Vedadots
Q1819/80Q20
Q19·CSAT · Prelims 2022

Data sufficiency to determine if x is an integer

DI / DSData SufficiencyFactual single● Medium

Question

Consider the Question and two Statements given below: Question: Is x an integer? Statement-1: x/3 is not an integer. Statement-2: 3x is an integer. Which one of the following is correct in respect of the Question and the Statements?

Options

a

Statement-1 alone is sufficient to answer the Question

b

Statement-2 alone is sufficient to answer the Question

c

Both Statement-1 and Statement-2 are sufficient to answer the Question

d

Both Statement-1 and Statement-2 are not sufficient to answer the Question

Answer

Explanation

Evaluate the mathematical possibilities for x under both statements:

Statement 1: x/3 is not an integer. This means x is not a multiple of 3.

x could be an integer like 1 (since 1/3 is not an integer).
x could also be a non-integer like 1.5 (since 1.5/3 = 0.5, which is not an integer).

Insufficient.

Statement 2: 3x is an integer.

x could be an integer like 1 (since 3 × 1 = 3).
x could be a fraction like 1/3 (since 3 × 1/3 = 1, an integer).

Insufficient.

Combine both statements: Test our previously established examples against both rules simultaneously:

If x = 1: 1/3 is not an integer (Statement 1 holds). 3 × 1 = 3 is an integer (Statement 2 holds). Here, x is an integer.
If x = 1/3: 1/3/3 = 1/9 is not an integer (Statement 1 holds). 3 × 1/3 = 1 is an integer (Statement 2 holds). Here, x is not an integer.

Since both an integer and a non-integer perfectly satisfy the combined system, the data remains insufficient.

For integer data sufficiency checks involving multiplication and division operators, always test fractional values (like 1/k) against the rules to aggressively hunt for non-integer solutions.

Answer: (d).

Question details

Year

2022

Paper

CSAT

Question

Q19

Section

Data Interpretation & Sufficiency

Sub-topic

Data Sufficiency

Type

Factual single

Difficulty

Medium

Source hint

Is x an integer?

Same sub-topic — other years

Data Sufficiency has appeared in multiple CSAT papers:

Q61

2026

Data Sufficiency — Diophantine Coin Systems

DI / DSHard

Q62

2026

Data Sufficiency — Real Number Properties

DI / DSMedium

Q63

2026

Data Sufficiency — Parity Rules

DI / DSEasy

Q64

2026

Data Sufficiency — Set Parity Restrictions

DI / DSHard

See all questions on Data Sufficiency

Browse every tagged question across all years

Explore →
Back to CSAT 2022