Overview of GMAT Math Question Types and Patterns on the GMAT

When x is divided by 7, the remainder is 3. When x3 is divided by 7, what is the remainder?

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

==> For remainder questions, it is important to use direct substitutions. From X=7p+3=3,10,17,…., if you substitute x=3, from x^3=3^3=27=7(3)+6, you get a remainder of 6.

Therefore, the answer is E.
Answer: E

st 2. x+2y is an integer- y can be 0.5, 2.5, 1 or 2 etc so st 2 is not sufficient

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What is the units digit of a positive integer n?

1) The units digit of n^2 is 4
2) The units digit of n^3 is 8

==> In the original condition, there is 1 variable (n) and in order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For con 1), you get n=~2, ~8, hence it is not unique and not sufficient. For con 2), you only get n=~2, hence it is unique and sufficient.

Therefore, the answer is B.
Answer: B

If m and n are non-negative integers, mn=?

1) 9^n=3^m
2) 2^n=5^m

==> In the original condition, there are 2 variables (m,n) and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), from con 1), you get 9^n=(3^2)^n=3^{2n}=3^m, which becomes 2n=m. In order for con 2) to satisfy as well, you only get m=n=0, hence it is unique and sufficient. The answer is C. However, this is an integer question, one of the key questions, so you apply CMT 4 (A: if you get C too easily, consider A or B). For con 1), the way to satisfy 9^n=(3^2)^n=3^{2n}=3^m to 2n=m is not unique and not sufficient. For con 2), from 2^n=5^m, you get 2^n=even and 5^m=odd, so even≠odd. Only m=n=0 satisfies this, hence it is unique and sufficient.

Therefore, the answer is B, not C.
Answer: B

If you are flipping the coin 4 times, what is the probability of landing on head two times?

A. 3/5
B. 4/5
C. 3/7
D. 4/7
E. 3/8

==> Probability=Want/Total. Total=since the number of ways when throwing the coins each becomes head or tail 2 times, you get 2*2*2*2=16. Want=if it lands on head 2 times, it lands on tail 2 times, so you get 4!/2!2!=6. Thus, the probability=6/16=3/8.

The answer is E.
Answer: E

Is \(x>(-3)^\frac{1}{3}\)?

1) \(x>(-2)^\frac{1}{3}\)
2) \(x>(-4)^\frac{1}{3}\)

The percent of employees participated in A program is 80% of the total employees. What is the total number of employees in the company?

1) 168 employees participated in this program.
2) 42 employees did not participate in this program.

==> If you modify the original condition and the question and set the number of people who participated in the program as a and number of people who did not participate in the program as b, from a=80%(a+b), there are 2 variables and 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer.
For con 1), from 168=80%(a+b) and a+b=168/80%=210, it is unique and sufficient.
For con 2), from 42=20%(a+b) and a+b=42/20%=210, it is unique and sufficient.

Therefore, the answer is D.
Answer: D

What is the value of (-2)^2+(1/3)^{-3}+(-4)^3?

A. -27 B. -29 C. -33 D. 33 E. 29

==> From (-2)^2+(1/3)^{-3}+(-4)^3=4+(3^{-1})^{-3}+(-4)^3=4+33-64=4+27-64=-33, the answer is C.

Answer: C

If the average (arithmetic mean) of 7 numbers is 21, what is the standard deviation of the numbers?

1) The smallest number of them is 21
2) The greatest number of them is 21

=>Condition 1)
Since the minimum number and the average are same, all numbers should be 21.

Condition 2)
Since the maximum number and the average are same, all numbers should be 21.

Ans: D

Is Circular question type and Race type frequently tested in GMAT?

An alarm of a certain clock rings every 20 minutes. If the clock's alarm first rings at 15:20, when will the 12th alarm of the clock ring?

A. 17:30 B. 18:00 C. 18:30 D. 19:00 E. 19:30

=>The third alarm rings at 16:00, the sixth alarm rings at 17:00. Thus every third alarm rings every hour on the hour. The 12th alarm rings at 19:00.

Ans: D

If xy≠0, is |x|>|y|？

1) x=-2y
2) x=y^4

=>
Condition 1)

|x| = |-2y| = 2|y| > |y|.
Thus this is sufficient.

Condition 2)

If y = 2, then x = 16 and so |x| > |y|.
If y = ½, then x = 1/16 and so |x| < |y|.
This is not sufficient.

Ans: A

What is the value of a positive integer k?

1) When k is divided by 5, the remainder is 3.
2) When k is divided by 3, the remainder is 2.


=> Condition 1) & 2)
k = 8, 23, …
Both conditions together are not sufficient either.

Ans: E

If x, y, and z are positive integers, is x+y divisible by 5?

1) x+z is divisible by 5
2) y+z is divisible by 5

=>Consider 1) & 2)

x = 1, y = 1, z = 4 : x + y is not divisible by 5
x = 5, y = 5, z = 0 : x + y is divisible by 5

Ans: E

What is the median of 12, y, and x?

1) x+y=24
2) y=6

=>Condition 1)
If x = y = 12, then the median of them is 12.
If x < y, then the median of them 12, since x < 12 < y.
If x > y, then the median of them 12, since y < 12 < x.
This is sufficient.

Condition 2)
Since we don’t know x, we don’t identify their median.
This is not sufficient.

Ans: A

If x-7=√x+√7, x=?

A. 8+2√7
B. 8-2√7
C. 8+√7
D. 8-√7
E. 7+2√6

=>x-7=√x+√7
(√x+√7)(√x-√7)=√x+√7
√x-√7 = 1
√x = √7 + 1
x = (√7 + 1)^2
x = 7 + 2√7 + 1 = 8 + 2√7

Ans: A

If |x+3|=|y+3|, what is the value of x+y?

1) xy<0
2) x>3 and y<3

=> 1) xy < 0
We can assume x > 0 and y < 0 without loss of generality.
Then we have x + 3 = -y - 3
x + y = -6
This is sufficient.

2) x > 3 and y < 3
Then we have x + 3 = -y - 3
x + y = -6
This is sufficient.

Ans: D