# Quantitative Section: Data Sufficiency

## Quantitative Section: Data Sufficiency

Directions: Each of the following GMAT sample data sufficiency problems contains a question followed by two statements, numbered (A) and (B). You need not solve the GMAT sample data sufficiency problem; rather you must decide whether the information given is sufficient to solve the problem.

The correct answer to a question is

1. if statement (A) ALONE is sufficient to answer the question but statement (B) alone is not sufficient;
2. if statement (B) ALONE is sufficient to answer the question but statement (1) alone is not sufficient;
3. if the two statements TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient;
4. if EACH statement ALONE is sufficient to answer the question;
5. if the two statements TAKEN TOGETHER are still NOT sufficient to answer the question.

Q.1)  Quantity A: (-6)4
Quantity B: (-6)5

1. if the quantity A is greater;
2. if the quantity B is greater;
3. if the two quantities are equal;
4. if the relationship cannot be determined from the information given.

Q.2)  Quantity A: Time to travel 95 miles at 50 miles per hour
Quantity B: Time to travel 125 miles at 60 miles per hour

1. Quantity A is greater
2. Quantity A equals Quantity B
3. Quantity B is greater
4. Relationship Indeterminate

Q.3)  Quantity A: (9/13)2
Quantity B: (9/13)1/2

1. Quantity A equals Quantity B
2. Relationship Indeterminate
3. Quantity B is greater
4. Quantity A is greater

Q.4)  Quantity A: 4 / 100
Quantity B: 0.012 / 3

1. Quantity B is greater
2. Quantity A equals Quantity B
3. Quantity A is greater
4. Relationship Indeterminate

Q.5)  x = 2y + 3
y = -2

Quantity A: x
Quantity B: -1

1. if the quantity in Column A is greater
2. if the quantity in Column B is greater
3. if the two quantities are equal
4. if the relationship cannot be determined from the information given

Q.6)  x + 2y > 8

Quantity A: 2x + 4y
Quantity B: 20

1. if the quantity in Column A is greater
2. if the quantity in Column B is greater
3. if the two quantities are equal
4. if the relationship cannot be determined from the information given.

Q.7)  Quantity A: The number of months in 7 years
Quantity B: The number of days in 12 weeks

1. if the quantity in Column A is greater
2. if the quantity in Column B is greater
3. if the two quantities are equal
4. if the relationship cannot be determined from the information given

Q.8)  Quantity A: 1-1/27
Quantity B: 8/9 + 1/81

1. if the quantity in is greater
2. if the quantity in is greater
3. if the two quantities are equal
4. if the relationship cannot be determined from the information given.

Q.9) r/>s/>0/>

Quantity A: rs/r
Quantity B: rs/s

1. if the quantity A is greater
2. if the quantity B is greater
3. if the two quantities are equal
4. if the relationship cannot be determined from the information given.

Q.10)  Quantity A: 0.83
Quantity B: 0.81/3

1. Quantity B is greater
2. Relationship Indeterminate
3. Quantity A is greater
4. Quantity A equals Quantity B

Q.11)  t is a positive integer.  4/7 = t/s

Quantity A: s
Quantity B:7

1. if the quantity in Column A is greater;
2. if the quantity in Column B is greater;
3. if the two quantities are equal;
4. if the relationship cannot be determined from the information given

Q.12)  Quantity A: (0.82)2(0.82)3
Quantity B:(0.82)6

1. if the quantity in Column A is greater;
2. if the quantity in Column B is greater;
3. if the two quantities are equal;
4. if the relationship cannot be determined from the information given.

Q.13)  For all real numbers a, let a* = 1 – a.

Quantity A: ((-1)*)*
Quantity B: 2*

1. if the quantity in Column A is greater;
2. if the quantity in Column B is greater;
3. if the two quantities are equal;
4. if the relationship cannot be determined from the information given.

Q.14)  Quantity A: (x – 1)(x)(x + 1)
Quantity B:(x)(x)(x)

1. if the quantity in Column A is greater;
2. if the quantity in Column B is greater;
3. if the two quantities are equal;
4. if the relationship cannot be determined from the information given.

Q.15)  Quantity A: (3 x 4 x 17) / (121 x 100)
Quantity B: (4 x 5 x 19) / (1000 x 121)

1. Quantity A is greater
2. Quantity A equals Quantity B
3. Relationship Indeterminate
4. Quantity B is greater

Q.16)  Consider a triangle PQR.

