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CAT 2019 Slot 1 — DILR Question 17

Coding & DecodingEasy
Passage / Data

Answer the following question based on the information given below.

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.

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Which digit does the letter A represent?

Answer & solution

Correct answer: 1

Answer: 1

Solution

Units place of (F + F) is F ⇒ F = 0 

Units place of (H + H) or (H + H + 1) is also F. This is possible only when H is 5 and there is no carry over.

So, F = 0 and H = 5

∴ (1 + B + A) = (10A + A)
⇒ 1 + B = 10A
⇒ A = 1 and B = 9

As units place of (G + K) = 1, actual value of G + K = 11

So, 1 + F + A = 1 + 1 + 0 = 2 = C

Now, 1 + J = G and G + K = 11

Also, G, J and K ∈ {3, 4, 6, 7, 8}

Therefore, (G, J, K) = (8, 7, 3) or (7, 6, 4) or (4, 3, 7), accordingly D and E can be represented by (4,6) or (3, 8) or (6, 8) in some order.

The letter A represents digit 1.

Answer: 1.

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CAT 2019 Slot 1 DILR Q17: Which digit does the letter A represent? — Solution | TheCATExam