SSC CGL 2025 Tier-I · 17 September 2025, Shift 2 · General Intelligence and Reasoning · Question 19 of 99

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.

If 2 $ 2 = 16 and 3 $ 3 = 36, what is 4 $ 4?

(a)48
(b)64
(c)72
(d)80

Answer

Why

Correct — B.
Rule: a $ b = (a + b)².

Check: 2 $ 2 = (2 + 2)² = 4² = 16 ✓
Check: 3 $ 3 = (3 + 3)² = 6² = 36 ✓

Apply: 4 $ 4 = (4 + 4)² = 8² = 64 → option (b).

Why the others are wrong

(a)
48 — 48 is 4 × 4 × 3, a multiplier of 3. The examples multiply by 4: 2 × 2 × 4 = 16 and 3 × 3 × 4 = 36, so 4 × 4 × 4 = 64.
(c)
72 — 72 doubles the previous answer, 36. The examples do not double: 16 × 2 = 32, not 36.
(d)
80 — 80 is 4 × 4 × 5, a multiplier of 5. Both examples use 4 (2 × 2 × 4 = 16), which gives 64.

Concept

When both numbers are equal, several rules give the same results: (a + b)², 4ab and (2a)² all produce 16, 36 and 64 here. That is why the item has one answer even though you cannot tell which formula the setter meant.

The quickest reading is the square of the sum: 2 + 2 = 4 → 16, 3 + 3 = 6 → 36, 4 + 4 = 8 → 64.

The results 16, 36, 64 are the squares of 4, 6 and 8. Spotting that the given answers are perfect squares gets you there without naming a formula.

Key facts

16 = 4², 36 = 6², 64 = 8².
With equal numbers, (a + b)² = 4a² = 4ab, so all three rules agree.
4 $ 4 = (4 + 4)² = 64.

Study next

Defined operations with unequal numbers, where (a + b)² and 4ab give different resultsDefined operations built on cubes, such as (a − b)³Number series of perfect squares, such as 16, 36, 64, 100

Common traps

Continuing 16, 36 by doubling to 72
Guessing a multiplier other than 4, which both lines use (2 × 2 × 4 and 3 × 3 × 4)

12 Sep 2025, 12:30, Reasoning Q.20 uses unequal numbers with a² + b²: 7 $ 3 = 58, 6 $ 2 = 40, keyed 5 $ 1 = 26.

23 Sep 2025, 16:00, Reasoning Q.17 cubes the difference: 5 $ 2 = 27, 7 $ 3 = 64, keyed 6 $ 4 = 8.

Related PYQs

No directly related past PYQ was found.

Topic: Symbolic/Number Analogy — all 210 SSC CGL questions on it, every solved shift.