Overview of GMAT Math Question Types and Patterns on the GMAT

[GMAT math practice question]

(algebra) Using the formula a^2–b^2 =(a+b)(a-b), find the value of (1+ 1/2 )(1+ 1/4)(1+1/16).

A. 255/128
B. 255/256
C. 257/128
D. 127/128
E. 555/128

=>

Let X = (1+1/2)(1+1/4)(1+1/16).
Then
(1-1/2)X = (1-1/2)(1+1/2)(1+1/4)(1+1/16)
=(1-1/4)(1+1/4)(1+1/16)
=(1-1/16)(1+1/16)
=1-1/256
=255/256.
So, (1/2)X = 255/256, and X = 255/128

Therefore, A is the answer.
Answer: A

[GMAT math practice question]

(algebra) <x,y> denotes x + y/2. What is the value of x?

1) <x,y> = y + x/2
2) <2x,2y>+1=<y,x> - 2

=>

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.

When we simply condition 2), we have
<2x, 2y>+1=<y, x>-2
=> 2x + 2y/2 + 1 = y + x/2 - 2
=> 2x + y + 1 = y + x/2 – 2
=> (3/2)x = -3
=> x = -2.
Condition 2) is sufficient.

Condition 1)
Since we have <x,y> = y + x/2 = x + y/2, we have y/2 = x/2 or x = y.
Condition 1) is not sufficient, since it does not yield a unique solution.

Therefore, B is the answer.
Answer: B

[GMAT math practice question]

(ratio) There is a% of saline solution of 500g. Alice wants to have b% of saline solution by boiling saline solution where b > a. What is the lost weight of the saline solution by boiling?

1) a = 20
2) a/b = 2/5

=>

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.

Let x be the lost weight of b% saline solution by boiling.
The question asks the value of x such that (a/100)500 = (b/100)(500-x).
(a/100)500 = (b/100)(500-x)
=> 500a = b(500-x)
=> 500a = 500b – bx
=> bx = 500(b-a)
=> x = 500(b-a)/b
=> x = (500)(1-a/b)
Thus, condition 2) is sufficient.

When a question asks for a ratio, if one condition includes a ratio and the other condition just gives a number, the condition including the ratio is most likely to be sufficient. This tells us that B is most likely to be the answer to this question.

Condition 1) is not sufficient obviously, since we don’t have any information about the variable a.

Therefore, B is the answer.
Answer: B

[GMAT math practice question]

(number Properties) A composite number n can be represented as a product of two different primes a and b (n=ab). If 100<nab<200, what is n-a-b?

A. 4
B. 5
C. 6
D. 7
E. 8

=>

Since we have n = ab, we have nab = n^2 and 100<n^2<200.
Perfect squares between 100 and 200 are 11^2 = 121, 12^2 = 144, 13^2 = 169 and 14^2 = 196.
n = 14 is the only one among those numbers, 11, 12, 13 and 14 which is a product of two different prime integers.
Thus we have a=2, b=7 or a=7, b=2.
Thus n – a – b = n – ( a + b ) = 14 – (2 + 7) = 14 – 9 = 5.

Therefore, B is the answer.
Answer: B

[GMAT math practice question]

(number properties) What is the value of p*q?

1) p and q are prime numbers
2) q-p=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.
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 2 variables (p and q) and 0 equations, C 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 p and q are prime numbers and q – p = 3 which is an odd number, p and q have different parities.
It means that either p or q is an even prime number. Then we have p = 2, since 2 is the smallest and unique even prime number.
So q = 5.

Since this question is a statistics 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 there many possibilities for (p, q), the condition is obviously not sufficient.

Condition 2)
If p = 2 and q = 5, then we have p*q = 10.
If p = 1 and q = 4, then we have p*q = 4.
Since condition 2) does not yield a unique solution, it is not sufficient.

Therefore, C is the answer.
Answer: C

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.

[GMAT math practice question]

(algebra) If 2x=3y(xy≠0), what is (5x^2+xy)/(3x^2 -4xy)?

A. 14
B. 16
C. 17
D. 19
E. 21

=>

Since 2x=3y, we have y = (2/3)x.
(5x^2+xy)/(3x^2 -4xy)
= (5x^2+x*(2/3)x)/(3x^2 -4x*(2/3)x)
= (5x^2+(2/3)x^2)/(3x^2 -4(2/3)x^2)
= ((17/3)x^2)/((1/3)x^2)
= 17.

