SSC CGL 2025 Tier-I · 20 September 2025, Shift 1 · Quantitative Aptitude · Question 6 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 13 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

What type of number is the result of multiplying a Rational Number with an Irrational Number?

(a)Always Rational
(b)Always Irrational
(c)Always Integer
(d)Sometimes Rational, Sometimes Irrational

Answer

Why

Correct — D. The answer turns on zero, which is a rational number.

Non-zero rational × irrational: if r ≠ 0 and r × s = q were rational, then s = q ÷ r would be rational too. So 2 × √2 = 2√2 is irrational.

Zero × irrational: 0 × √2 = 0, which is rational.

Both outcomes occur, so the product is sometimes rational, sometimes irrational → option (d)

Why the others are wrong

(a)
Always Rational — 2 × √2 = 2√2 is irrational, so the product is not always rational. A rational result needs the rational factor to be 0.
(b)
Always Irrational — Fails for zero: 0 × √2 = 0, and 0 is rational. 'Always irrational' holds only when the rational factor is non-zero.
(c)
Always Integer — 1⁄2 × √2 = √2⁄2 is not an integer, and neither is 1 × √2 = √2.

Concept

A rational number can be written as p⁄q with integers p and q, q ≠ 0. Zero is 0⁄1, so it is rational. An irrational number, such as √2 or π, cannot be written that way.

For a non-zero rational r and an irrational s, r × s is always irrational, because dividing by r would make s rational. Zero is the one exception: 0 × s = 0 for every s.

The familiar rule 'rational × irrational = irrational' is true only for a non-zero rational. The stem says 'a Rational Number' without excluding zero, so zero counts, and the key takes 'sometimes'.

Key facts

Zero is a rational number (0 = 0⁄1).
A non-zero rational times an irrational is always irrational.
An irrational times an irrational can be rational (√2 × √2 = 2) or irrational (√2 × √3 = √6).
A rational plus an irrational is always irrational.

Study next

Closure of rational and irrational numbers under the four operationsWhy √2 is irrational (proof by contradiction)Classifying real numbers: natural, whole, integer, rational, irrational

Common traps

Forgetting that 0 is rational and marking 'Always Irrational'.
Assuming an irrational times an irrational stays irrational: √2 × √2 = 2.

The options are four claims, three of them 'always'. A single counter-example rejects each 'always', so test 0, 1⁄2 and 2 against √2 before choosing.

Related PYQs

No directly related past PYQ was found.

Topic: Ratio & Proportion — all 96 SSC CGL questions on it, every solved shift.