Divisor
1 card- 01
How many positive divisors does 72 have?
- A
8
- B
10
- C
6
- D
12
- A
Parity (mathematics)
2 cards- 02
If $n$ is an odd integer, which of the following must be even?
- A
$n^2 + n$
- B
$n^2$
- C
$2n + 1$
- D
$n^2 + 1 + n$
- A
- 03
Data Sufficiency. Is the integer $n$ even?
(1) $n^2$ is even
(2) $n + 1$ is odd
- A
Statement (1) ALONE is sufficient, but statement (2) alone is not
- B
Statement (2) ALONE is sufficient, but statement (1) alone is not
- C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
- D
EACH statement ALONE is sufficient
- E
Statements (1) and (2) TOGETHER are NOT sufficient
- A
Trailing zero
1 card- 04
How many zeros are at the end of $25!$ (25 factorial)?
- A
10
- B
2
- C
5
- D
6
- A
Modular arithmetic
2 cards- 05
What is the remainder when $3^{100}$ is divided by 4?
- A
1
- B
3
- C
0
- D
2
- A
- 06
Data Sufficiency. What is the remainder when the positive integer $n$ is divided by 6?
(1) When $n$ is divided by 12, the remainder is 5
(2) When $n$ is divided by 3, the remainder is 2
- A
Statement (1) ALONE is sufficient, but statement (2) alone is not
- B
Statement (2) ALONE is sufficient, but statement (1) alone is not
- C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
- D
EACH statement ALONE is sufficient
- E
Statements (1) and (2) TOGETHER are NOT sufficient
- A
Divisibility rule
1 card- 07
If $n$ is a positive integer, the product $n(n+1)(n+2)$ must be divisible by which of the following?
- A
4
- B
6
- C
9
- D
8
- A
Digit sum
1 card- 08
The digits of a two-digit number add up to 9. Reversing the digits gives a number that is 27 greater. What is the original number?
- A
27
- B
36
- C
63
- D
45
- A
Percentage
2 cards- 09
A retailer marks a coat up by 25% over cost, then sells it at a 20% discount from the marked price. The selling price is what percent of the cost?
- A
80%
- B
95%
- C
105%
- D
100%
- A
- 10
Data Sufficiency. What percent of the students in a class are boys?
(1) There are 12 boys in the class
(2) The ratio of girls to boys in the class is 2 : 1
- A
Statement (1) ALONE is sufficient, but statement (2) alone is not
- B
Statement (2) ALONE is sufficient, but statement (1) alone is not
- C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
- D
EACH statement ALONE is sufficient
- E
Statements (1) and (2) TOGETHER are NOT sufficient
- A
Mixture
1 card- 11
20 litres of a 30% acid solution are mixed with 30 litres of a 50% acid solution. What is the concentration of the mixture?
- A
44%
- B
42%
- C
45%
- D
40%
- A
Rate (mathematics)
1 card- 12
Pipe A fills a tank in 3 hours. Pipe B drains the full tank in 6 hours. If both are open and the tank starts empty, how long does it take to fill?
- A
6 hours
- B
2 hours
- C
9 hours
- D
4 hours
- A
Speed
1 card- 13
Two trains are 300 km apart and travel toward each other on parallel tracks, one at 60 km/h and the other at 40 km/h. After how many hours do they meet?
- A
3
- B
5
- C
2.5
- D
7.5
- A
Ratio
1 card- 14
If $a : b = 2 : 3$ and $b : c = 4 : 5$, what is $a : b : c$?
- A
2 : 4 : 5
- B
6 : 12 : 20
- C
8 : 12 : 15
- D
2 : 3 : 5
- A
Inclusion–exclusion principle
1 card- 15
In a survey of 100 people, 60 drink tea, 50 drink coffee and 20 drink neither. How many drink both?
- A
40
- B
20
- C
10
- D
30
- A
Arithmetic mean
1 card- 16
The average of five numbers is 20. When one number is removed, the average of the remaining four is 18. What number was removed?
- A
28
- B
2
- C
20
- D
18
- A
Median
2 cards- 17
The set {3, 8, 5, 12, 9, 7} has how many values that are greater than its median?
- A
1
- B
3
- C
4
- D
2
- A
- 18
Data Sufficiency. What is the median of set $S$?
(1) The mean of $S$ is 10
(2) $S$ consists of 5 consecutive integers
- A
Statement (1) ALONE is sufficient, but statement (2) alone is not
- B
Statement (2) ALONE is sufficient, but statement (1) alone is not
- C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
- D
EACH statement ALONE is sufficient
- E
Statements (1) and (2) TOGETHER are NOT sufficient
- A
Exponentiation
1 card- 19
If $8^x = 2^{12}$, what is $x$?
