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Overview of GMAT Math Question Types and Patterns on the GMAT

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New post 19 Mar 2019, 18:14
[GMAT math practice question]

The point (p,q) lies in which quadrant of the x-y plane?

1) (p+1, q) lies in the 2nd quadrant
2) (q-1, p) lies in the 4th quadrant

=>

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) tells us that p + 1 < 0 and q > 0, which is equivalent to p < -1 < 0 and q > 0. Thus, (p, q) is in the 2nd quadrant.
Condition 1) is sufficient.

Condition 2) tells us that q - 1 > 0 and p < 0, which is equivalent to p < 0 and q > 1 > 0. Thus, (p, q) is in the 2nd quadrant.
Condition 2) is sufficient.

Therefore, D is the answer.
Answer: D

FYI, Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.
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New post 21 Mar 2019, 18:28
[GMAT math practice question]

If n, n/3 and n/4 are positive integers, and n is less than or equal to 100, how many values of n are possible?

A. 6
B. 7
C. 8
D. 9
E. 10

=>

The condition n/3 is a positive integer tells us that n is a positive multiple of 3.
The condition n/4 is a positive integer tells us that n is a positive multiple of 4.
Thus, n is a positive multiple of 12.

The number of positive multiples of 12 less than or equal to 100 is 8 since 100 = 12*8 + 4.

Therefore, the answer is C.
Answer: C
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New post 25 Mar 2019, 18:19
[GMAT math practice question]

If m and n are prime numbers, what is the value of m+n?

1) 15≤m<n≤20
2) mn = 323

=>

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)
15≤m<n≤20 tells us that m = 17 and n = 19. So, m + n = 17 + 19 = 36.
Condition 1) is sufficient since it yields a unique solution.

Condition 2)
mn=323 tells us that m = 17 and n = 19, or m = 19 and n = 17.
In both cases, m + n is 36.
Condition 2) is sufficient since it yields a unique solution.

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 27 Mar 2019, 18:20
[GMAT math practice question]

Jeonghee has 5 different red cards and 5 different blue cards. She shuffles the10 cards, and then places 5 of the cards in a row. What is the probability that all red cards are adjacent to each other and all blue cards are adjacent to each other in her row?

A. 2/5
B. 28/125
C. 31/126
D. 33/140
E. 25/216

=>

The total number of ways in which 5 cards can be chosen out of 10 cards is 10P5 = 10*9*8*7*6.

There are 5*4*3*2*1 arrangements of each of BBBBB and RRRRR.
There are 5*4*3*2*5 arrangements of each of BBBBR, RBBBB, RRRRB and BRRRR.
There are 5*4*3*5*4 arrangements of each of BBBRR, RRBBB, RRRBB and BBRRR.

Thus, the total number of arrangements with all red cards adjacent to each other and all blue cards adjacent to each other is (5*4*3*2*1)*2 + (5*4*3*2*5)*4 + (5*4*3*5*4)*4.
The required probability is ( 5*4*3*2*1*2 + 5*4*3*2*5*4 + 5*4*3*5*4*4 ) / 10*9*8*7*6 = { 5*4*3(4+40+80) } / { 10*9*8*7*6 } = 124 / 2*9*2*7*2 = 31/126.

Therefore, the answer is C.
Answer: C
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New post 28 Mar 2019, 18:35
[GMAT math practice question]

Express 2^20-2^19-2^18-2^17 as a power of 2.

A. 2^15
B. 2^16
C. 2^17
D. 2^18
E. 2^19


=>

2^20-2^19-2^18-2^17
=2^32^17- 2^22^17-2^12^17-2^17
= 2^17 (8-4-2-1)
= 2^17(1)
= 2^17

Therefore, the answer is C.
Answer: C

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New post 31 Mar 2019, 18:38
[GMAT math practice question]

p, q, and r are different prime numbers. What is the value of q?

1) (pq)^2=36
2) (qr)^2= 225

=>

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 (p, q and r) 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)

Since p^2q^2=2^23^2 and q^2r^2 = 3^25^2, we have p = 2, q = 3 and r = 5.
Conditions 1) & 2) are sufficient, when applied together.

Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
Since p^2q^2=2^23^2, we must have p = 2, q = 3 or p = 3, q = 2.
Condition 1) is not sufficient since it does not yield a unique solution.

Condition 2)
Since q^2r^2=3^25^2, we have q = 3, r = 5 or q = 5, r = 3.
Condition 2) is not sufficient since it does not yield a unique solution.

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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New post 03 Apr 2019, 18:37
[GMAT math practice question]

The diagram below contains four right triangles with legs a and b. What is the area of the larger square?

Attachment:
3.29.png
3.29.png [ 8.7 KiB | Viewed 91 times ]


1) a = 12
2) b = 9

=>

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.

If we assume c is the length of the hypotenuse of the right triangle, we have c^2 = a^2 + b^2 and c^2 is the area the larger square.
We need the values of both a and b. Thus, conditions 1) & 2) are sufficient, when applied together, but neither condition is sufficient on its own.

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 04 Apr 2019, 18:29
[GMAT math practice question]

√r + 2/√r = 4. What is the value of r + 4/r?

A. 12
B. 14
C. 16
D. 32
E. 64

=>

(√r + 2/√r)^2 = r + 2(√r)(2/√r) + 4/r = r + 4/r + 4 = 4^2 = 16
So, r + 4/r = 16 -4 = 12.

Therefore, A is the answer.
Answer: A
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New post 07 Apr 2019, 18:44
[GMAT math practice question]

If |2x|>|3y|, is x >y?

1) x>0
2) 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.

From condition 1), we have 3x > 2x = |2x| > |3y| ≥ 3y since |x| = x. So, x > y and the answer is ‘yes’.
Thus, condition 1) is sufficient.

Condition 2)
If x = 10, and y = 1, then x > y and the answer is ‘yes’.
If x = -10, and y = 1, then x < y and the answer is ‘no’.
Thus, condition 2) is not sufficient, since it does not yield a unique solution.

Therefore, A is the answer.
Answer: A
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New post 09 Apr 2019, 18:48
[GMAT math practice question]

Is x < 0?

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

Condition 1)
x^3 + 1 < 0
=> (x+1)(x^2-x+1) < 0
=> x + 1 < 0 since x^2-x+1 > 0
=> x < -1 < 0
Thus, condition 1) is sufficient, and the answer is ‘yes’.

Condition 2)
x^3 + x + 1 < 0
=> x^3 + x < -1
=> x(x^2 + 1) < -1
=> x < -1/(x^2 + 1) since x^2 + 1 > 0
=> x < -1/(x^2 + 1) < 0 since x^2 + 1 > 0
Thus, condition 2) is sufficient, and the answer is ‘yes’.

Therefore, D is the answer.
Answer: D
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New post 11 Apr 2019, 19:24
[GMAT math practice question]

x^3-y^3 = 90 and x-y = 3. What is the value of xy?

A. 3
B. 4
C. 5
D. 6
E. 7

=>

x^3-y^3 = (x-y)(x^2+xy+y^2) = 90
Since x – y = 3, x^2+xy+y^2 = 30
Now, 9 = (x-y)^2 = x^2 – 2xy + y^2 = x^2+xy+y^2 – 3xy = 30 – 3xy.
So, 3xy = 21 and xy = 7.

Therefore, the answer is E.
Answer: E
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New post 14 Apr 2019, 18:41
[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.

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 18 Apr 2019, 18:24
[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.

Therefore, the answer is A.
Answer: A
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT   [#permalink] 18 Apr 2019, 18:24

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Overview of GMAT Math Question Types and Patterns on the GMAT

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