Cannot be the sum of M and N

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umaa: Legendary Member; Posts: 727; Joined: Sun Jun 08, 2008 9:32 pmFollowed by: 1 member; Thanked: 8 times

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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Source: Beat The GMAT — Problem Solving | Mon Jan 05, 2009 5:26 pm

pandeyvineet24: Legendary Member; Posts: 527; Joined: Mon Jun 02, 2008 9:14 am; Location: Atlanta; Thanked: 17 times

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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umaa: Legendary Member; Posts: 727; Joined: Sun Jun 08, 2008 9:32 pmFollowed by: 1 member; Thanked: 8 times

by umaa » Mon Jan 05, 2009 5:37 pm

Nice approach. Thanks

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

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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pandeyvineet24: Legendary Member; Posts: 527; Joined: Mon Jun 02, 2008 9:14 am; Location: Atlanta; Thanked: 17 times

by pandeyvineet24 » Mon Jan 05, 2009 6:07 pm

good one Cramya.

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umaa: Legendary Member; Posts: 727; Joined: Sun Jun 08, 2008 9:32 pmFollowed by: 1 member; Thanked: 8 times

by umaa » Mon Jan 05, 2009 6:18 pm

cramya, thanks.. Good approach

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chiller: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Tue Jan 06, 2009 4:27 am

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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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

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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