- A
1.5
- B
3
- C
4
- D
6
- A
Square root
1 card- 20
Simplify $\sqrt{50} + \sqrt{18}$.
- A
$\sqrt{68}$
- B
$8\sqrt{2}$
- C
$34\sqrt{2}$
- D
$2\sqrt{17}$
- A
Absolute value
2 cards- 21
How many integers satisfy $|2x - 3| \le 5$?
- A
4
- B
10
- C
6
- D
5
- A
- 22
Data Sufficiency. Is $|x - 2| < 3$?
(1) $x > -1$
(2) $x < 5$
- A
Statement (1) ALONE is sufficient, but statement (2) alone is not
- B
Statement (2) ALONE is sufficient, but statement (1) alone is not
- C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
- D
EACH statement ALONE is sufficient
- E
Statements (1) and (2) TOGETHER are NOT sufficient
- A
Quadratic equation
2 cards- 23
If $x^2 - x - 12 = 0$ and $x > 0$, what is $x$?
- A
−3
- B
6
- C
4
- D
3
- A
- 24
Data Sufficiency. What is the value of $x$?
(1) $x^2 - 5x + 6 = 0$
(2) $x^2 - 4x + 4 = 0$
- A
Statement (1) ALONE is sufficient, but statement (2) alone is not
- B
Statement (2) ALONE is sufficient, but statement (1) alone is not
- C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
- D
EACH statement ALONE is sufficient
- E
Statements (1) and (2) TOGETHER are NOT sufficient
- A
Recurrence relation
1 card- 25
A sequence is defined by $a_1 = 1$ and $a_n = 2a_{n-1} + 1$ for $n \ge 2$. What is $a_4$?
- A
7
- B
31
- C
9
- D
15
- A
Inscribed figure
1 card- 26
A circle is inscribed in a square of side 4. What is the area of the square that lies outside the circle?
- A
$16 - 16\pi$
- B
$4 - \pi$
- C
$16 - 4\pi$
- D
$16 - 2\pi$
- A
Thales's theorem
1 card- 27
A triangle is inscribed in a circle so that one of its sides is a diameter of length 10. Another side has length 6. What is the triangle's area?
- A
15
- B
24
- C
48
- D
30
- A
Linear equation
2 cards- 28
A line passes through the points $(2, 3)$ and $(4, 7)$. What is its $y$-intercept?
- A
−2
- B
1
- C
−1
- D
2
- A
- 29
Data Sufficiency. What is the value of $x + y$?
(1) $2x + 2y = 10$
(2) $x - y = 3$
- A
Statement (1) ALONE is sufficient, but statement (2) alone is not
- B
Statement (2) ALONE is sufficient, but statement (1) alone is not
- C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
- D
EACH statement ALONE is sufficient
- E
Statements (1) and (2) TOGETHER are NOT sufficient
- A
Combination
1 card- 30
A committee of 2 is chosen from 5 men and 3 women. How many committees include at least one woman?
- A
28
- B
18
- C
15
- D
10
- A
Probability
1 card- 31
A bag holds 3 red and 2 blue marbles. Two are drawn without replacement. What is the probability that both are red?
- A
$\dfrac{9}{25}$
- B
$\dfrac{3}{10}$
- C
$\dfrac{1}{5}$
- D
$\dfrac{3}{5}$
- A
Compound interest
2 cards- 32
$10,000 is invested for one year at 8% per year. How much more is earned if the interest is compounded semiannually rather than annually?
- A
$0
- B
$800
- C
$16
- D
$400
- A
- 33
Data Sufficiency. What is the value of an investment after 2 years?
(1) $10,000 was invested at 5% per year, compounded annually
(2) The interest earned in the first year was $500
- A
Statement (1) ALONE is sufficient, but statement (2) alone is not
- B
Statement (2) ALONE is sufficient, but statement (1) alone is not
- C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
- D
EACH statement ALONE is sufficient
- E
Statements (1) and (2) TOGETHER are NOT sufficient
- A
Profit margin
1 card- 34
An item costs a store $80 and sells for $100. What is the profit as a percent of cost, and as a percent of the selling price?
- A
25% of cost; 25% of selling price
- B
25% of cost; 20% of selling price
- C
20% of cost; 25% of selling price
- D
20% of cost; 20% of selling price
- A
Sign (mathematics)
3 cards- 35
Data Sufficiency. Is $x > 0$?
