Practice Questions
Concept Explanation
Data Sufficiency (DS) questions ask whether given statements are enough to answer uniquely—not merely to compute a value.
Standard Answer Choices
- A — Statement I alone is sufficient; Statement II alone is not.
- B — Statement II alone is sufficient; Statement I alone is not.
- C — Both statements together are sufficient, but neither alone is.
- D — Each statement alone is sufficient.
- E — Even both statements together are not sufficient.
Number-Based DS Focus
Problems involve divisibility, HCF/LCM, remainders, primes, and digit properties. A statement is sufficient only if it pins down one unique answer.
DS Decision Flow
- Fix the exact question (value, yes/no, comparison).
- Test Statement I alone.
- Test Statement II alone.
- If needed, combine both statements.
Common Traps in Number Problems
- Assuming positivity without the stem requiring it.
- Confusing “divisible by” with “leaves remainder.”
- Treating digit-sum facts as sufficient when many numbers share the same sum.
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Q1 Easy
What is the remainder when 47 is divided by 5?
Explanation47 = 9 × 5 + 2. Remainder = 2. -
Q2 Easy
How many factors does 36 have?
Explanation36 = 2² × 3². Number of factors = (2+1)(2+1) = 9. -
Q3 Easy
HCF of 24 and 36 is:
ExplanationHCF(24, 36) = 12. -
Q4 Easy
LCM of 15 and 20 is:
ExplanationLCM(15, 20) = 60. -
Q5 Easy
Is 91 a prime number?
Explanation91 = 7 × 13, so it is not prime. -
Q6 Medium
Unit digit of 7&sup4; is:
ExplanationPowers of 7 cycle: 7, 9, 3, 1. So 7&sup4; ends in 1. -
Q7 Easy
If N is divisible by 6, N must be divisible by:
Explanation6 = 2 × 3; divisibility by 6 requires both 2 and 3.
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Q8 Medium
Remainder when 10³ is divided by 7 is:
Explanation10 ≡ 3 (mod 7); 10³ ≡ 27 ≡ 6 (mod 7). -
Q9 Easy
Sum of first 10 natural numbers is:
Explanationn(n+1)/2 = 10 × 11/2 = 55. -
Q10 Medium
How many trailing zeroes in 25!?
ExplanationCount of 5s: 25/5 + 25/25 = 5 + 1 = 6. -
Q11 Medium
For “What is integer N?” — I: N is even; II: N is prime. Which DS choice applies?
ExplanationEven alone gives infinitely many values. Prime alone gives N = 2 (only even prime). -
Q12 Hard
For “Is N divisible by 4?” — I: N is divisible by 8; II: N is divisible by 2. DS answer?
ExplanationDivisible by 8 ⇒ divisible by 4. Divisible by 2 alone does not guarantee divisibility by 4. -
Q13 Medium
Smallest 3-digit number divisible by 7 is:
Explanation100 leaves remainder 2 when divided by 7; next multiple is 105. -
Q14 Hard
If x and y are positive integers with x/y = 12/5 in lowest terms, the smallest possible x + y is:
ExplanationSmallest pair: x = 12, y = 5; sum = 17.
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DS1 Easy
What is the value of positive integer N?
Statement IN is divisible by both 12 and 15.
Statement IIN equals the LCM of 12 and 15.
ExplanationLCM(12, 15) = 60. Each statement alone gives N = 60. -
DS2 Easy
What is the remainder when N is divided by 7?
Statement IN leaves remainder 3 when divided by 7.
Statement IIN = 24.
ExplanationStatement I gives remainder 3 directly. Statement II: 24 ÷ 7 leaves remainder 3.
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DS3 Medium
Is N divisible by 6?
Statement IN is divisible by 2.
Statement IIN is divisible by 3.
ExplanationEach alone is insufficient (N = 2 from I; N = 3 from II). Together: divisible by 2 and 3 ⇒ divisible by 6. -
DS4 Hard
How many positive divisors does N have?
Statement IN = 72.
Statement IIN is divisible by every integer from 1 to 6.
ExplanationStatement I: 72 = 2³ × 3² ⇒ (3+1)(2+1) = 12 divisors. Statement II alone allows many values (60, 120, โฆ).