Is x an integer ?

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Deepthi Subbu: Master | Next Rank: 500 Posts; Posts: 298; Joined: Tue Feb 16, 2010 1:09 am; Thanked: 2 times; Followed by:1 members

Is x an integer ?

by Deepthi Subbu » Sun Sep 11, 2011 6:59 pm

If m and n are both two digit numbers ,and m-n = 11x , is x an integer ?

a.The tens digit and units digit of m are same.
b.m+n is a multiple of 11.

OA to follow

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Source: Beat The GMAT — Data Sufficiency | Sun Sep 11, 2011 6:59 pm

n@resh: Senior | Next Rank: 100 Posts; Posts: 61; Joined: Tue Apr 13, 2010 3:29 am; Thanked: 8 times

by n@resh » Sun Sep 11, 2011 7:30 pm

Deepthi Subbu wrote:If m and n are both two digit numbers ,and m-n = 11x , is x an integer ?

a.The tens digit and units digit of m are same.
b.m+n is a multiple of 11.

OA to follow

from statement 1: number can be: 11,22,33,44...99 but you can't have control over n!
it can be 10 or 11..etc which lead to different values of x not restricted to integers...hence it's not sufficient.

from statement 2: As m and n values aren't fixed. eg: 10 + 12 ..then m-n = -2 that means x = -2/11 is not integer! but if you consider m+n as 11 + 22 ..then m-n = -11 => x ( = -1 )is an integer!
Clearly,not sufficient.

combine both, m must be multiple of 11, then from 2nd statement m + n is multiple of 11, leads to 'n' which must be multiple of 11.

Hence m - n will be always multiple of 11..hence x is integer!

Ans:C!

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shrivast: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Sat May 07, 2011 2:10 pm

by shrivast » Sun Sep 11, 2011 7:38 pm

IMO : C

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saketk: Legendary Member; Posts: 608; Joined: Sun Jun 19, 2011 11:16 am; Thanked: 37 times; Followed by:8 members

by saketk » Mon Sep 12, 2011 4:14 am

Deepthi Subbu wrote:If m and n are both two digit numbers ,and m-n = 11x , is x an integer ?

a.The tens digit and units digit of m are same.
b.m+n is a multiple of 11.

OA to follow

rephrase the question -- is (m-n) divisible by 11

statement 1: tens and units digit of m are same.

i.e. m can be 11, 22, 33 etc

not sufficient because we dont know anything about n yet.

Statement 2: m+n is a multiple of 11. since m and n are both 2 digits number

we can say m+n is 22,33,44,55,66 etc.

but this statement alone is also NS.

combine the 2 statements: -

we know that m is a multiple of 11.
and m+n is a multiple of 11.

this implies n is also a multiple of 11.

This also means that m-n wil also be a multiple of 11.

Answer C.