BPSC 71st CCE Prelims General Studies · Question 7 of 150

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.

• (b)87 — 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)140 — 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 — 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.

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.

Translate first, compute second, and write the rewritten line out in full even with the clock at roughly 48 seconds a question — the entire difficulty of this item is bookkeeping, and bookkeeping done in the head is where the mark goes. Read the substitution instructions once and note their shape: + → × → − → ÷ → + is a closed loop, so every symbol moves and none stays put; if your rewritten line still shows the same symbol in the same place as the original, you have missed a replacement. There is a subtler directional trap too. The rule says '+ means ×', which tells you what to put in place of a printed +; it does not tell you to replace every × with a +. Writing the four substitutions in a column on the rough sheet before touching the expression removes both risks at once. Then apply precedence to the new line only: 175 ÷ 25 + 5 × 20 − 3 × 10 has three high-priority operations to clear before any addition or subtraction happens. The single discriminating recognition is that the leading minus has become a division, because that is what shrinks 175 to 7 and turns a line that looks as though it must yield hundreds into one that yields 77. Every wrong option sits downstream of it — 140 assumes the answer stays large, 70 loses the quotient, 87 double-counts the tail.

• The code here: a printed + stands for ×, a printed × stands for −, a printed ÷ stands for +, and a printed − stands for ÷ — four instructions that form the single closed cycle + → × → − → ÷ → +, so no symbol survives the rewrite unchanged.
• Rewritten in full, 175 − 25 ÷ 5 + 20 × 3 + 10 becomes 175 ÷ 25 + 5 × 20 − 3 × 10, and it is that rewritten line, never the printed one, to which the order of operations applies.
• Clearing the high-priority operations gives 175 ÷ 25 = 7, 5 × 20 = 100 and 3 × 10 = 30, so the value is 7 + 100 − 30 = 77, option (a).
• The decisive structural change is that the leading − is promoted from the lowest-priority operation on the page to the highest-priority operation in the rewrite, collapsing 175 to 7 before anything else is evaluated.
• A free bound for checking under time pressure: after the rewrite only 7 and 100 are positive, so the value cannot exceed 107 — that alone rules out 140, and subtracting the single negative term 30 pins the answer to 77.
• Precedence rule these papers keep exploiting: × and ÷ rank equally and run left to right, as do + and −, so 48 ÷ 6 × 2 equals 16 rather than 4.

• Evaluating the printed expression before translating it — the printed line is a code, not an arithmetic statement
• Reversing the direction of a rule, for example replacing every × with a + when the rule was '+ means ×'
• Rewriting only some of the symbols, which the closed-cycle structure of this rule makes fatal since no symbol is meant to remain unchanged
• Working the rewritten line strictly left to right, ignoring that × and ÷ must be cleared before + and −
• Assuming a large printed number forces a large answer, when here the leading subtraction becomes a division and 175 collapses to 7

BPSC sets one symbol-substitution or sign-interchange item in most reasoning blocks and asks it as a bare computation with clean numbers, an exact division and four numerically close options, so the mark turns purely on whether the rewrite was done on paper — one mark against a 48-second average and a one-third-mark penalty for a wrong tick. UPSC has not set an operator-substitution sum in the General Studies paper since mental ability moved to Prelims Paper-II in 2011, and that paper has been merely qualifying at 33 per cent since 2015. When the older General Studies papers tested the same idea they tested it as substitution of meaning rather than of arithmetic signs — a planet where the word for water is 'light', or a value fed into an algebraic expression where sign discipline decides the answer — so the underlying skill of decode first, compute second is identical while the surface is verbal or algebraic rather than symbolic.

• practice — not a real PYQ

  If '+' means '÷', '−' means '×', '÷' means '+' and '×' means '−', then what is the value of 15 − 3 + 5 × 2 ÷ 8 ?

  • (a)9
  • (b)17
  • (c)15
  • (d)12

  Answer(c) 15 — the line rewrites as 15 × 3 ÷ 5 − 2 + 8; clearing the equal-ranked × and ÷ left to right gives 45 ÷ 5 = 9, then 9 − 2 + 8 = 15.

• practice — not a real PYQ

  If P means +, Q means −, R means × and S means ÷, then what is the value of 18 R 3 S 9 P 12 Q 6 ?

  • (a)18
  • (b)12
  • (c)6
  • (d)24

  Answer(b) 12 — the line reads 18 × 3 ÷ 9 + 12 − 6, so 54 ÷ 9 = 6 and 6 + 12 − 6 = 12. Answering 24 comes from working left to right and adding before the division is cleared.