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CAT 2005 — QA Question 13

Number TheoryEasy

The digits of a three-digit number A are written in the reverse order to form another three-digit number B. If B > A and B − A is perfectly divisible by 7, then which of the following is necessarily true?

Answer & solution

Correct answer: 106 < A < 305

  • A

    100 < A < 299

  • 106 < A < 305

  • C

    112 < A < 311

  • D

    118 < A < 317

Solution

Let A = 100x + 10y + z (x ≠ 0, x, y, z are single-digit numbers)

∴ B = 100z + 10y + x

∴ B – A = 99(z – x)

As (B – A) is divisible by 7 and 99 is not, (z – x) is divisible by 7.

∴ z and x can have values (8, 1) or (9, 2).
[Since B > A, z > x]

y can have any value from 0 to 9.

A = 1y8 or 2y9

∴ Lowest possible value of A is 108 and the highest possible value of A is 299.

Hence, option (b).

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CAT 2005 QA Q13: The digits of a three-digit number A are written in the reverse order to form another three-digit number B. If — Solution | TheCATExam