We can also substitute x = 3 and y = 2 for a short-cut and get 17.

Therefore, C is the answer.
Answer: C

[GMAT math practice question]

(number properties) For a positive integer n, P(n) is denoted as the product of each digit of n. For example, P(29)=2*9=18, P(457)=4*5*7=140. a, b and c are 2-digit positive integers with P(a)P(b)P(c)=9. What is the maximum value of a+b+c?

A. 91
B. 102
C. 113
D. 124
E. 135

=>

In order to have a maximum value of P(a)P(b)P(c), the possible cases of tuples (a,b,c) we should consider are (91,11,11) and (31,31,11).
For (91,11,11), we have 91 + 11 + 11 = 113.
For (31,31,11), we have 31 + 31 + 11 = 73.
Thus, the maximum of a + b + c is 113.

Therefore, C is the answer.
Answer: C

[GMAT math practice question]

(algebra) abc ≠ 0. What is the value of a(1/b + 1/c) +b(1/c + 1/a) + c(1/a + 1/b)?

1) |a+b+c|≤0
2) a+b+c = 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.
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.

So, we will first simply the original condition as follows:

a(1/b + 1/c) +b(1/c + 1/a) + c(1/a + 1/b)
= a/b + a/c + b/c + b/a + c/a + c/b
= (b+c)/a + (a+c)/b + (a+b)/c
= (a+b+c-a)/a + (a+b+c-b)/b + (a+b+c-c)/c
= (a+b+c)/a – a/a + (a+b+c)/b – b/b + (a+b+c)/c – c/c
= (a+b+c)[(1/a)+(1/b)+(1/c)] – 3
If a+b+c= 0, then we have (a+b+c)[(1/a)+(1/b)+(1/c)] – 3 = -3.

Condition 1)
|a+b+c|≤0 means a+b+c=0 since |a+b+c|≥0
So, we have a(1/b + 1/c) +b(1/c + 1/a) + c(1/a + 1/b) = -3.
Since condition 1) yields a unique solution, it is sufficient.

Condition 2)
Since we have a+b+c=0, we have a(1/b + 1/c) +b(1/c + 1/a) + c(1/a + 1/b) = -3.
Since condition 2) yields a unique solution, it is also sufficient.

Therefore, D is the answer.
Answer: D

Note: Tip 1) of the VA method states that D is most likely to be the answer if condition 1) gives the same information as condition 2).

[GMAT math practice question]

(number properties) f(x) denotes the maximum prime factor of x, where x is a positive integer. For example, f(30)=f(2*3*5)=5. What is the value of f(abc)?

1) f(a) = 2
2) f(b)+f(c)=14

=>

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 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 = 2, b = 7 and c = 7, then f(abc) = f(2*7^2) = 7.
If a = 2, b = 3 and c = 11, then f(abc) = f(2*3*11) = 11.
Both conditions together do not yield a unique solution, so 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 when the answer is A, B, C, or D.

[GMAT math practice question]

(arithmetic) What is the value of 1/(5*6) + 2/(6*8) + 3/(8*11) + 4/(11*15)?

A. 1/10
B. 3/10
C. 3/14
D. 2/15
E. 3/16

=>

Remember the following properties.
1/n(n+1) = 1/n – 1/(n+1).
2/n(n+2) = 1/n – 1/(n+2).
3/n(n+3) = 1/n – 1/(n+3).
4/n(n+4) = 1/n – 1/(n+4).
…
Then we have
1/(5*6) + 2/(6*8) + 3/(8*11) + 4/(11*15)
= (1/5-1/6)+(1/6-1/8)+(1/8-1/11)+(1/11-1/15)
= 1/5 – 1/15
= 2/15

Therefore, D is the answer.
Answer: D

[GMAT math practice question]

(function) f(x) is a function. What is the value of a?

1) f(a)+ 4f(1/a)=15a
2) f(a)=f(-a)

=>

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 many variables to determine a function 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)
When we substitute a by 1/a in condition 1), we have f(1/a) + 4f(a) = 15(1/a) or 4f(1/a)+16f(a) = 60(1/a). Then, since we have 4f(1/a) = 15a – f(a) from condition 1), we have 4f(1/a) + 16f(a) = (15a – f(a)) + 16f(a) = 15f(a) + 15a = 60/a or f(a) = -a + 4/a.
When we substitute a by –a, we have f(-a) = a – 4/a and –a + 4/a = a – 4/a.
Then, we have a = 4/a or a2 = 4 and we have solutions a = 2 or -2.

