SSC CGL 2025 Tier-I · 24 September 2025, Shift 2 · General Intelligence and Reasoning · Question 22 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.

The sum of two numbers is 40 and their difference is 4. What is the product of the numbers?

(a)390
(b)396
(c)400
(d)404

Answer

Why

Correct — B.
Rule: larger = (sum + difference) ÷ 2, smaller = (sum − difference) ÷ 2.

Larger: (40 + 4) ÷ 2 = 22
Smaller: (40 − 4) ÷ 2 = 18
Check: 22 + 18 = 40 and 22 − 18 = 4.

Product: 22 × 18 = 396 → option (b).

Why the others are wrong

(a)
390 — 390 is 6 below the true product. The sum 40 and difference 4 fix the pair at 22 and 18, and 22 × 18 is 396.
(c)
400 — 400 is 20 × 20, the product when the difference is 0. A difference of 4 splits 20 and 20 into 22 and 18, and the product drops to 396.
(d)
404 — 404 adds where the identity subtracts: (40² + 4²) ÷ 4 = 1616 ÷ 4 = 404. The product is (40² − 4²) ÷ 4 = 396.

Concept

Two numbers are fixed by their sum and difference. Adding the two facts cancels the smaller number, so the larger is (sum + difference) ÷ 2. Subtracting them cancels the larger, so the smaller is (sum − difference) ÷ 2.

For the product there is a shortcut: xy = [(x + y)² − (x − y)²] ÷ 4. Here (1600 − 16) ÷ 4 = 396, without finding the numbers at all.

Key facts

The two numbers are 22 and 18.
(x + y)² − (x − y)² = 4xy.
For a fixed sum, the product is largest when the two numbers are equal: 20 × 20 = 400.

Study next

Two numbers from their ratio and sumSum of squares from sum and product: x² + y² = (x + y)² − 2xyTwo numbers from their sum and product

Common traps

Adding the squares instead of subtracting them, (1600 + 16) ÷ 4 = 404
Stopping at 20 × 20 because the sum splits evenly, which ignores the difference

12 Sep 2025, 16:00, Reasoning Q.18 also asks for two numbers from their sum, 64, but fixes them with a ratio, 3 : 5, keyed 24 and 40.

Related PYQs

No directly related past PYQ was found.