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

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? 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. 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