Quantity A: length of PQ + length of QR
Quantity B: length of PR

1. Quantity A is greater
2. Quantity B is greater
3. Relationship Indeterminate
4. Quantity A equals Quantity B

Q.17)  Quantity A: (27 – 13) (296 + 534)
Quantity B: (27 + 13) (534 + 296)

1. Quantity B is greater
2. Quantity A equals Quantity B
3. Relationship Indeterminate
4. Quantity A is greater

Q.18)  Quantity A: A = 1.1
Quantity B: 12.11/2

1. Relationship Indeterminate
2. Quantity B is greater
3. Quantity A equals Quantity B
4. Quantity A is greater

Q.19)  100 < y < 200 and 100 < z < 210

Quantity A: y
Quantity B: z

1. Quantity A is greater
2. Quantity A equals Quantity B
3. Quantity B is greater
4. Relationship Indeterminate

Q.20)  y2 + z2 = 34 and yz = 15

Quantity A: y2 + 2yz + z2
Quantity B: (y + z)2

1. Quantity B is greater
2. Relationship Indeterminate
3. Quantity A is greater
4. Quantity A equals Quantity B

Q.21)  Consider a rectangle. The length of its shorter side is 8, and the length of its diagonal is 16.

Quantity A: 30o
Quantity B: measure of angle formed by diagonal and shorter side

1. Relationship Indeterminate
2. Quantity A equals Quantity B
3. Quantity A is greater
4. Quantity B is greater

Q.22)  Quantity A: (y + 5)2
Quantity B: (y – 5)2

1. Quantity B is greater
2. Relationship Indeterminate
3. Quantity A equals Quantity B
4. Quantity A is greater

Q.23)  Quantity A: (1/25)1/2 + (1/144)1/2
Quantity B: [(1/25) + (1/144)]1/2

1. Relationship Indeterminate
2. Quantity A is greater
3. Quantity B is greater
4. Quantity A equals Quantity B

Q.24)  y2 + z2 = 34 and yz = 15

Quantity A: y2 + 2yz + z2
Quantity B: (y + z)2

1. Quantity A is greater
2. Relationship Indeterminate
3. Quantity A equals Quantity B
4. Quantity B is greater

Q.25)  100 < y < 200 and 100 < z < 210

Quantity A: y
Quantity B: z

1. Quantity A is greater
2. Quantity A equals Quantity B
3. Quantity B is greater
4. Relationship Indeterminate

Q.26)  Quantity A: (y + 5)2
Quantity B: (y – 5)2

1. Quantity A equals Quantity B
2. Quantity A is greater
3. Relationship Indeterminate
4. Quantity B is greater

Q.27)  Consider a rectangle. The length of its shorter side is 8, and the length of its diagonal is 16.

Quantity A: 30o
Quantity B: measure of angle formed by diagonal and shorter side

1. Quantity A is greater
2. Quantity A equals Quantity B
3. Quantity B is greater
4. Relationship Indeterminate

Q.28)  The sum of three consecutive even numbers is 18.

Quantity A: Their average
Quantity B: 6

1. Relationship Indeterminate
2. Quantity A is greater
3. Quantity A equals Quantity B
4. Quantity B is greater

Q.29)  x – y > 10

Quantity A: y – x
Quantity B: 12

1. Quantity B is greater
2. Quantity A is greater
3. Quantity A equals Quantity B
4. Relationship Indeterminate

Q.30)  x = 0, y > 0

Quantity A: xy
Quantity B: yx

1. Quantity A equals Quantity B
2. Quantity A is greater
3. Quantity B is greater
4. Relationship Indeterminate

Q.31)

Diagram is illustrative and is not drawn to scale.

Quantity A: Measure of angle 3 – Measure of angle 2
Quantity B: Measure of angle 5 – Measure of angle 6

1. Relationship Indeterminate
2. Quantity A equals Quantity B
3. Quantity B is greater
4. Quantity A is greater

Q.32) Quantity A: 29

Quantity B: 92

1. Quantity B is greater
2. Quantity A is greater
3. Relationship Indeterminate
4. Quantity A equals Quantity B

Q.33)   0 < -x < 10

11 < -y < 20

Quantity A: x
Quantity B: y

1. Relationship Indeterminate
2. Quantity A equals Quantity B
3. Quantity B is greater
4. Quantity A is greater

Q.34)

Diagram is illustrative and is not drawn to scale.
Given angles 1 and 2 are equal,
length of side AB = x, length of side BC = y, length of side AC = z.

