If ÷ means +, – means ÷, × means – and + means ×, then the value of ((36 × 4) – 8 × 4) / (4 + 8 × 2 + 16 ÷ 1) is

Question

UnlockIAS · Accepted Answer

Correct — A, 0. Write the substitution table out before touching the expression, because every error in this kind of question comes from doing the replacement in your head: ÷ becomes +, – becomes ÷, × becomes −, and + becomes ×. The long slash that separates the two brackets is the fraction bar of the expression itself, not one of the four redefined symbols, so it stays as an ordinary division. Now translate the numerator. (36 × 4) – 8 × 4 becomes (36 − 4) ÷ 8 − 4. Work the bracket first: 36 − 4 = 32. Then, by the order of operations, division before subtraction: 32 ÷ 8 = 4, and 4 − 4 = 0. The numerator is zero. Translate the denominator the same way. 4 + 8 × 2 + 16 ÷ 1 becomes 4 × 8 − 2 × 16 + 1. Multiplication before addition and subtraction gives 32 − 32 + 1 = 1. So the expression is 0 ÷ 1 = 0, which is option (a). Two features of this item are worth registering. The denominator coming out to exactly 1 is a strong signal that the substitution has been read the way the setter intended — a mis-substitution would almost certainly produce something messier. And the answer is unusually robust: since the numerator is exactly zero, the value is zero for any non-zero denominator, so even a candidate who mishandles the second bracket still arrives at 0, provided the first bracket is done correctly. The mark therefore rests entirely on the numerator.

Why the other options are wrong — (b) A plausible-looking whole number that no straightforward mis-substitution actually produces; it is filler. If your working returns 10, you have most likely applied the original symbols to part of the expression and the substituted ones to the rest, which is the commonest way this question goes wrong.  (c) The number 8 appears in the numerator, and an option that echoes a number visible in the question is always attractive to a candidate who has run out of time and is pattern-matching. Neither the substituted numerator nor the substituted denominator evaluates to 8.  (d) Also filler, and it catches the candidate who ignores the order of operations and works strictly left to right in places where the substituted expression demands division and multiplication first. A tidy answer is not evidence of a correct one.

Concept: Symbol-substitution questions test two separate abilities and reward the candidate who keeps them separate. The first is faithful translation: replacing each operator by the one the stem assigns to it, exactly once, without letting the visual habit attached to the printed sign leak back in. The second is the order of operations — BODMAS: brackets first, then orders (powers and roots), then division and multiplication, worked left to right, then addition and subtraction, also left to right. Division and multiplication rank equally, and so do addition and subtraction; the left-to-right rule breaks the tie. The trap in a substituted expression is that the symbol you can see and the operation you must perform are different, so the eye keeps applying the wrong precedence — a printed '+' that now means multiply must be done BEFORE a printed '×' that now means subtract, which is the reverse of what the page looks like it is saying. Writing the translated expression out in full on paper, before evaluating any part of it, removes that whole class of error at a stroke.

State PCS 2024 Q83 — Science & Technology PYQ with Answer

State PCS 2024 Q83 — Science & Technology PYQ with Answer