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# Overview of GMAT Math Question Types and Patterns on the GMAT

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Joined: 16 Aug 2015
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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14 Apr 2019, 17:41
[GMAT math practice question]

x, y and z are different integers. Is their average equal to their median?

1) Their range is 11.
2) Their median is 11.

=>

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.

Suppose x, y and z are different integers with x < y < z.
For their average ( x + y + z ) / 3 to be equal to their median y,
we must have z – y = y – x, and so their range is z – x = z – y + y – x = 2(y-x).
This implies that z – x is an even integer.

Condition 1)
Since condition 1) gives an odd value for the range, the answer is ‘no’. Thus, condition 1) is sufficient by CMT (Common Mistake Type) 1.

Condition 2)
If x = 10, y = 11 and z = 12, then the average and the median are the same, and the answer is ‘yes’
If x = 10, y = 11 and z = 15, then the average 12 is different from the median 11, and the answer is ‘no’.
Thus, condition 2) is not sufficient, since it does not yield a unique solution.

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

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18 Apr 2019, 17:24
[GMAT math practice question]

(number property) If the sum of n consecutive positive integers is 42, which of these could be the value of n?

A. 7
B. 8
C. 9
D. 10
E. 11

=>

Recall that the sum of terms of an arithmetic sequence is {(a+l)/2}*n where a is the first term, l is the last term and n is the number of terms.

We are told that {(a+l)/2}*n = 42 or n(a+l) = 84.
Thus, n is a factor of 84.
7 is the unique factor of 84 among the choices.

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22 Apr 2019, 17:52
[GMAT math practice question]

(geometry) What is the area of triangle ABC?
1) Triangle ABC has two sides of lengths 3 and 4
2) Triangle ABC is a right triangle

=>

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 a triangle has 3 variables in geometry, 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.

Conditions 1) & 2)

Attachment:

4.19.png [ 4.29 KiB | Viewed 404 times ]

There are two right triangles with sides of lengths 3 and 4 as shown above.
Thus, there are two possible areas: (1/2)*4*3 = 6 and (3/2) √7.

Since the conditions don’t yield a unique answer when applied together, they are not sufficient.

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

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25 Apr 2019, 00:29
[GMAT math practice question]

(number property) If a, b, and c are integers, is a+b+c an even integer?

1) a^2+b^2 is an even integer
2) b^2+c^2 is an even 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.

Since we have 3 variables (x, y and z) 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.

Conditions 1) & 2)
If a = 1, b = 1 and c = 1, then a + b + c = 3 is not an even integer and the answer is ‘no’.
If a = 2, b = 2 and c = 2, then a + b + c = 6 is an even integer and the answer is ‘yes’.
Since the conditions don’t yield a unique answer when applied together, they are not sufficient.

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

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27 Apr 2019, 06:34

Example 9:
Stations M and N are connected by two separate, straight and parallel rail lines that are 500 miles long. Freight train A and freight train B simultaneously left Station M and Station N, respectively, and each freight train traveled to the other’s point of departure. The two freight trains passed each other after traveling for 4 hours. When the two freight trains passed, which train was nearer to its destination?

(1) At the time when the two freight trains passed, freight train A had averaged a speed of 60 miles per hour.
(2) Freight train B averaged a speed of 130 miles per hour for the entire trip.

Statement 1 Analysis:
From question stem: Given that both the train traveled for 4hours when they meet. So, A traveled for 4hours.
I states that A had an average speed of 60mph when it passed B.

So, A had traveled 4*60 = 240miles, when both the trains passed each other.
This implies B traveled 260miles.

On a total distance of 500miles, B is near to its destination.

I this statement I is sufficient to answer the question.

But the OA is E.

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29 Apr 2019, 17:34
[GMAT math practice question]

(number properties) If n is a positive integer, what is the value of n?

1) n(n-1) is a prime number
2) n(n+1) has 4 factors

=>

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

Condition 1)
Only n =2 makes n(n-1) a prime number.
Thus, condition 1) is sufficient.

Condition 2)
Integers with four factors have the form p*q or p^3, where p and q are prime integers.
It is impossible to have n(n+1)=p^3, where n is an integer and p is a prime number.
The only time n(n+1) = pq is when n(n+1) = 2*3 and n =2.
Condition 2) is sufficient since it yields a unique solution.

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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02 May 2019, 17:58
[GMAT math practice question]

(number properties) What is the smallest positive multiple of 15 that has only 0 and 1 as digits?

