SSC CGL 2024 Tier-I · 17 September 2024, Shift 3 · Quantitative Aptitude · Question 11 of 98

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 −7⁄6 + 4⁄9 ÷ 5⁄3 × 1⁄16

Answer

Why

Correct — B. The stem is a picture: simplify −7⁄6 + 4⁄9 ÷ 5⁄3 × 1⁄16.

BODMAS puts division and multiplication ahead of the addition, and those two run left to right.

4⁄9 ÷ 5⁄3 = 4⁄9 × 3⁄5 = 12⁄45 = 4⁄15
4⁄15 × 1⁄16 = 4⁄240 = 1⁄60

Now the addition, over LCM 60:
−7⁄6 + 1⁄60 = −70⁄60 + 1⁄60 = −69⁄60

Divide top and bottom by 3 → −23⁄20, the fraction pictured in option (b).

Why the others are wrong

(a)
Option (a) shows −18⁄23 with the 23 underneath. Here 23 is born as 69 ÷ 3 and stays in the numerator, over 60 ÷ 3 = 20. No step produces an 18.
(c)
Option (c) shows −23⁄18. The numerator is right but 18 appears nowhere: the addition is done over LCM 60, and 69⁄60 reduces to 23⁄20.
(d)
Option (d) shows −20⁄23, the keyed fraction inverted. Taking a reciprocal is the move used on 5⁄3 inside the division, not something applied to the final value.

Concept

Two rules carry this item. Division outranks addition, so 4⁄9 ÷ 5⁄3 × 1⁄16 is settled before −7⁄6 is brought in.

And division and multiplication sit on the same rank, so they are worked strictly left to right. Dividing by a fraction means multiplying by its reciprocal, which is where 3⁄5 comes from. Only then does the negative fraction join, over a common denominator.

Every printed choice is negative and every one carries a 23, an 18 or a 20, so eyeballing the sign or the numerator will not separate them. The denominator is what the working has to pin down.

Key facts

Division and multiplication share one precedence level and are performed left to right.
Dividing by 5⁄3 is the same as multiplying by 3⁄5.
4⁄9 ÷ 5⁄3 × 1⁄16 = 1⁄60, and −7⁄6 + 1⁄60 = −69⁄60 = −23⁄20.

Study next

BODMAS on an expression that also carries brackets and the word 'of'Simplifying a complex fraction that has a fraction in both numerator and denominatorOrdering negative fractions by size before choosing among close options

Common traps

Adding −7⁄6 and 4⁄9 first. BODMAS forbids it, and the value it produces is not among the four printed fractions.
Computing 5⁄3 × 1⁄16 before the division, on the belief that multiplication outranks division.
Leaving the result as −69⁄60 and hunting for it among the choices. All four pictures are in lowest terms, so the reduction by 3 has to be done before comparing.

SSC types this item as an image: the expression is set as stacked fractions and each of the four choices is its own picture.

So the first task is transcribing it without dropping the minus sign or misreading which operator sits between which pair. What the question really tests is the rank of ÷ against ×.

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