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If m and n are both 2 digit numbers and m-n=11x, is x an

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Manager
Joined: 29 Aug 2006
Posts: 156
If m and n are both 2 digit numbers and m-n=11x, is x an  [#permalink]

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07 Nov 2006, 13:01
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(N/A)

Question Stats:

100% (00:02) correct 0% (00:00) wrong based on 13 sessions

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If m and n are both 2 digit numbers and m-n=11x, is x an integer?
1)The tens digit and units digit of m are the same
2) m+n is a multiple of 11.

This is the way I approached it .
m=10u+v
n =10 a+b

m-n= 10(u-a) +(v-b)

Since m-n=11x

10(u-a)+ (v-b)=10x+x
Comparing both sides,

u-a= x and v-b=x

Hence, u-a=v-b--------(A)

From S1, u=v, hence a=b, hence it follows that x is an integer. hence suff.

from S2, m+n=11y
10(u+a)+(v+b)=10 y+ y
Hence, u+a=v+b-----(B)

Solving A nd B simultaneosly,
u= v and a=b, hence suff.

I get D, but thats not the correct answer.
Can someone pls tell me why?...have i made a fundamental mistake?. :help2

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Senior Manager
Joined: 01 Sep 2006
Posts: 297
Location: Phoenix, AZ, USA

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07 Nov 2006, 14:29
1
3
If m and n are both 2 digit numbers and m-n=11x, is x an integer?
1)The tens digit and units digit of m are the same
2) m+n is a multiple of 11.

22+11= 33 == 11*3 is an integer
22+9=31 == 11*2 + 9/11 not an integer

insuff

21+23=44 23-22 = 2 not a multiple of 11
33+11=44 33-11 = 22 is a multiple of 11

insuff

Togather

22+11=33 22-11 is multiple of 11
33+ 11=44 33-11 i multiple of 11

i think u r asuumption is wrong we need to prove if m-n=11 x if x is int u r assuming x to be int
Since m-n=11x

10(u-a)+ (v-b)=10x+x
Comparing both sides,
Director
Joined: 21 Aug 2006
Posts: 938

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07 Nov 2006, 20:34
are m and n different?

If we assume m = n, then we wont get D

Question says: "If m and n are both 2 digit numbers"

No where is it said that they are two different numbers.
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The path is long, but self-surrender makes it short;
the way is difficult, but perfect trust makes it easy.

Manager
Joined: 29 Aug 2006
Posts: 156

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07 Nov 2006, 20:55
Thanks Damager!
Hi AK, I've repeated it verbatim from Kaplan, but u do have a point!
Senior Manager
Joined: 30 Aug 2006
Posts: 364

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08 Nov 2006, 06:25
C

i) m is a mutliple of 11, INS we know nothing about n
ii) m+n is multiple of 11, INS m = 10 n = 23

Using both, m is a multiple of 11 (from i) and n must be a multiple of 11 (from ii) so remainder is multiple of 11.

point here is that m & n are a multiple of 11, then m+n and m-n are also multiples of 11.
Director
Joined: 21 Aug 2006
Posts: 938

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08 Nov 2006, 07:05
Huh..I was under impression that ZERO is not an integer..
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Joined: 09 Sep 2013
Posts: 8849
Re: If m and n are both 2 digit numbers and m-n=11x, is x an  [#permalink]

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06 Oct 2017, 08:56
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Re: If m and n are both 2 digit numbers and m-n=11x, is x an &nbs [#permalink] 06 Oct 2017, 08:56
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