Quantity A: x + y
Quantity B: y + z

1. Quantity A is greater
2. Quantity A equals Quantity B
3. Quantity B is greater
4. Relationship Indeterminate

Q.35)

Diagram is illustrative and is not drawn to scale.
In triangle ABC, AB = AC and measure of angle 1 = 100o.

Quantity A: Measure of angle 2 + Measure of angle 3
Quantity B: 90o

1. Quantity B is greater
2. Relationship Indeterminate
3. Quantity A is greater
4. Quantity A equals Quantity B

Q.36)  x and y are both positive and x/y > 5

Quantity A: 0.2x
Quantity B: y

1. Quantity A is greater
2. Quantity B is greater
3. Relationship Indeterminate
4. Quantity A equals Quantity B

Q.37)

Diagram is illustrative and is not drawn to scale.
Given AB = AC and angle BAC = 60o

Quantity A: Length of side AB
Quantity B: Length of side BC

1. Quantity A equals Quantity B
2. Quantity B is greater
3. Relationship Indeterminate
4. Quantity A is greater

Q.38)  y2 = 36

Quantity A: y
Quantity B: 6

1. Relationship Indeterminate
2. Quantity A is greater
3. Quantity B is greater
4. Quantity A equals Quantity B

Q.39)

Diagram is illustrative and is not drawn to scale.

Quantity A: Measure of angle 1 + Measure of angle 2 + Measure of angle 4
Quantity B: 180o

1. Relationship Indeterminate
2. Quantity A is greater
3. Quantity B is greater
4. Quantity A equals Quantity B

Q.40)

Diagram is illustrative and is not drawn to scale.
In triangle ABC, angle A = 60o and AB = AC.

Quantity A: Measure of angle 1 + Measure of angle 2
Quantity B: 120o

1. Relationship Indeterminate
2. Quantity A is greater
3. Quantity A equals Quantity B
4. Quantity B is greater

Q.41)

Diagram is illustrative and is not drawn to scale.

Quantity A: Measure of angle 2 + Measure of angle 3
Quantity B: 180o

1. Quantity B is greater
2. Quantity A is greater
3. Quantity A equals Quantity B
4. Relationship Indeterminate

Q.42)

Diagram is illustrative and is not drawn to scale.
AB is the diameter of the circle.

Quantity A: Measure of angle 1
Quantity B: Measure of angle 2

1. Relationship Indeterminate
2. Quantity A is greater
3. Quantity B is greater
4. Quantity A equals Quantity B

Q.43)

Diagram is illustrative and is not drawn to scale.

Quantity A: Measure of angle 1 + Measure of angle 3
Quantity B: Measure of angle 2 + Measure of angle 4

1. Relationship Indeterminate
2. Quantity A is greater
3. Quantity A equals Quantity B
4. Quantity B is greater

Q.44)

Diagram is illustrative and is not drawn to scale.
In triangle ABC, AB = AC and measure of angle 1 = 100o.

Quantity A: Measure of angle 2 + Measure of angle 3
Quantity B: 90o

1. Quantity B is greater
2. Quantity A equals Quantity B
3. Relationship Indeterminate
4. Quantity A is greater

Q.45)

Diagram is illustrative and is not drawn to scale.
Given angles 1 and 2 are equal,
length of side AB = x, length of side BC = y, length of side AC = z.

Quantity A: x + y
Quantity B: y + z

1. Quantity B is greater
2. Quantity A equals Quantity B
3. Quantity A is greater
4. Relationship Indeterminate

Q.46)  x and y are both positive and x/y > 5

Quantity A: 0.2x
Quantity B: y

1. Quantity B is greater
2. Relationship Indeterminate
3. Quantity A equals Quantity B
4. Quantity A is greater

Q.47)  yz < 0

Quantity A: (y – z)2
Quantity B: y2 + z2

1. Quantity A is greater
2. Quantity B is greater
3. Quantity A equals Quantity B
4. Relationship Indeterminate

Q.48)  For any positive integer n,
n! is the product of all positive integers less than or equal to n.

Quantity A: 20! / 17!
Quantity B: 80! / 78!

1. Quantity A is greater
2. Quantity B is greater
3. Quantity A equals Quantity B
4. Relationship Indeterminate

Q.49)  2 < z < 4

Quantity A: π2z3
Quantity B: π3z2

1. Quantity A is greater
2. Quantity B is greater
3. Quantity A equals Quantity B
4. Relationship Indeterminate

Q.50)  Amy, Beth and Charlie divided a pizza amongst themselves.
Amy took 30% of the pizza and ate (3/4) of what she took.
Beth took 20% of the pizza.
Charlie ate (2/5) of what he took.

