GMAT Math Problems Exam with
Accurate Solutions
True/False: if x^3 > 0 , then x > 0 - ANSWER-True
3^(-2) - ANSWER-1/3^2 = 1/9
How many integers can be squared to get an integer less than 10? - ANSWER-6
integers
+/- 1, 2, 3
(2*sqrt(3))^3 - ANSWER-8*sqrt(3)^2*sqrt(3) = 24*sqrt(3)
cuberoot(64) - ANSWER-4
T/F: sqrt(10) > cuberoot(29) - ANSWER-Cube both sides, then square both sides. At
this point, it will be obvious that the left side is larger
sqrt(-¼) = x - ANSWER-You can't solve this because you can't square root a negative
sqrt(p x q) - ANSWER-sqrt(p) x sqrt(q)
simplify (x-y)/(y-x) - ANSWER--1
factor x^2 + 5x -24 - ANSWER-(x+8)(x-3)
If N is a multiple of p, what is the LCM of N and p? - ANSWER-N
T/F: If A > B, and if A & B are multiples of p, then A/B is a multiple of p - ANSWER-
False - (35, 21, with p being 7 is a counter example)
What is the smallest possible integer that is not a factor of 20!? - ANSWER-All of 20 x
19 x 18 etc. are factors by very definition
21 is a multiple of 7 and 3, so it doesn't count
Same with 22
23 is a prime number and is the answer
1/(2-.25) - ANSWER-1/(8/4 - ¼) = 1/(7/4) = 4/7
3 x ? = 11 - ANSWER-3 x 11/3 = 11
,Sqrt(p/q) - ANSWER-sqrt(p) / sqrt(q)
A circle has its center at the origin and passes through the point (7,2). What is its area?
- ANSWER-Draw it out!
Use pythagorean theorem to find the missing side (which is the r^2). 7^ + 2^2 = r^2
Use area formula pi*r^2.
53pi
Is 0 even, odd, or neither? - ANSWER-even
If x < y, and we do x/y, what is the quotient and the remainder? - ANSWER-Quotient is
0 and the remainder is x
A theater company has 10 scripts for fall, winter, and spring. How many possible
seasons are there? - ANSWER-10 * 9 * 8 = 720
University reading list consists of 1 play, 2 short stories, and one novel. There are 5 of
each option, so how many reading lists can be created? - ANSWER-5 x 5c2 x 5 = 5 x 10
x 5 = 250 reading lists
Esther is giving Christmas presents to her family members. Each family member gets
the same number of presents and no presents were leftover. If each family member
gets at least one present, did each family member receive more than one present?
(1) Esther has forty Christmas presents to give out.
(2) If the number of family members were doubled, it would not be possible for each
family member to get at least one present. - ANSWER-For statement 2, you can rewrite
it as:
number of presents/number of family members*2 < 1
Therefore number of presents/number of family members < 2
Each family member did not get at least one present (answer is NO), meaning
statement 2 is sufficient
A codebreaking device is made up of a rectangular box filled with x cylinders of ball
bearings placed together such that the diameter of the bearings and the cylinders are
equal, and the cylinders line up evenly, touching, with no extra room inside the device. If
the cylinders are the same height as the box, and the box is 18 inches long and 10
inches wide, what's the value of x?
, (1) 9 cylinders can line up along the length of the box.
(2) Each ball bearing has a radius of 1. - ANSWER-Each alone is sufficient
For statement 1, 18 length/9 = 2 diameter
For statement 2, radius 1 = 2 diameter
How many girls are members of both the Diving Team and the Swim Team?
(1) At a joint meeting of the Diving and Swim Teams, no members were absent and 18
girls were present.
(2) The Diving Team has 27 members, one-third of whom are girls, and the Swim Team
has 24 members, half of whom are girls. - ANSWER-From the first statement, 18 is the
total number of girls
From the second statement, 9 girls from the diving and 12 from the swim team makes
21 girls. 21-18 = 3, which are the number of girls from both teams
J and K are positive numbers. Is J/K > 1?
(1) JK < 1
(2) J-K > 0 - ANSWER-J*K < 1means that one of them is a fraction
1/1/2 >1 but 1/2/1 is not. Insufficient
J-K>0 must mean that J/K > 1. Statement 2 alone.
A designer purchased 20 mannequins that each cost an equal amount and then sold
each one at a constant price. What was the designer's gross profit on the sale of the 20
mannequins?
(1) If the selling price per mannequin had been double what it was, the gross profit on
the total would have been $2400.
