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Overview of GMAT Math Question Types and Patterns on the GMAT

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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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New post 15 Mar 2018, 08:09
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mahrah wrote:
Can someone provide detailed solution to this problem? Any strategies for setting up these kind of word problems? Thanks! Bunuel or chetan2u

Of all of the apples inspected last week at a certain orchard, 4.5 percent failed to pass inspection. Of the apples that failed inspection, 2/3 of them were rotten and the rest was unmatured. If all of the apples that were rotten or unmatured failed inspection, how many of apples inspected last week at the plant were unmatured?
(1) 450 of apples inspected last week at the orchard failed to pass inspection.
(2) 9,550 of apples inspected last week at the orchard passed inspection.



hi...
what is given?
let the apples be A..
1) 4.5 percent failed to pass inspection so \(\frac{95.5}{100} * A\) passed inspection.
2) Of the apples that failed inspection, 2/3 of them were rotten and the rest was unmatured- \(\frac{2}{3} * \frac{4.5}{100} *\)A rotten and \(\frac{1}{3}*\frac{4.5}{100} *A\) unmatured
3)how many of apples inspected last week at the plant were unmatured? = \(\frac{1}{3}*\frac{4.5}{100} *A\)

what we require is A.

lets see the statements..
(1) 450 of apples inspected last week at the orchard failed to pass inspection.
so \(\frac{4.5A}{100} = 450...... A= 10000\)..
suff

(2) 9,550 of apples inspected last week at the orchard passed inspection
so 95.5% of A = 9550..... A = 10000
suff

D
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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New post 19 Mar 2018, 18:08
[GMAT math practice question]

What is the reminder when n^2 is divided by 4?

1) When n is divided by 2, the reminder is 1.
2) When n is divided by 3, the reminder is 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.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
Plugging-in numbers is suggested for remainder questions.
The integers which have a remainder of 1 when divided by 2 are odd.
So,
n: 1, 3, 5, 7, 9, …
and
n^2: 1, 9, 25, 49, 81, …
Each value of n2 has a remainder of 1 when it is divided by 4.
So, condition 1) is sufficient.

Condition 2)
When n = 1, n^2= 1 has a remainder of 1 when it is divided by 4.
When n = 4, n^2=16 has a remainder of 0 when it is divided by 4.
Since we don’t have a unique answer, condition 2) is not sufficient.

Therefore, A is the answer.

Answer: A

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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New post 22 Mar 2018, 18:03
[GMAT math practice question]

X is proportional to Y. If Y is increased by 30%, by approximately what percent is X^2 increased?

A. 30%
B. 40%
C. 50%
D. 60%
E. 70%

=>

X = kY for some k.
Since (1.3kY)^2 = 1.69k^2Y^2 = 1.69(kY)^2 = 1.69X^2, we have (1.69X^2 – X^2) / X^2 = 0.69, which is approximately 70%.

Therefore, the answer is E.

Answer: E
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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New post 25 Mar 2018, 18:23
[GMAT math practice question]

If |x+1/2|=|y+1/2|, what is the value of x+y?

1) xy<0
2) x>0 and y<0

=>

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.

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

|x+1/2|=|y+1/2|
=> |x+1/2|^2=|y+1/2|^2
=> (x+1/2)^2=(y+1/2)^2
=> x^2 + x + 1/4 = y^2 + y + 1/4
=> x^2 - y^2 + x - y = 0
=> (x-y)(x+y)+(x-y) = 0
=> (x-y)(x+y+1) = 0
=> x=y or x+y=-1

Condition 1)
Since xy < 0, we have x≠y and x+y = -1 from the original condition.

Condition 2)
Since x > 0 and y < 0, we have x≠y and x+y = -1 from the original condition.

Therefore, D is the answer.

By Tip 1), D is most likely to be the answer.

Answer: D
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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New post 27 Mar 2018, 18:09
[GMAT math practice question]

Alice studies for a hours on each of Monday, Tuesday, and Thursday. She also studies for b hours on Wednesday, and for c hours on Friday. What is her median study time for the school week?

1) a=10
2) b+c=30

=>

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.

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

Depending on their values, it is possible to rearrange a, a, a, b, c into ascending order in the following ways:
a, a, a, b, c
a, a, a, c, b
b, a, a, a, c
c, a, a, a, b
b, c, a, a, a
c, b, a, a, a
In every order, the median (middle value) is a. So, the question asks for the value of a.

Thus, only condition 1) is sufficient.


Therefore, A is the answer.

Answer: A
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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New post 29 Mar 2018, 19:38
[GMAT math practice question]

Which of the following is the greatest?

A. (1+2)^5
B. 10^3
C. (1^2+2^2)^4
D. (2^2+2^2+2^2)^3
E. (2^2+2^2+2^2+2^2)^2

=>

A. (1+2)^5 = 3^5 = 243
B. 10^3 = 1000
C. (1^2+2^2)^4 = 5^4 = 625
D. (2^2+2^2+2^2)^3 = 12^3 = 1728
E. (2^2+2^2+2^2+2^2)^2 = 16^2 = 256

Therefore, D is the answer.

Answer: D
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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New post 01 Apr 2018, 18:49
[GMAT math practice question]

If 50-√7<x<50+√7, then x=?

1) x is an odd integer
2) √x is an integer.

=>

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.