A.15
B. 30
C. 110
D. 1110
E. 111000

=>

A multiple of 15 is a number divisible by both 3 and 5.
Since it is divisible by 5, its units digit must be 0 or 5.
Since it is divisible by 3, the sum of its digits must be a multiple of 3.
1110 is the smallest number with only 0 and 1 as its digits that has a units digit of 0 or 5 and the sum of its digits a multiple of 3.

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06 May 2019, 17:42
[GMAT math practice question]

(inequality) a, b, c, d and e are real numbers with a<b<c<d<e. Is abcde negative?

1) abc < 0
2) cde < 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 5 variables and 4 equations, D is most likely to be the answer. So, we should consider each condition on its own first. If a question is an inequality, then inequalities in the original condition can be counted as equations.

Condition 1)
If a = -1, b = 1, c = 2, d = 3, e = 4, then abcde < 0, and the answer is ‘yes’
If a = -4, b = -3, c = -2, d = -1, e = 1, then abcde > 0, and the answer is ‘no’.
Condition 1) is not sufficient since it doesn’t yield a unique answer.

Condition 2)
There are two cases to consider:

i) 0 lies between c and d
ii) 0 is greater than e.

If 0 lies between c and d, then abcde < 0 and the answer is ‘yes’.
If 0 is greater than e, then abcde < 0 and the answer is ‘yes’.
Condition 2) is sufficient since it gives a unique answer.

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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08 May 2019, 17:28
[GMAT math practice question]

x^2 + 4x + 1 = 0. What is the value of x^2 + 1/x^2?

A. 10
B. 12
C. 14
D. 16
E.18

=>

x^2 + 4x + 1 = 0
=> x + 4 + 1/x = 0
=> x + 1/x = -4
So, (x + 1/x)^2 = (-4)^2 and x^2 +2x(1/x) + 1/x^2 = 16.
Therefore,
x^2 +2 + 1/x^2 = 16
and x^2 + 1/x^2 = 14.

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

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12 May 2019, 17:54
[GMAT math practice question]

(number properties) If x, y, and z are integers, is xyz a multiple of 6?

1) x+y+z is a multiple of 6
2) x, y, and z are consecutive

=>

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 the product of three consecutive integers is a multiple of 6, condition 2) is sufficient. Without loss of generality, since condition 2) tells us that x, y and z are consecutive, we can write y = x + 1 and z = x + 2. Then xyz = x(x+1)(x+2) is a multiple of 6 since x(x+1) is a multiple of 2 and x(x+1)(x+2) is a multiple of 3.

Condition 1)
If x = 1, y = 2 and z = 3, then xyz = 6 and the answer is ‘yes’.
If x = 2, y = 2 and z = 2, then xyz = 8 and the answer is ‘no’.
Condition 1) is not sufficient, since it doesn’t yield a unique answer.

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

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14 May 2019, 17:17
[GMAT math practice question]

(geometry) Is triangle ABC a right triangle?

1) The perimeter of triangle ABC is 12
2) The length of the shortest side of triangle ABC is 3

=>

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 questions about triangles require 3 variables, 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.

Let x, y and z be the side-lengths of triangle ABC, and suppose x ≤ y ≤ z.
Then x = 3 and x + y + z = 12.
If y = 4 and z = 5, triangle ABC has side lengths 3, 4 and 5. Thus it is a right triangle, and the answer is ‘yes’.
If y = 4.5 and z = 4.5, triangle ABC has side lengths 3, 4.5 and 4.5. It is not a right triangle, and the answer is ‘no’.
Since the two conditions don’t yield a unique answer when applied together, they are not sufficient,

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

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16 May 2019, 17:11
[GMAT math practice question]

The sum of two numbers is 1 and their product is -1. What is the sum of their cubes?

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

=>

Let the numbers be x and y. Then x + y = 1 and xy = -1.
Since (x+y)^2 = x^2 + 2xy + y^2 = x^2 + y^2 – 2, we have x^2 + y^2 = 3,
and x^3 + y^3 = (x+y)(x^2-xy+y^2) = 1*(x^2+ 1 + y^2) = x^2+y^2+1 = 4.

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

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19 May 2019, 17:09
[GMAT math practice question]

(number properties) If k/mn, where k, m and n are positive integers, is a fraction in its lowest terms, is k/mn a terminating decimal?

1) 1/m is a terminating decimal
2) 1/n is a terminating decimal

=>

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.

In order for k/mn to a terminating decimal, mn must have no prime factors other than 2 and 5. This implies that neither m nor n have prime factors other than 2 and 5. Thus, we need both conditions 1) & 2) together.

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

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21 May 2019, 17:18
[GMAT math practice question]

(number properties) n is a positive odd integer. What is the value of n?

1) n, n + 2, n + 4 are prime numbers.
2) n - 1 is an even prime number.