(2) If the selling price per mannequin had been $2 more, the store's gross profit on the
total would have been $440. - ANSWER-Write out the equations:
Statement 1: (20(2s-c) = 2400. Insufficient data
Statement 2: 20(s+2-c) = 440
20s +40 -20c = 440
20(s-c) = 400. It's only asking us for the gross profit, which is s-c
A shopping center increased its revenues by 10% between 2010 and 2011. The
shopping center's costs increased by 8% during the same period. What is the firm's
Accurate Solutions
True/False: if x^3 > 0 , then x > 0 - ANSWER-True
3^(-2) - ANSWER-1/3^2 = 1/9
How many integers can be squared to get an integer less than 10? - ANSWER-6
integers
+/- 1, 2, 3
(2*sqrt(3))^3 - ANSWER-8*sqrt(3)^2*sqrt(3) = 24*sqrt(3)
cuberoot(64) - ANSWER-4
T/F: sqrt(10) > cuberoot(29) - ANSWER-Cube both sides, then square both sides. At
this point, it will be obvious that the left side is larger
sqrt(-¼) = x - ANSWER-You can't solve this because you can't square root a negative
sqrt(p x q) - ANSWER-sqrt(p) x sqrt(q)
simplify (x-y)/(y-x) - ANSWER--1
factor x^2 + 5x -24 - ANSWER-(x+8)(x-3)
If N is a multiple of p, what is the LCM of N and p? - ANSWER-N
T/F: If A > B, and if A & B are multiples of p, then A/B is a multiple of p - ANSWER-
False - (35, 21, with p being 7 is a counter example)
What is the smallest possible integer that is not a factor of 20!? - ANSWER-All of 20 x
19 x 18 etc. are factors by very definition
21 is a multiple of 7 and 3, so it doesn't count
Same with 22
23 is a prime number and is the answer
1/(2-.25) - ANSWER-1/(8/4 - ¼) = 1/(7/4) = 4/7
3 x ? = 11 - ANSWER-3 x 11/3 = 11
,Sqrt(p/q) - ANSWER-sqrt(p) / sqrt(q)
A circle has its center at the origin and passes through the point (7,2). What is its area?
- ANSWER-Draw it out!
Use pythagorean theorem to find the missing side (which is the r^2). 7^ + 2^2 = r^2
Use area formula pi*r^2.
53pi
Is 0 even, odd, or neither? - ANSWER-even
If x < y, and we do x/y, what is the quotient and the remainder? - ANSWER-Quotient is
0 and the remainder is x
A theater company has 10 scripts for fall, winter, and spring. How many possible
seasons are there? - ANSWER-10 * 9 * 8 = 720
University reading list consists of 1 play, 2 short stories, and one novel. There are 5 of
each option, so how many reading lists can be created? - ANSWER-5 x 5c2 x 5 = 5 x 10
x 5 = 250 reading lists
Esther is giving Christmas presents to her family members. Each family member gets
the same number of presents and no presents were leftover. If each family member
gets at least one present, did each family member receive more than one present?
(1) Esther has forty Christmas presents to give out.
(2) If the number of family members were doubled, it would not be possible for each
family member to get at least one present. - ANSWER-For statement 2, you can rewrite
it as:
number of presents/number of family members*2 < 1
Therefore number of presents/number of family members < 2
Each family member did not get at least one present (answer is NO), meaning
statement 2 is sufficient
A codebreaking device is made up of a rectangular box filled with x cylinders of ball
bearings placed together such that the diameter of the bearings and the cylinders are
equal, and the cylinders line up evenly, touching, with no extra room inside the device. If
the cylinders are the same height as the box, and the box is 18 inches long and 10
inches wide, what's the value of x?
, (1) 9 cylinders can line up along the length of the box.
(2) Each ball bearing has a radius of 1. - ANSWER-Each alone is sufficient
For statement 1, 18 length/9 = 2 diameter
For statement 2, radius 1 = 2 diameter
How many girls are members of both the Diving Team and the Swim Team?
(1) At a joint meeting of the Diving and Swim Teams, no members were absent and 18
girls were present.
(2) The Diving Team has 27 members, one-third of whom are girls, and the Swim Team
has 24 members, half of whom are girls. - ANSWER-From the first statement, 18 is the
total number of girls
From the second statement, 9 girls from the diving and 12 from the swim team makes
21 girls. 21-18 = 3, which are the number of girls from both teams
J and K are positive numbers. Is J/K > 1?
(1) JK < 1
(2) J-K > 0 - ANSWER-J*K < 1means that one of them is a fraction
1/1/2 >1 but 1/2/1 is not. Insufficient
J-K>0 must mean that J/K > 1. Statement 2 alone.
A designer purchased 20 mannequins that each cost an equal amount and then sold
each one at a constant price. What was the designer's gross profit on the sale of the 20
mannequins?
(1) If the selling price per mannequin had been double what it was, the gross profit on
the total would have been $2400.
(2) If the selling price per mannequin had been $2 more, the store's gross profit on the
total would have been $440. - ANSWER-Write out the equations:
Statement 1: (20(2s-c) = 2400. Insufficient data
Statement 2: 20(s+2-c) = 440
20s +40 -20c = 440
20(s-c) = 400. It's only asking us for the gross profit, which is s-c
A shopping center increased its revenues by 10% between 2010 and 2011. The
shopping center's costs increased by 8% during the same period. What is the firm's
