## Problem of the day 16.7.09

**What is the sum of the digits of a two digit number which is 32 less than the square of the product of its digits?**

**A. 12 B. 11 C. 10 . D. 9 E. 8**

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8

anonymousJuly 16, 2009 at 8:27 am

I got the same by trial & error.. trying dif combs till i got the answer as 17 .

Could you please elaborate the method that you might have used ?

HariJuly 16, 2009 at 8:39 am

I started with 36-32=4 not works

49-32=17 which is 7^2

so we r done..

it can be done algebraically, but its a bit tedious

RahulJuly 16, 2009 at 8:48 am

ok thanks man …

HariJuly 16, 2009 at 9:06 am

answer : 17

Method : tens place cannot be 2 since after 24 the differences hugely . so tens place has to be one and becomes quite apparent that it has among 15,16,17, 18 .

nikhilJuly 16, 2009 at 11:50 am

Nice, Nikhil

RahulJuly 16, 2009 at 1:38 pm

8

kuldeepJuly 20, 2009 at 1:11 pm

method

max possible number 99+32=131 and minimum is 10+32=42

we have to watch for squares b/w them.

we are left with 36/49/64/81

(1×7)^2=49 =>49-32=17

shivamJuly 24, 2009 at 8:30 am

hai shivam , yours approach is excellent

rahulJuly 25, 2009 at 2:51 pm

i started out wit 12 but due to huge diff. shifted directly 2 option e and gotten the ans by trial n error… bt i suppose its a bit stupid coz its tym consuming… it ws nice anyways.

AakashAugust 11, 2009 at 11:16 am