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CAT-2005-Previous Years Paper

Question
13 out of 30
 

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?



A 100<A<299
B 106<A<305

C 112<A<311
D 118<A<317

Ans. B

Let A = abc, then B = cba

Given, B > A which implies c > a … (1)

As B – A = (100c+10b+a) – (100a + 10b + 1)

B – A = 100 (ca) + (ac)

B – A = 99 (ca) and (B−A) is divisible by 7; and 99 is not divisible by 7 (no factor like 7 or 72) therefore (ca) must be divisible by 7 {i.e., (ca) must be 7, 72 etc) as c and a are single digits. (ca) must be 7 only, the possible values (c, a) {with c>a} are (2) and (8,1) with this we can write A as A : abc = 1b8 or 2b9

As b can take values from 0 to 9, the smallest and the largest possible values are:

Amin = 108

and Amax = 299

Only (b) satisfies so (b) is the answer.

CAT-2005-Previous Years Paper Flashcard List

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