(1) $x^2 > 0$
(2) $x^3 > 0$
- A
Statement (1) ALONE is sufficient, but statement (2) alone is not
- B
Statement (2) ALONE is sufficient, but statement (1) alone is not
- C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
- D
EACH statement ALONE is sufficient
- E
Statements (1) and (2) TOGETHER are NOT sufficient
- A
- 36
Data Sufficiency. Is $\dfrac{x}{y} > 0$?
(1) $xy > 0$
(2) $x + y > 0$
- A
Statement (1) ALONE is sufficient, but statement (2) alone is not
- B
Statement (2) ALONE is sufficient, but statement (1) alone is not
- C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
- D
EACH statement ALONE is sufficient
- E
Statements (1) and (2) TOGETHER are NOT sufficient
- A
- 37
Data Sufficiency. Is $abc > 0$?
(1) $ab > 0$
(2) $bc > 0$
- A
Statement (1) ALONE is sufficient, but statement (2) alone is not
- B
Statement (2) ALONE is sufficient, but statement (1) alone is not
- C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
- D
EACH statement ALONE is sufficient
- E
Statements (1) and (2) TOGETHER are NOT sufficient
- A
Equation solving
1 card- 38
Data Sufficiency. What is the value of $x$?
(1) $x^2 = 9$
(2) $x > 0$
- A
Statement (1) ALONE is sufficient, but statement (2) alone is not
- B
Statement (2) ALONE is sufficient, but statement (1) alone is not
- C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
- D
EACH statement ALONE is sufficient
- E
Statements (1) and (2) TOGETHER are NOT sufficient
- A
Prime number
1 card- 39
Data Sufficiency. Is the positive integer $n$ a prime number?
(1) $n$ is odd
(2) $n$ has exactly two positive factors
- A
Statement (1) ALONE is sufficient, but statement (2) alone is not
- B
Statement (2) ALONE is sufficient, but statement (1) alone is not
- C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
- D
EACH statement ALONE is sufficient
- E
Statements (1) and (2) TOGETHER are NOT sufficient
- A
Integer
1 card- 40
Data Sufficiency. Is $x$ an integer?
(1) $2x$ is an integer
(2) $\dfrac{x}{2}$ is an integer
- A
Statement (1) ALONE is sufficient, but statement (2) alone is not
- B
Statement (2) ALONE is sufficient, but statement (1) alone is not
- C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
- D
EACH statement ALONE is sufficient
- E
Statements (1) and (2) TOGETHER are NOT sufficient
- A
Inequality (mathematics)
2 cards- 41
Data Sufficiency. Is $x < y$?
(1) $x^2 < y^2$
(2) $x$ and $y$ are both positive
- A
Statement (1) ALONE is sufficient, but statement (2) alone is not
- B
Statement (2) ALONE is sufficient, but statement (1) alone is not
- C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
- D
EACH statement ALONE is sufficient
- E
Statements (1) and (2) TOGETHER are NOT sufficient
- A
- 42
Data Sufficiency. Is $x > 5$?
(1) $x > 3$
(2) $x < 8$
- A
Statement (1) ALONE is sufficient, but statement (2) alone is not
- B
Statement (2) ALONE is sufficient, but statement (1) alone is not
- C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
- D
EACH statement ALONE is sufficient
- E
Statements (1) and (2) TOGETHER are NOT sufficient
- A
Rectangle
1 card- 43
Data Sufficiency. What is the area of rectangle $R$?
(1) The perimeter of $R$ is 20
(2) The length of a diagonal of $R$ is $2\sqrt{13}$
- A
Statement (1) ALONE is sufficient, but statement (2) alone is not
- B
Statement (2) ALONE is sufficient, but statement (1) alone is not
- C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
- D
EACH statement ALONE is sufficient
- E
Statements (1) and (2) TOGETHER are NOT sufficient
- A
Least common multiple
1 card- 44
Data Sufficiency. Is the positive integer $a$ divisible by 12?
(1) $a$ is divisible by 4 and by 6
(2) $a$ is divisible by 3 and by 8
- A
Statement (1) ALONE is sufficient, but statement (2) alone is not
- B
Statement (2) ALONE is sufficient, but statement (1) alone is not
- C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
- D
EACH statement ALONE is sufficient
- E
Statements (1) and (2) TOGETHER are NOT sufficient
- A
Pythagorean theorem
1 card- 45
Data Sufficiency. Is triangle $ABC$ a right triangle?
(1) Angle $A$ plus angle $B$ equals 90°
(2) $AB^2 = AC^2 + BC^2$
- A
Statement (1) ALONE is sufficient, but statement (2) alone is not
- B
Statement (2) ALONE is sufficient, but statement (1) alone is not
- C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
- D
EACH statement ALONE is sufficient
- E
Statements (1) and (2) TOGETHER are NOT sufficient
- A
End of deck · 45 cards