If + means ×, × means −, ÷ means + and − means ÷, then 175 − 25 ÷ 5 + 20 × 3 + 10 equals to:

Question

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Correct — A, 77. Work in two sealed stages and never let them overlap. Stage one is pure translation: rewrite the printed line replacing every symbol by the meaning the question assigns it, and change nothing else — no arithmetic yet, not even the easy bits. The four instructions happen to form one closed cycle, + becomes ×, × becomes −, − becomes ÷ and ÷ becomes +, so a single loop written in the margin generates every replacement without re-reading the stem, and it also warns you that no symbol is meant to survive unchanged. Applying it, 175 − 25 ÷ 5 + 20 × 3 + 10 rewrites as 175 ÷ 25 + 5 × 20 − 3 × 10. Stage two is ordinary arithmetic on the new line only: multiplication and division bind before addition and subtraction, so 175 ÷ 25 = 7, 5 × 20 = 100 and 3 × 10 = 30, leaving 7 + 100 − 30 = 77. The structural fact that decides this item is what happens to the leading symbol. On the page, 175 − 25 is a subtraction — the lowest-priority operation in the line and the last thing you would normally touch. After substitution it is a division, the highest-priority operation, so it fires first and collapses the largest number in the question from 175 to 7 before anything else happens. That single promotion is why the answer is small, and it hands you a free upper bound: once the rewrite is done only two terms are positive, 7 and 100, so no order of evaluation can push the value above 107, which eliminates 140 before the arithmetic is even finished. The numbers themselves were chosen to be kind — 175 ÷ 25 is exact, and 5 × 20 and 3 × 10 are one-glance products — so every wrong option on this question is a bookkeeping failure rather than a computational one.

Why the other options are wrong — (b) 87 is exactly 77 plus 10 — the trailing operand counted twice, once correctly inside 3 × 10 = 30 and again as a leftover addition, which is what happens when the rewrite is done in the head and the final term is read off the printed line rather than the new one. The same 87 appears if 175 ÷ 25 is slipped from 7 to 17, since 17 + 100 − 30 = 87. Both routes leave the structure right and exactly one number wrong, which is why it reads as plausible.  (c) The magnitude decoy, and the only option above 100. It is 7 × 20 — the first quotient multiplied into the 20 instead of the 5 being multiplied by it — and it appeals to the instinct that a line beginning with 175 must yield a big answer. In 175 ÷ 25 + 5 × 20 the product 5 × 20 is formed first and then added to 7. The rewrite also makes 140 arithmetically unreachable: the positive terms are only 7 and 100, so the value cannot exceed 107 under any order of evaluation.  (d) 70 is 5 × 20 − 3 × 10, that is 100 − 30, with the leading 175 ÷ 25 = 7 left out of the sum altogether. It is the answer of a candidate who translates the middle and the tail correctly, banks the two easy products, and forgets that the head of the line is still waiting — and the head is the easiest term to lose precisely because its symbol changed from a familiar subtraction into a division. The whole distance between 70 and 77 is that discarded quotient.

Concept: A symbol-substitution question hands you a private code for the four operators and then prints an expression in the ordinary symbols, so the line on the paper is not an arithmetic statement at all — it is a coded one, and the only legitimate first move is to decode it in full. The work is two strictly separated steps: rewrite the expression symbol by symbol in the meanings you have been given, then evaluate the rewritten expression by the normal order of operations — brackets, powers, division and multiplication left to right, then addition and subtraction left to right. The printed expression is never evaluated as it stands. Two precedence details are worth fixing in memory because these papers exploit both: multiplication and division rank equally and are worked left to right, so 48 ÷ 6 × 2 is 16 and not 4, and addition and subtraction likewise rank equally and run left to right. Substitution bites so hard here because it does not merely rename operations, it re-ranks them. A printed − carries the lowest priority on the page, but if the question turns it into ÷ that same position jumps to the highest priority in the rewritten line and the shape of the whole calculation inverts. The four instructions in this particular question form a single four-step cycle rather than two swapped pairs, which is why a partial rewrite produces a wrong answer rather than an approximately right one.

State PCS 2025 Q7 — Science & Technology PYQ with Answer

State PCS 2025 Q7 — Science & Technology PYQ with Answer