=>

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.

Condition 1):
The triple 3, 5 and 7 is the unique triple made up of three consecutive odd prime numbers number. So, n = 3.
Thus, condition 1) is sufficient.

Condition 2):
Since n – 1 = 2 is the unique even prime number, we must have n = 3. Thus, condition 2) is sufficient.

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

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22 May 2019, 17:15
[GMAT math practice question]

(number properties) n is an integer. What is the units digit of n^5-5n^3+4n?

A. 0
B. 2
C. 4
D. 6
E. 8

=>

n^5-5n^3+4n = n(n^4-5n^2+4) = n(n^2-1)(n^2-4) = n(n+1)(n-1)(n-2)(n-2) = (n-2)(n-1)n(n+1)(n+2). Thus, n^5-5n^3+4n is a product of five consecutive integers.
Since it is divisible by 2, 3, 4, and 5, it is a multiple of 10.
Thus, its units digits is 0.

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

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26 May 2019, 18:00
[GMAT math practice question]

(number properties) If m and n are positive integers, is m/n a terminating decimal?

1) m is divisible by 9
2) n is divisible by 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.

Since we have 2 variables (x and y) and 0 equations, 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.

Conditions 1) & 2)

If m = 9 and n = 30, then m/n = 9 / 30 = 3/10 = 0.3 is a terminating decimal and the answer is ‘yes’.
If m = 9 and n = 210, then m/n = 9 / 210 = 3/70 is not a terminating decimal since the denominator, 70, has a prime factor other than 2 and 5. The answer is ‘no’.
Both conditions together are not sufficient, since they don’t yield a unique solution.

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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27 May 2019, 17:29
[GMAT math practice question]

(inequality) x is a positive number. Is x > 1?

1) √x > x
2) x^3 - 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 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first.

In inequality questions, the law “Question is King” tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient

Condition 1)
√x > x
=> x > x^2 by squaring
=> x^2 – x < 0
=> x(x-1) < 0
=> 0 < x < 1
Since ‘no’ is also a unique answer by CMT (Common Mistake Type) 1, condition 1) is sufficient.

Condition 2)
x^3 - x < 0
=> x(x^2-1) < 0
=> (x+1)x(x-1) < 0
=> x<-1 or 0 < x < 1
=> 0 < x < 1 since x is positive.
Since ‘no’ is also a unique answer by CMT (Common Mistake Type) 1, condition 2) is sufficient.

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

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30 May 2019, 00:43
[GMAT math practice question]

(number property) If a=2b=6c for positive integers a, b, and c, which of the following could be the value of abc?

A. 1000
B. 1230
C. 2250
D. 2367
E. 2488

=>

Since 2b = 6c, we have b = 3c. Thus, abc = (6c)*(3c)*c = 18c^3 and abc is a multiple of 18. This implies that abc is a multiple of both 2 and 9.

Of the above answer choices, only 2250 is a multiple of both 2 and 9.

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

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02 Jun 2019, 17:07
[GMAT math practice question]

(number properties) x = -1. What is the value of x + x^n + x^{n+1} + x^{n+2}?

1) n is a prime number
2) n is an odd number

=>

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 condition on its own first.

Condition 1)
If n = 2, then x + x^n + x^{n+1} + x^{n+2} = (-1) + (-1)^2 + (-1)^3 + (-1)^4? = (-1) + 1 + (-1) + 1 = 0.
If n = 3, then x + x^n + x^{n+1} + x^{n+2} = (-1) + (-1)^3 + (-1)^4 + (-1)^5 = (-1) + (-1) + (-1) + 1 = -2.
Condition 1) is not sufficient since it doesn’t yield a unique solution.

Condition 2)
If n is an odd number, then x + x^n + x^{n+1} + x^{n+2} = (-1) + (-1)^n + (-1)^{n+1} + (-1)^{n+2} = (-1) + (-1) + 1 + (-1) = -2.
Condition 2) is sufficient since it yields a unique solution.

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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04 Jun 2019, 17:23
[GMAT math practice question]

(inequality) When -1/2<h<0, which of the following has the greatest value?

A. h^2-2h+1
B. h^2+h
C. h
D. h^2
E. h^3

=>

Test each expression by plugging in h = -1/4.
h^2-2h+1 = (h-1)^2 = (-(5/4))^2 = 25/16
h^2+h = h(h+1) = -(1/4)(3/4) = -(3/16)
h = -1/4
h^2 = (-(1/4))^2 = 1/16
h^3 = (-(1/4))^3 = -(1/64)

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Re: Overview of GMAT Math Question Types and Patterns on the GMAT   [#permalink] 04 Jun 2019, 17:23

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