CSAT Solved Papers/ 2025/Q57

2025 CSAT — Q57

Quant Logical & quantitative reasoning 2.5 marks Hard

If FRANCE is coded as 654321654321 and GERMANY is coded as 91584379158437, then how is YEMEN coded?

  1. A 54321
  2. B 81913
  3. C 71913
  4. D 71813 Answer

Worked rationale

This is a fixed substitution cipher: each letter maps to one digit, recoverable by lining up each code against its word, position by position.

From FRANCE →654321\to 654321:

F→6, R→5, A→4, N→3, C→2, E→1.F\to6,\ R\to5,\ A\to4,\ N\to3,\ C\to2,\ E\to1.

From GERMANY →9158437\to 9158437:

G→9, E→1, R→5, M→8, A→4, N→3, Y→7.G\to9,\ E\to1,\ R\to5,\ M\to8,\ A\to4,\ N\to3,\ Y\to7.

Consistency check (the proof the rule is real): the overlapping letters agree across both words — E→1E\to1, R→5R\to5, A→4A\to4, N→3N\to3 all match. So the per-letter map is consistent and the answer is forced.

Now decode YEMEN =Y E M E N= Y\,E\,M\,E\,N:

Y→7, E→1, M→8, E→1, N→3  ⟹  71813.Y\to7,\ E\to1,\ M\to8,\ E\to1,\ N\to3 \;\Longrightarrow\; 71813.

Answer: (d) 71813.

Why the other options miss

  • A
    solved the wrong question: assumes a “reverse-position” rule (last letter =1=1, etc.) read off FRANCE alone, which GERMANY’s code immediately contradicts.
  • B
    an arithmetic slip: correct M, E, N but mis-codes Y as 88 (and a stray 99), scrambling the first two digits.
  • C
    an arithmetic slip: the engineered near-miss — uses M→9M\to9 instead of the cross-checked M→8M\to8, the single-digit error that looks right at a glance.

Specialist insight

The trap is solving from one word: FRANCE →654321\to 654321 tempts you into a tidy “reverse-position” rule, which is wrong — GERMANY proves the map is an arbitrary substitution (G→9,M→8,Y→7G\to9, M\to8, Y\to7 follow no positional formula). The disciplined method is to cross-reference both words to lock each letter’s digit, confirming via the shared letters (E,R,A,NE,R,A,N agree), then decode YEMEN. The deadliest decoy (c) differs only in MM‘s digit — so reading M off GERMANY (M→8M\to8), not guessing, is exactly what scores the mark. This is fully deductive (the answer is uniquely forced by the data), which is why it is in-scope as quantitative coding.

The trap, in one line

It is an arbitrary substitution, not reverse-position: cross-check both words to get Y→7,E→1,M→8,N→3Y\to7, E\to1, M\to8, N\to3, so YEMEN =71813= 71813.

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