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Cannot be the sum of M and N

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Cannot be the sum of M and N

by umaa » Mon Jan 05, 2009 5:26 pm
If the two digit integer M and N are positive and have the same digits, but in reverse order, which of the following CANNOT be the sum of M and N?

A. 181

B. 165

C. 121

D. 99

E. 44

If you work our, you'll get the answer easily. But its taking more than 2 mins. Is there a way to work out this problem within 2 mins?
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by pandeyvineet24 » Mon Jan 05, 2009 5:34 pm
the highest sum for reversed 2 digit numbers (different) would be
98 + 89 = 187.

the next highest would be 97 + 79 = 176. Hence the answer is A.

i also went thru eliminating all the answers before i reached A and thought of the above approach.
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by umaa » Mon Jan 05, 2009 5:37 pm
Nice approach. Thanks :)
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by cramya » Mon Jan 05, 2009 5:46 pm
10x+y

10y+x

sum = 10x+y+10y+x
= 11(x+y)

The answer that's not a multiple of 11 would be it

Choose A)
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by pandeyvineet24 » Mon Jan 05, 2009 6:07 pm
good one Cramya.
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by umaa » Mon Jan 05, 2009 6:18 pm
cramya, thanks.. Good approach
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by chiller » Tue Jan 06, 2009 7:09 am
Great answer cramya, but what logic did you follow to attain: 10x+y & 10y+x?

Thanks.
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by cramya » Tue Jan 06, 2009 7:15 pm
Great answer cramya, but what logic did you follow to attain: 10x+y & 10y+x?
Hi Chiller,

Thanks.

For the first number x is the tens digit so u multiply by 10 to get the place value y -> units digit

For the second number reverse this y->tens digit (u multiply by 10) and x the units digit.

Hope this helps!

Regards,
CR
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