Data Sufficiency MCQs: Determining if given information is sufficient to answer a question

Is 𝑥+𝑦>10x+y>10?

Statement 1: 𝑥>5x>5
Statement 2: 𝑦>4y>4
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: C

What is the value of 𝑥+𝑦x+y?

Statement 1: 𝑥=5x=5
Statement 2: 𝑦=3y=3
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: C

Is 𝑎>𝑏a>b?

Statement 1: 𝑎+𝑏>10a+b>10
Statement 2: 𝑎−𝑏>2a−b>2
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: E

Is 𝑥x an even number?

Statement 1: 𝑥2×2 is even.
Statement 2: 𝑥−2x−2 is even.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: D

What is the value of 𝑎a?

Statement 1: 𝑎+𝑏=10a+b=10
Statement 2: 𝑏=4b=4
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: A

Is 𝑦y an integer?

Statement 1: 2𝑦+12y+1 is odd.
Statement 2: 𝑦2y2 is an integer.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: E

What is the value of 𝑥x?

Statement 1: 𝑥2=9×2=9
Statement 2: 𝑥>0x>0
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: A

Is 𝑝>𝑞p>q?

Statement 1: 𝑝2>𝑞2p2>q2
Statement 2: 𝑝+𝑞>0p+q>0
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: E

Is 𝑛n a prime number?

Statement 1: 𝑛n is odd.
Statement 2: 𝑛2n2 is not prime.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: B

Is 𝑥x positive?

Statement 1: 𝑥3×3 is positive.
Statement 2: 𝑥2×2 is negative.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: E

Is 𝑚m a multiple of 4?

Statement 1: 𝑚m is even.
Statement 2: 𝑚−2m−2 is a multiple of 4.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: D

What is the value of 𝑥x?

Statement 1: 𝑥−𝑦=5x−y=5
Statement 2: 𝑥+𝑦=11x+y=11
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: C

Is 𝑝p an integer?

Statement 1: 𝑝2−4𝑝+4=0p2−4p+4=0
Statement 2: 𝑝p is not equal to 1221
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: A

Is 𝑥x a positive integer?

Statement 1: 𝑥+2x+2 is even.
Statement 2: 𝑥−3x−3 is odd.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
**Answer: E

Is 𝑎a an even number?

Statement 1: 𝑎+4a+4 is even.
Statement 2: 𝑎×𝑏a×b is even.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: D

Is 𝑥x a prime number?

Statement 1: 𝑥x is odd.
Statement 2: 𝑥+2x+2 is prime.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: E

Is 𝑛n a positive integer?

Statement 1: 𝑛2−1=0n2−1=0
Statement 2: 𝑛−2n−2 is positive.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: C

Is 𝑥x a multiple of 3?

Statement 1: 𝑥2−1×2−1 is divisible by 3.
Statement 2: 𝑥+2x+2 is divisible by 3.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: E

What is the value of 𝑎+𝑏a+b?

Statement 1: 𝑎−𝑏=5a−b=5
Statement 2: 𝑎×𝑏=12a×b=12
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: C

Is 𝑦y an integer?

Statement 1: 𝑦2=25y2=25
Statement 2: 𝑦y is not equal to −5−5
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: A

Is 𝑥x a positive integer?

Statement 1: 𝑥2+1=10×2+1=10
Statement 2: 𝑥−2x−2 is negative.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: E

Is 𝑛n a perfect square?

Statement 1: 𝑛2+4𝑛+4=0n2+4n+4=0
Statement 2: 𝑛+2n+2 is a perfect square.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: C

Is 𝑥x greater than 4?

Statement 1: 𝑥2−5𝑥+4=0x2−5x+4=0
Statement 2: 𝑥−2x−2 is positive.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: B

Is 𝑝p a prime number?

Statement 1: 𝑝p is odd.
Statement 2: 𝑝−1p−1 is not divisible by 3.
A. Statement 1 alone is sufficient.
B. Statement

Is 𝑥x an even number?

Statement 1: 𝑥+4x+4 is even.
Statement 2: 𝑥×2x×2 is even.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: E

Is 𝑛n a prime number?

Statement 1: 𝑛n is odd.
Statement 2: 𝑛+2n+2 is prime.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: E

Is 𝑥x a positive integer?

Statement 1: 𝑥2−1=0x2−1=0
Statement 2: 𝑥−2x−2 is positive.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: B

Is 𝑥x a multiple of 3?

What is the value of 𝑎+𝑏a+b?

