CSAT Solved Papers/ 2024/Q75

2024 CSAT — Q75

Quant Logical & quantitative reasoning 2.5 marks Medium

If $a+b$ means $a-b$ ; $a-b$ means $a\times b$ ; $a\times b$ means $a\div b$ ; $a\div b$ means $a+b$ , then what is the value of $10 + 30 - 100 \times 50 \div 25$ ? (Operations are to be replaced simultaneously)

A $15$
B $0$
C $-15$
D $-25$ Answer

Worked rationale

Build the symbol-swap table once, replace every operator simultaneously, then apply normal BODMAS.

printed	means
$+$	$-$
$-$	$\times$
$\times$	$\div$
$\div$	$+$

Rewrite $10 + 30 - 100 \times 50 \div 25$ symbol-for-symbol:

10 \;-\; 30 \;\times\; 100 \;\div\; 50 \;+\; 25.

Now evaluate with real precedence ( $\times,\div$ before $+,-$ ):

30 \times 100 \div 50 = \frac{30 \times 100}{50} = 60,

10 - 60 + 25 = -25.

Answer: (d) $-25$ .

Why the other options miss

A

wrong formula: swaps the operators correctly but then evaluates left to right ignoring BODMAS: $((10-30)\times 100)\div 50 + 25$ mishandled to a positive value.
B

solved the wrong question: applies only some of the substitutions (e.g. leaves $\times$ as $\times$ ), so the $30\times100\div50$ block is mis-evaluated to cancel the constants.
C

an arithmetic slip: gets the structure $10 - 60 + 25$ but slips the final arithmetic (e.g. $10 - 60 - 25$ partially), landing $10$ short.

Specialist insight

Two disciplines decide this item and both are easy to skip under pressure. First, substitute every symbol before computing anything — the word “simultaneously” warns that you cannot resolve operators in reading order. Second, after the swap, BODMAS still governs the new symbols: the $\times$ and $\div$ in the rewritten line ( $30 \times 100 \div 50$ ) bind tighter than the $-$ and $+$ . A tidy swap table kills the first trap; remembering precedence kills the second. The wrong answers are precisely the values you get by dropping one of these two disciplines.

The trap, in one line

Swap all operators first ( $+\to-,\ -\to\times,\ \times\to\div,\ \div\to+$ ), then obey BODMAS on the rewritten line $10-30\times100\div50+25 = -25$ $=(d)$ — left-to-right or partial swaps both mislead.

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