
B. -5
C. 4
D. 5
E. 6

=>

Since (-3x^2 + 2x + 1)(x - 1)^2 = (-3x^2 + 2x + 1)(x – 1)(x – 1)
= (-3x^2 + 2x + 1)(x^2 – 2x + 1)
= -3x^4 + 6x^3 – 3x^2 + 2x^3 – 4x^2 + 2x + x^2 – 2x + 1
= -3x^4 + 8x^3 - 6x^2 + 1, and the coefficient of x^2 is -6.

Therefore, A is the answer.
Answer: A

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28 Apr 2020, 18:57

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[GMAT math practice question]

(Number Properties) What is the sum of all possible solutions of the equation (3^n-9)^3+(9^n-3)^3=(3^n+9^n-12)^3, where n is a positive integer?

A. 1
B. 2
C. 3
D. 4
E. 5

=>

Assume a = 3^n - 9 and b = 9^n - 3.

We have the equation a^3 + b^3 = (a + b)^3 or 3ab(a + b) = 0, since (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 = a^3 + b^3 + 3ab(a + b).
Then we have a = 0, b = 0 or a + b = 0.

Case 1: a = 0
Since we have 3^n – 9 = 0, we have n = 2.

Case 2: b = 0
Since we have 9^n – 3 = 0, we have n = ½, which is not a solution, since n is a positive integer.

Case 3: a + b = 0
3^n + 9^n – 12 = 0
=> 9^n + 3^n – 12 = 0
=> 3^2n + 3^n – 12 = 0
=> (3^n - 3)(3^n + 4) = 0
=> 3^n = 3 since 3^n + 4 > 0
=> n = 1

Then, the sum of all solutions is 1 + 2 = 3.

Therefore, C is the answer.
Answer: C

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Updated on: 03 May 2020, 21:14

Originally posted by AliciaSierra on 28 Apr 2020, 23:26.
Last edited by AliciaSierra on 03 May 2020, 21:14, edited 1 time in total.

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MathRevolution

@MathRevolution--How will I judge that I should change 447 to 455 ?

MathRevolution

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01 May 2020, 03:59

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[GMAT math practice question]

(Algebra) What is the equivalent expression of (1/x+y+z)(1/x+1/y+1/z)(1/xy+yz+zx)(1/xy+1/yz+1/zx)?

A. 1/x+y+z
B. 1/xy+yz+zx
C. 1/xyz
D. (1/xyz)2
E. xy+yz+zx/x+y+z

=>

(1/x+y+z)(1/x+1/y+1/z)(1/xy+yz+zx)(1/xy+1/yz+1/zx)
=(1/x+y+z)(xy+yz+zx/xyz)(1/xy+yz+zx)(x+y+z/xyz)
=(1/xyz)^2

Therefore, D is the answer.
Answer: D

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03 May 2020, 20:44

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[GMAT math practice question]

(Algebra) abc ≠ 0. What is the value of a^2+b^2+c^2?

1) a+b+c=3.
2) a^3+b^3+c^3=27.

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have 3 variables (a, b, and c) and 0 equations, E is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)

If a = 1, b = -1, c = 3, then we have a^2 + b^2 + c^2 = 1 + 1 + 9 = 11.
If a = 2, b = -2, c = 3, then we have a^2 + b^2 + c^2 = 4 + 4 + 9 = 17.

Since both conditions together do not yield a unique solution, they are not sufficient.

Therefore, E is the answer.
Answer: E

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B, or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2) when taken together. Obviously, there may be occasions on which the answer is A, B, C, or D.

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06 May 2020, 19:06

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[GMAT math practice question]

(Geometry) The figure shows a quadrangle ABCD with ∠ADC = 90°, ∠DCB = 90° and AD = 6, AB = 8 and BC = 10. What is the length BD?

Attachment:

5.4ps.png [ 14.35 KiB | Viewed 2557 times ]

A. 2√37
B. 10
C. 3√39
D. 14
E. 5√41

=>

Attachment:

5.4PS(A).png [ 18.47 KiB | Viewed 2551 times ]

From the above figure, since we have EC = 6, we have BE = 4. Then we use Pythagorean Theorem to solve for AE, giving us AE = √8^2- 4^2 = √64-16 = √48 = 4√3 and AE = DC = 4√3.
Thus, we have x = √10^2+(4√3)^2 = √100+48 = 2√37.

Therefore, A is the answer.
Answer: A