Is 𝑦y an integer?

Is 𝑥x a positive integer?

Is 𝑛n a perfect square?

Is 𝑥x greater than 4?

Is 𝑝p a prime number?

Statement 1: 𝑝p is odd.
Statement 2: 𝑝−1p−1 is not divisible by 3.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: A

Is 𝑞q an integer?

Statement 1: 𝑞2=16q2=16
Statement 2: 𝑞+2q+2 is an even number.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: A

Is 𝑟r a multiple of 5?

Statement 1: 𝑟+3r+3 is divisible by 5.
Statement 2: 𝑟−2r−2 is not divisible by 5.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: E

What is the value of 𝑠s?

Statement 1: 𝑠2+4𝑠+4=0s2+4s+4=0
Statement 2: 𝑠=−2s=−2
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: B

Is 𝑡t a perfect square?

Statement 1: 𝑡2−16=0t2−16=0
Statement 2: 𝑡=−4t=−4
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: A

Is 𝑢u divisible by 6?

Statement 1: 𝑢=12u=12
Statement 2: 𝑢+6u+6 is divisible by 3.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: C

What is the value of 𝑣v?

Statement 1: 𝑣2=49v2=49
Statement 2: 𝑣+3v+3 is an even number.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: C

Is 𝑤w a prime number?

Statement 1: 𝑤w is odd.
Statement 2: 𝑤+1w+1 is not divisible by 3.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: C

Is 𝑥x greater than 2?

Statement 1: 𝑥−3x−3 is positive.
Statement 2: 𝑥2−5𝑥+6=0x2−5x+6=0
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: A

Is 𝑦y an even number?

Statement 1: 𝑦2y2 is even.
Statement 2: 𝑦+3y+3 is even.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: B

Is 𝑧z a positive integer?

Statement 1: 𝑧2+1=10z2+1=10
Statement 2: 𝑧−2z−2 is negative.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: E

Is 𝑎a divisible by 4?

Statement 1: 𝑎=16a=16
Statement 2: 𝑎+2a+2 is divisible by 4.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: E

What is the value of 𝑏b?

Statement 1: 𝑏−3b−3 is positive.
Statement 2: 𝑏2=25b2=25
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: C

Is 𝑑d an even number?

Statement 1: 𝑑+4d+4 is even.
Statement 2: 𝑑÷2d÷2 is an integer.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: C

Is 𝑒e a prime number?

Statement 1: 𝑒e is odd.
Statement 2: 𝑒+2e+2 is prime.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: E

Is 𝑓f a multiple of 6?

Statement 1: 𝑓f is an even number.
Statement 2: 𝑓−2f−2 is divisible by 3.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: E

What is the value of 𝑔g?

Statement 1: 𝑔2=64g2=64
Statement 2: 𝑔g is positive.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: A

Is ℎh a perfect square?

Statement 1: ℎ2−9ℎ+18=0h2−9h+18=0
Statement 2: ℎ−3h−3 is an integer.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: B

Is 𝑖i divisible by 5?

Statement 1: 𝑖=25i=25
Statement 2: 𝑖+1i+1 is divisible by 5.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: C

What is the value of 𝑗j?

Statement 1: 𝑗2=49j2=49
Statement 2: 𝑗+3j+3 is an even number.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: B

Is 𝑘k a prime number?

Statement 1: 𝑘k is odd.
Statement 2: 𝑘+1k+1 is not divisible by 3.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: A

Is 𝑙l greater than 3?

Statement 1: 𝑙+1l+1 is positive.
Statement 2: 𝑙2−4𝑙+3=0l2−4l+3=0
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: C

Is 𝑚m an even number?

Statement 1: 𝑚2m2 is even.
Statement 2: 𝑚m is divisible by 2.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: C

What is the value of 𝑛n?

Statement 1: 𝑛2+16=25n2+16=25
Statement 2: 𝑛−2n−2 is an integer.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: C

Is 𝑝p divisible by 7?

Statement 1: 𝑝+3p+3 is divisible by 7.
Statement 2: 𝑝−2p−2 is not divisible by 7.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone is not sufficient.
E. Statements 1 and 2 together are not sufficient.
Answer: C

What is the value of 𝑞q?

Statement 1: 𝑞2+9=25q2+9=25
Statement 2: 𝑞−2q−2 is an integer.
A. Statement 1 alone is sufficient.
B. Statement 2 alone is sufficient.
C. Both statements together are sufficient.
D. Each statement alone