Data Sufficiency Quiz: Reasoning and Quant Practice

Spoilers! These are the Starter quiz’s answers. Easy, Medium, Hard and Mixed rounds show their own answers when you finish.

1. How is J related to K? I. J is the son of M, who is the sister of K's father. II. K is the daughter of N, who is the brother of M.

   • Statement I alone is sufficient
   • Statement II alone is sufficient
   • Either statement alone is sufficient
   • Both statements together are needed

   Answer: Statement I alone is sufficient. From I, J's mother is K's paternal aunt, so J is K's cousin. II says nothing about J, so it cannot answer the question.

2. n is a positive integer. Is n divisible by 6? I. n is divisible by 12. II. n is divisible by 3.

   • Statement I alone is sufficient
   • Statement II alone is sufficient
   • Neither statement is sufficient, even together
   • Both statements together are needed

   Answer: Statement I alone is sufficient. Every multiple of 12 is a multiple of 6, so I gives a definite 'yes'. II allows n = 9 (no) or n = 12 (yes), so it is not enough.

3. In a code language, what is the code for 'sky'? I. 'sky is blue' is written as 'ka lo mi'. II. 'clear sky above' is written as 'pe lo ra' and 'sky looks blue' is written as 'su lo ta'.

   • Statement I alone is sufficient
   • Statement II alone is sufficient
   • Either statement alone is sufficient
   • Both statements together are needed

   Answer: Statement II alone is sufficient. In II, 'sky' is the only word common to both sentences and 'lo' the only common code, so sky = lo. I alone gives three codes for three words with no way to match them.

4. What is Ravi's present age? I. Ravi is 4 years older than Sam. II. Six years ago, Ravi's age was half of what it will be 10 years from now.

   • Statement I alone is sufficient
   • Statement II alone is sufficient
   • Either statement alone is sufficient
   • Neither statement is sufficient, even together

   Answer: Statement II alone is sufficient. II gives R - 6 = (R + 10) ÷ 2, so 2R - 12 = R + 10 and R = 22. I only links Ravi to Sam, whose age is unknown.

5. Which direction is Raj facing? I. The sun is rising and it is on his left. II. If he turns 90° clockwise, he will face west.

   • Statement I alone is sufficient
   • Statement II alone is sufficient
   • Either statement alone is sufficient
   • Both statements together are needed

   Answer: Either statement alone is sufficient. I: the rising sun is in the east; east on his left means he faces south. II: the only direction that becomes west after a 90° clockwise turn is south. Each alone answers it.

6. What is the principal? I. The simple interest on it for 3 years at 8% per annum is Rs 1,800. II. At 8% per annum simple interest, it amounts to Rs 10,500 in 5 years.

   • Statement I alone is sufficient
   • Statement II alone is sufficient
   • Either statement alone is sufficient
   • Neither statement is sufficient, even together

   Answer: Either statement alone is sufficient. I: P × 8 × 3 ÷ 100 = 1,800 gives P = Rs 7,500. II: P + P × 8 × 5 ÷ 100 = 1.4P = 10,500 gives P = Rs 7,500. Either alone works.

7. In which month was Asha born? I. She was born in a month that has 31 days. II. She was born in the second half of the year (July to December).

   • Statement I alone is sufficient
   • Statement II alone is sufficient
   • Neither statement is sufficient, even together
   • Both statements together are needed

   Answer: Neither statement is sufficient, even together. Together they still leave July, August, October and December, so the month cannot be fixed.

8. On which day of the week did Rita visit the museum? I. She visited after Tuesday but before Friday of that week. II. She did not visit on a Wednesday or a Saturday.

   • Statement I alone is sufficient
   • Statement II alone is sufficient
   • Either statement alone is sufficient
   • Both statements together are needed

   Answer: Both statements together are needed. I leaves Wednesday or Thursday; II alone leaves five days. Together, Wednesday is removed and the answer is Thursday.

9. What is the value of x? I. 3x + 2y = 18. II. x - y = 1.

   • Statement I alone is sufficient
   • Statement II alone is sufficient
   • Neither statement is sufficient, even together
   • Both statements together are needed

   Answer: Both statements together are needed. Each equation alone has two unknowns. Together, y = x - 1, so 3x + 2x - 2 = 18 and x = 4.

10. What is the area of a rectangle? I. Its perimeter is 28 cm. II. Its diagonal is 10 cm.

    • Statement I alone is sufficient
    • Statement II alone is sufficient
    • Either statement alone is sufficient
    • Both statements together are needed

    Answer: Both statements together are needed. I gives l + w = 14 and II gives l² + w² = 100. Then 2lw = 14² - 100 = 96, so the area lw = 48 cm². Neither alone fixes it.