Since both conditions 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 when the answer is A, B, C, or D.

[GMAT math practice question]

(geometry) AB is a straight line. What is the measure of the angle ∠AOD?

1) ∠EOB = (4/5)∠AOD
2) ∠DOE = ∠AOB/2



=>

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.

Assume <AOD = x, <DOE = y and <EOB = z.
Then we have x + y + z = 180.

Since we have 3 variables (x, y and z) and 1 equation (x + y + z = 180), C 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)
We have z = (4/5)x from condition 1) and y = 90 from condition 2).
Then we have x + z = 90 and x + (4/5)x = 90, or (9/5)x = 90.
Then, x = 50.

Therefore, C is the answer.
Answer: C

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.

[GMAT math practice question]

(arithmetic) If 1 + 1/(1+ 1/x) = 13/11, what is the value of x?

A. 1/9
B. 2/9
C. 1/3
D. 4/9
E. 5/9

=>

1 + 1 / ( 1 + (1/x) ) = 13/11
=> 1 + 1 / ((x/x) + (1/x)) = 13/11
=> 1 + 1 / ((x+1)/x) = 13/11
=> 1 + x / ( x + 1 ) = 13/11
=> (x + 1) / (x + 1) + x / (x + 1) = 13/11
=> (2x + 1)/(x + 1) = 13/11
=> 11(2x+1) = 13(x+1)
=> 22x + 11 = 13x + 13
=> 9x = 2
=> x = 2/9

Therefore, B is the answer.
Answer: B

[GMAT math practice question]

(statistics) f(x) is a function. What is the value of f(x)?

1) f(x)+f(1-x)=7
2) x + f(x/3)= f(x)/2

=>

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 many variables to determine a function 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)

We have 0 + f(0) = (1/2)f(0) or f(0) = 2, when we substitute 0 for x, since we have x+f(x/3)=f(x)/2.
We have f(0) + f(1) = 7, when we substitute 0 for x, since we have f(x)+f(1-x)=7.
When we substitute 1 for x in condition 2), we have 1+f(1/3) = (1/2)f(1) or f(1/3)=(1/2)f(1)-1=7/2-1-5/2.
When we substitute 1/3 for x in condition 2), we have1/3+f(1/9)=(1/2)f(1/3) or f(1/9)=(1/2)f(1/3)-1/3 = (1/2)(5/2)-1/3=5/4-1/3=11/12.

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 when the answer is A, B, C, or D.

[GMAT math practice question]

(Statics) The table shows the heights of students in a class. What is the value of y?



1) The number of students with a height greater than 155 is 4 times that of students with a height less than 155.
2) The students with a height less than 160 are 40% of all the students in the class.

=>

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 2 variables (x and y) and 0 equations, C 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)
Condition 1) tells us that (x+5+3+y)=4(1+6) or x+y+8=28 and it is equivalent to x+y=20.
Condition 2) tells us that (1+6+x)=(40/100)(1+6+x+5+3+y), (7+x)=(2/5)(15+x+y) or 5(x+7)=2(x+y+15). Since x+y=20 from condition 1) we have 5(x+7)=2(20+15) or 5(x+7) = 70. Therefore, x+7=14, and x=7. Substituting x=7 into x+y=20 gives us y=13.
Then we have x=7 and y=13.

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

Since this question is a statistics 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)
Condition 1) tells x+y=20.
Since condition 1) does not yield a unique solution, it is obviously not sufficient.

Condition 2)
Condition 2) tells 5(x+7)=2(x+y+15) or 3x+5 = 2y.
Since condition 2) does not yield a unique solution, it is not sufficient.

Therefore, C is the answer.
Answer: C

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.

[GMAT math practice question]

What is the angle between the hour hand and the minute hand at the time of 5 hours 44 minutes?

A. 89° B. 90° C. 91° D. 92° E. 93°

=>



The minute hand moves 6° every minute and <x = 44*6°=264°.
The hour hand moves 0.5° every minute and <y = 44*0.5°+150 = 172°.
Then the angle between the minute hand and the hour hand is 264°-172°=92°.

Therefore, D is the answer.
Answer: D

Can you expand more on what do you mean on the Integer and Equation question types.
For instance which tag do I use in the Gmatclub filter Question bank for these types of questions.
The rest are available only these are not.
Could you help me out??MathRevolution