SSC CGL 2025 Tier-I · 17 September 2025, Shift 3 · General Intelligence and Reasoning · Question 21 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 11 September 2026.

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If 8 # 2 = 65 and 7 # 3 = 55, then 6 # 5 = ?

(a)35
(b)44
(c)58
(d)69

Answer

Why

Correct — C.
Rule: a # b = a² + b² − 3.

8 # 2 = 64 + 4 − 3 = 65 ✓
7 # 3 = 49 + 9 − 3 = 55 ✓
6 # 5 = 36 + 25 − 3 = 58 → option (c).

Why the others are wrong

(a)
35 — 35 is below 6² alone (36). The rule adds 5² = 25 before taking off 3, and both examples land above the first number's square (65 > 64, 55 > 49).
(b)
44 — 44 is 17 below 6² + 5² = 61. The examples take exactly 3 off the sum of squares (68 → 65, 58 → 55), not 17.
(d)
69 — 69 is 8 above 6² + 5² = 61. The examples never add to the sum of squares. They take 3 off it.

Concept

Start with what the examples share: 8 + 2 and 7 + 3 both make 10, yet the results differ (65 and 55). So the rule cannot depend on the sum alone.

Squares separate the pairs: 8² + 2² = 68 and 7² + 3² = 58, each exactly 3 above its result. That fixed gap across both examples is the rule: a² + b² − 3.

Two examples can fit more than one rule. 10a − 15 also gives 65 and 55, but for 6 # 5 it gives 45, which is not an option. The sum-of-squares rule gives 58, which is.

Key facts

Rule here: a² + b² − 3.
When the example pairs share a sum (8 + 2 = 7 + 3 = 10), the rule must use more than the sum.
6² + 5² = 61, so the answer sits 3 below 61.

Study next

Symbol operations of the form a² + b and a × (a + b)Operations of the form a × b + (a − b), tested on three examplesThe identity (a + b)² = a² + b² + 2ab, for spotting sum-of-squares rules

Common traps

Fitting a rule to one example only: 8 # 2 = 65 is also 8² + 1, which gives 50 for 7 # 3, not 55
Settling on a rule the options do not contain, such as 10a − 15 (45), instead of testing another

15 Sep 2025, 12:30, Reasoning Q.21 also has pairs with a shared sum (5 + 2 = 4 + 3 = 7): 5 * 2 = 35 and 4 * 3 = 28 fit a × (a + b), keyed 60 for 6 * 4.

Reasoning Q.5 of this shift fits a × b + (a − b): 3 @ 2 = 7, 6 @ 3 = 21, 8 @ 2 = 22, keyed 21 for 5 @ 4.

Related PYQs

No directly related past PYQ was found.

Topic: Symbolic/Number Analogy — all 169 SSC CGL questions on it, every solved shift.