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

Since 2< √7< 3, we have 47< x < 53 from the original condition ‘50-√7<x<50+√7’.

Condition 1)
As x is an odd integer, it could be 49 or 51.
Since we don’t have a unique solution, condition 1) is not sufficient.

Condition 2)
If √x is an integer, then x is the square of an integer.
49 is the only perfect square of an integer between 47 and 53.
Thus, x=49 and condition 2) is sufficient.

Therefore, B is the answer.

Answer: B
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Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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New post 05 Apr 2018, 18:33
[GMAT math practice question]

The number 123,k50 is a 6-digit integer, and k is a positive 1 digit integer. Which of the following cannot be a factor of 123,k50?

A. 2
B. 3
C. 4
D. 5
E. 6

=>

The last two digits tell us whether the number is divisible by 4.
Since 50 is not a multiple of 4, the number cannot be a multiple of 4.

Therefore, the answer is C.

Answer: C

Let’s see why the number could be divisible by each of the other options:

A: Since the units digit is an even number, the whole number is a multiple of 2.
B: A number is divisible by 3 if the sum of its digits is divisible by 3. If k = 4, then the sum of the digits is 1 + 2 + 3 + 4 + 5 + 0 = 15, which is a multiple of 3, and so the number is a multiple of 3.
D: Since the units digit is a multiple of 5, the number is a multiple of 5.
E: If k = 4, the number is divisible by 3 as seen in part B. Since it is also divisible by 2 (see part A), the number is divisible by 6.
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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New post 09 Apr 2018, 18:24
[GMAT math practice question]

If the average (arithmetic mean) price of apples, bananas and oranges is $3.00 per pound, what is their median price?

1) The price of apples is $3.00 per pound.
2) The price of bananas is $2.97 per pound.

=>

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.

Since we have 3 variables (a for apples, b for bananas and o for oranges) and 1 equation ( ( a + b + o ) / 3 = 3), C is most likely to be 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.

This question is a new type of GMAT question. The average is provided in the original condition and the question asks for the value of the median. The same average applies for each of the conditions.

Conditions 1) & 2)
If a = 3.00 and b = 2.97, then ( a + b + o ) / 3 = 3.
So,
3.00 + 2.97 + o = 9
and
o = 3.03. Therefore, the median is 3.00.
Thus, both conditions together are sufficient.

Condition 1)
We consider three cases.
Case 1: a = b = c = 3.00
Since all prices are the same, the median is 3.00.

Case 2: b < 3.00
If b < 3.00, then we must have c > 3.00.
Therefore, the median is 3 since b < a < c.

Case 3: b > 3.00
If b > 3.00, then we must have c < 3.00.
Therefore, the median is 3 since c < a < b.

Thus, condition 1) is sufficient on its own.

Condition 2)
If a = 3.00, b = 2.97 and c = 3.03, then the median is 3.00.
If a = 2.00, b = 2.97 and c = 3.00, then the median is 2.97.
Since we don’t have a unique solution, condition 2) is not sufficient on its own.

Therefore, A is the answer.

Answer: A

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.

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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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New post 11 Apr 2018, 18:39
[GMAT math practice question]

Is √x+x>-√y?

1) √x+√y = 1
2) x>0

=>

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.

Since we have 2 variables (x and y) and 0 equations, E is most likely to be 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.

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

√x+x>-√y
=> √x+√y+ x>0
Since √x+√y≥0 is always true, we just need to check if x > 0.
Condition 2) is sufficient and since condition 1) is hard to check and condition 2) is easy to check, the answer is D by CMT (Common Mistake Type) 4B.

Condition 1)

We have x ≥ 0 from √x,
Then √x+√y + x ≥ 1 > 0.
Thus condition 1) is sufficient.


Condition 2)

Since √x+√y ≥ 0 and x > 1, we have √x+√y + x > 1 > 0.
Thus condition 2) is sufficient.

Therefore, D is the answer.

Answer: D

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.

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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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New post 15 Apr 2018, 18:31
[GMAT math practice question]

A jar contains 4 balls, labeled 1,2,3, and 4. A ball is selected from the jar, and its number is recorded before it is returned to the jar. If a second ball is then selected from the jar, what is the probability that the difference between the numbers on the two balls selected is 1?

A. 1/3
B. 3/4
C. 1/2
D. 5/8
E. 3/8

=>

The total number of ways the two balls may be selected is 4C2 = ( 4 * 3 ) / ( 1 * 2 ) = 6.
There are three ways in which the numbers on the two balls selected can have a difference of 1: ( 1, 2 ), ( 2, 3 ), and ( 3, 4 ).

Thus, the probability is 3/6 or 1/2

Therefore, C is the answer.
Answer: C
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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New post 17 Apr 2018, 18:17
[GMAT math practice question]

In the x-y plane, what is the slope of the line segment joining the y-intercept and the positive x-intercept of the curve y=x2-5x-6?

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

=>

First, we find the x-intercepts of the curve. These occur when y = 0. Now,
y=x^2-5x-6
=> y = (x+1)(x-6).

Thus, the x-intercepts are the points (-1,0) and (6,0), and the positive x-intercept is (6,0).
As the y-intercept occurs when x = 0, it is the point (0,-6).

Thus, the required slope is (6 – 0) / ( 0 – (-6) ) = 1.

Therefore, the answer is A.
Answer: A
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT   [#permalink] 17 Apr 2018, 18:17

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