CANNOT be the sum

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gmatblood: Master | Next Rank: 500 Posts; Posts: 489; Joined: Tue Jul 05, 2011 11:10 amFollowed by: 5 members; Thanked: 28 times

by gmatblood » Mon Oct 31, 2011 10:30 am

If the two-digit integers 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

Would like to know if there is any shortcut to check it!

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Source: Beat The GMAT — Problem Solving | Mon Oct 31, 2011 10:30 am

ripulgupta: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Mon Sep 26, 2011 9:12 amFollowed by: 3 members; Thanked: 3 times; GMAT Score:710

by ripulgupta » Mon Oct 31, 2011 11:08 am

As we are adding two two-digit numbers and both the number contain the same digits but in reverse order. The last two digits of there addition have to be either same or tens digit can be one more than the units digits. This condition is true for all the options except A. Thus the solution.

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Mon Oct 31, 2011 11:09 am

Well it should be a multiple of 11.
10X+Y +10Y+X = 11(X+Y) A is not.

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gmatblood: Master | Next Rank: 500 Posts; Posts: 489; Joined: Tue Jul 05, 2011 11:10 amFollowed by: 5 members; Thanked: 28 times

by gmatblood » Mon Oct 31, 2011 11:14 am

shankar.ashwin wrote:Well it should be a multiple of 11.
10X+Y +10Y+X = 11(X+Y) A is not.

Is this condition valid all the time?

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gmatblood: Master | Next Rank: 500 Posts; Posts: 489; Joined: Tue Jul 05, 2011 11:10 amFollowed by: 5 members; Thanked: 28 times

by gmatblood » Mon Oct 31, 2011 11:14 am

ripulgupta wrote:As we are adding two two-digit numbers and both the number contain the same digits but in reverse order. The last two digits of there addition have to be either same or tens digit can be one more than the units digits. This condition is true for all the options except A. Thus the solution.

Is this a valid condition! Thanks anyways

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Mon Oct 31, 2011 11:24 am

Yup, it is. Similarly if the digits of 2 numbers are reversed and subtracted,

10X+Y -10Y-X = 9(X-Y), the number would be a multiple of 9.

gmatblood wrote:
shankar.ashwin wrote:Well it should be a multiple of 11.
10X+Y +10Y+X = 11(X+Y) A is not.
Is this condition valid all the time?

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