Quantity A: The amount Amy ate
Quantity B: The amount Charlie ate

1. Quantity A is greater
2. Quantity B is greater
3. Quantity A equals Quantity B
4. Relationship Indeterminate

Q.51)  p > 0 > q

Quantity A: p + q
Quantity B: pq

1. The quantity in Column A is greater.
2. The quantity in Column B is greater.
3. The quantities are equal.
4. The relationship cannot be determined from the information given.

Q.52)  Quantity A: The average (arithmetic mean) of x and y
Quantity B: The average (arithmetic mean) of x – 1 and y + 1

1. The quantity in Column A is greater.
2. The quantity in Column B is greater.
3. The quantities are equal.
4. The relationship cannot be determined from the information given.

Q.53)  The integer (x – 1) is a prime number between 40 and 50.

Quantity A: The sum of all different prime factors of x
Quantity B: 14

1. The quantity in Column A is greater.
2. The quantity in Column B is greater.
3. The quantities are equal.
4. The relationship cannot be determined from the information given.

Q.54)  A < C
B > D > 0

Quantity A: A – B
Quantity B: C – D

1. The quantity in Column A is greater.
2. The quantity in Column B is greater.
3. The quantities are equal.
4. The relationship cannot be determined from the information given.

Q.55)  In a particular jellybean jar, the number of red jellybeans exceeds the number of white ones by a ratio of 3:2. If two red jellybeans were removed, the ratio of red to white jellybeans would be 1:1.

Quantity A: The number of white jellybeans in the jar
Quantity B: 4

1. The quantity in Column A is greater.
2. The quantity in Column B is greater.
3. The quantities are equal.
4. The relationship cannot be determined from the information given.

Q.56)  Is x equal to 0?

Quantity A: (x + 1)2 = 12
Quantity B: x2 + 3x = 0

1. Quantity A on its own is sufficient to answer the question but Quantity B on its own is not.
2. Quantity B on its own is sufficient to answer the question but Quantity A on its own is not.
3. Both statements together are sufficient to answer the question but neither statement is sufficient on its own.
4. Either statement on its own is sufficient to answer the question
5. Both statements put together are still insufficient to answer the question

Q.57)  Is p a positive number?

Quantity A: p3 > 0
Quantity B: 10p > 1

1. Quantity A on its own is sufficient to answer the question but Quantity B on its own is not.
2. Quantity B on its own is sufficient to answer the question but Quantity A on its own is not.
3. Both statements together are sufficient to answer the question but neither statement is sufficient on its own.
4. Either statement on its own is sufficient to answer the question
5. Both statements put together are still insufficient to answer the question

Q.58)  Lioudmila took a test where there were two types of questions, type I and type II. 2 points were awarded for getting a type I question correct. 5 points were awarded for getting a type II question correct, and there is no penalty for getting questions wrong. How many type I questions did she answer correctly?

Quantity A: She answered 11 questions correctly.
Quantity B: She was awarded 43 points.

1. Quantity A on its own is sufficient to answer the question but Quantity B on its own is not.
2. Quantity B on its own is sufficient to answer the question but Quantity A on its own is not.
3. Both statements together are sufficient to answer the question but neither statement is sufficient on its own.
4. Either statement on its own is sufficient to answer the question
5. Both statements put together are still insufficient to answer the question

Q.59)  a and b are integers. What are the values of a and b?

Quantity A: 2a.3b = 144
Quantity B: 2a+1.3b-1 = 96

1. Quantity A on its own is sufficient to answer the question but Quantity B on its own is not.
2. Quantity B on its own is sufficient to answer the question but Quantity A on its own is not.
3. Both statements together are sufficient to answer the question but neither statement is sufficient on its own.
4. Either statement on its own is sufficient to answer the question
5. Both statements put together are still insufficient to answer the question

Q.60)  Is x bigger than 5?

Quantity A: 2x + 9 < 4y + 1
Quantity B: 8y + 2 < 5x + 7

1. Quantity A on its own is sufficient to answer the question but Quantity B on its own is not.
2. Quantity B on its own is sufficient to answer the question but Quantity A on its own is not.
3. Both statements together are sufficient to answer the question but neither statement is sufficient on its own.
4. Either statement on its own is sufficient to answer the question
5. Both statements put together are still insufficient to answer the question