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Previous Year Paper

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CAT-2005-Previous Years Paper

Question
19 out of 30
 

For a positive integer n, let pn, denote the product of the digits of n and Sn denote the sum of the digits of n. The number of integers between 10 and 1000 for which pn + sn = n is



A 81
B 16
C 18
D 9

Ans. D

10 < n < 1000

Let n be two digit number

n = 10a + b pn = ab, sn = a + b

Then ab + a + b = 10a + b

ab = 9a b = 9

There are 9 such numbers 19, 29, 33,…99

Then let n be three digit number

n = 100a + 10b + c Pn = abc, sn = a + b + c

Then ab + a + b + c = 100a + 10b + c

abc = 99a + 9b

bc = 99 + 9

But the minimum value for bc = 81 (i.e.,when both b and c are 9)

And RHS is more than 99. Hence, no such number is possible.

Hence, option (d).

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