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Letter Coding Cryptarithm

CAT 2019 Slot 1 · Data Interpretation & Logical Reasoning · Medium · Logical Reasoning

This is a medium Data Interpretation & Logical Reasoning question set from the CAT 2019 Slot 1 paper. It tests Logical Reasoning. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Passage / data set

The following table represents addition of two six-digit numbers given in the first and the second rows, while the sum is given in the third row. In the representation, each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 has been coded with one letter among A, B, C, D, E, F, G, H, J, K, with distinct letters representing distinct digits.

& & B & H & A & A & G & F \\ + & & A & H & J & F & K & F \\ \hline & A & A & F & G & C & A & F \end{array}$$

Question 1 of 4

Which digit does the letter A represent?

Answer

1

Explanation

Since adding two 6-digit numbers yields a 7-digit sum starting with A, A must be the carry over, so A=1A = 1.

Question 2 of 4

Which digit does the letter B represent?

Answer

9

Explanation

In the leading column, B+A(+carry)=AA=11B + A (+ \text{carry}) = AA = 11. Since A=1A = 1, B+1(+1)=11  ⟹  B=9B + 1 (+ 1) = 11 \implies B = 9.

Question 3 of 4

Which among the digits 3, 4, 6 and 7 cannot be represented by the letter D?

Answer

7

Explanation

By mapping all letters to unique digits: A=1,B=9,F=0,G=2,H=5,C=4,J=6,K=8A=1, B=9, F=0, G=2, H=5, C=4, J=6, K=8. The remaining available digits are 3 and 7. Testing assignments reveals that D cannot represent 7.

Question 4 of 4

Which among the digits 4, 6, 7 and 8 cannot be represented by the letter G?

Answer

6

Explanation

From the solved system, G=2G = 2. Thus among 4, 6, 7, and 8, the digit 6 cannot be represented by G.

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