SSC CGL 2024 Tier-I · 18 September 2024, Shift 1 · Quantitative Aptitude · Question 10 of 99

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 6 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

Simplify the following:

Answer

Why

Correct — A. The stem is an image: [ (5½ − 3⅓) of 1 5⁄13 + 1 − 2 × 3 5⁄2 ÷ 2¾ ].

Bracket first, then 'of', then × and ÷ left to right, then + and −.

5½ − 3⅓ = 11⁄2 − 10⁄3 = 13⁄6
13⁄6 of 1 5⁄13 = 13⁄6 × 18⁄13 = 3

Now the ×÷ chain:
2 × 3 5⁄2 = 2 × 11⁄2 = 11
11 ÷ 2¾ = 11 × 4⁄11 = 4

3 + 1 − 4 = 0 → option (a)

Why the others are wrong

(b)
3½ would need the tail 2 × 3 5⁄2 ÷ 2¾ to be worth ½. It is worth 4, because 2 × 11⁄2 = 11 and 11 ÷ 11⁄4 = 4.
(c)
−2 would need the tail to be worth 6. The tail closes at 4, so the expression can fall no further than 3 + 1 − 4 = 0.
(d)
11⁄2 is the improper form of the mixed number 3 5⁄2 — a value picked up in the middle of the working, before the × 2 and the ÷ 2¾ are applied.

Concept

BODMAS fixes the order: brackets, then 'of', then division and multiplication together, then addition and subtraction together, each pair left to right.

'Of' behaves like a multiplication that has already been bracketed. SSC uses it precisely because a candidate who lets it wait its turn in the ÷× sweep gets a different number.

Convert every mixed number before you start: 5½ = 11⁄2, 3⅓ = 10⁄3, 1 5⁄13 = 18⁄13, 2¾ = 11⁄4.

The paper prints the fourth mixed number as 3 5⁄2 — a whole number beside an improper fraction, which looks like a typo but is not fatal.

Read it the way any mixed number is read, 3 + 5⁄2 = 11⁄2, and the chain closes on 0, the keyed value.

Key facts

'Of' is settled before ÷ and ×, so 13⁄6 of 18⁄13 is evaluated as one quantity, 3.
Division and multiplication rank equally and run left to right: 2 × 11⁄2 ÷ 11⁄4 = 11 ÷ 11⁄4 = 4.
Dividing by a fraction is multiplying by its reciprocal: 11 ÷ 11⁄4 = 11 × 4⁄11 = 4.

Study next

Simplification with nested brackets in the order ( ), { }, [ ]Mixed numbers and improper fractions inside a single ÷ chain'Of' versus × in a BODMAS string

Common traps

Treating 'of' as an ordinary × and letting it wait its turn in the left-to-right sweep
Reading 3 5⁄2 as 3½ because the printed fraction looks improper
Applying the minus sign before the ÷, so the tail is subtracted before it is evaluated

SSC prints the whole expression as a picture, so the bracket structure has to be read off the image before any arithmetic starts.

Simplification with 'of' is also asked at 13 Sep 2024, 09:00, Quant Q.15 and at 26 Sep 2024, 12:30, Quant Q.19.

Related PYQs

No directly related past PYQ was found.