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

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If m and n are both two digit numbers and m-n = 11x, is x an [#permalink] New post 30 May 2012, 12:36
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If m and n are both two digit numbers and m-n = 11x, is x an integer?

(1) The tens digit and the units digit of m are same
(2) m+n is a multiple of 11
[Reveal] Spoiler: OA
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Re: If m and n are both two digit numbers and m-n = 11x, is x an [#permalink] New post 31 May 2012, 01:24
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If m and n are both two digit numbers and m-n = 11x, is x an integer?

The question basically asks whether m-n is a multiple of 11.

(1) The tens digit and the units digit of m are same --> m could be: 11, 22, 33, ..., 99 --> m is a multiple of 11. Not sufficiient since no info about n.

(2) m+n is a multiple of 11 --> if m=n=11 then the m-n is a multiple of 11 but if m=12 and n=10 then m-n is NOT a multiple of 11. Not sufficient.

(1)+(2) From (1) we have that m={multiple of 11} and from (2) we have that m+n={multiple of 11} --> {multiple of 11}+n={multiple of 11} --> n={multiple of 11} --> m-n={multiple of 11}-{multiple of 11}={multiple of 11}. Sufficient.

Answer: C.

Below might help to understand this concept better.

If integers a and b are both multiples of some integer k>1 (divisible by k), then their sum and difference will also be a multiple of k (divisible by k):
Example: a=6 and b=9, both divisible by 3 ---> a+b=15 and a-b=-3, again both divisible by 3.

If out of integers a and b one is a multiple of some integer k>1 and another is not, then their sum and difference will NOT be a multiple of k (divisible by k):
Example: a=6, divisible by 3 and b=5, not divisible by 3 ---> a+b=11 and a-b=1, neither is divisible by 3.

If integers a and b both are NOT multiples of some integer k>1 (divisible by k), then their sum and difference may or may not be a multiple of k (divisible by k):
Example: a=5 and b=4, neither is divisible by 3 ---> a+b=9, is divisible by 3 and a-b=1, is not divisible by 3;
OR: a=6 and b=3, neither is divisible by 5 ---> a+b=9 and a-b=3, neither is divisible by 5;
OR: a=2 and b=2, neither is divisible by 4 ---> a+b=4 and a-b=0, both are divisible by 4.

Hope it's clear.
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If M and N are both two digit numbers and M-N=11X, is X an [#permalink] New post 14 Nov 2012, 07:27
If M and N are both two 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

I have a problem with this.
Two digit numbers means 13, 24... OR can it also be 22.1 (with decimal/fraction)?

I dont have the OA and thats why im asking..
btw, any good resources here to deal with multiples and divisors?
thanks.
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Re: If M and N are both two digit numbers and M-N=11X, is X an [#permalink] New post 14 Nov 2012, 07:30
Expert's post
roygush wrote:
If M and N are both two 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

I have a problem with this.
Two digit numbers means 13, 24... OR can it also be 22.1 (with decimal/fraction)?

I dont have the OA and thats why im asking..
btw, any good resources here to deal with multiples and divisors?
thanks.


Merging similar topics.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If m and n are both two digit numbers and m-n = 11x, is x an [#permalink] New post 10 Sep 2013, 21:25
Hi Banuel,

one confusion here.

from (1) we know that m is a multiple of 11. we also know that m-n= multiple of 11.
now, if we consider m to be 99 than , 99-n=multiple of 11. can we have any other 2 digit no. which is NOT a multiple of 11 for n in this case ? I think no. so effectively shouldn't the answer be A ? Have I missed something here ?
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Re: If m and n are both two digit numbers and m-n = 11x, is x an [#permalink] New post 10 Sep 2013, 23:17
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vishalrastogi wrote:
Hi Banuel,

one confusion here.

from (1) we know that m is a multiple of 11. we also know that m-n= multiple of 11.
now, if we consider m to be 99 than , 99-n=multiple of 11. can we have any other 2 digit no. which is NOT a multiple of 11 for n in this case ? I think no. so effectively shouldn't the answer be A ? Have I missed something here ?


The highlighted portion is the problem. When you say (m-n) is a multiple of 11, that implies that you ARE saying that x IS an integer. But that is something which is in-fact being asked. You can't assume it while solving for the question stem.
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Re: If m and n are both two digit numbers and m-n = 11x, is x an [#permalink] New post 16 Feb 2014, 08:52
First we know that m is a a multiple of 11 but we still don’t know anything about 'n' therefore insufficient. Then we know that m+n is a multiple of 11 but that doesn't mean that they are both multiples of 11, it could be that they are both not non multiples of 11. Both together since m is a multiple of 11 then n must also be a multiple of 11. The difference of two multiples of 11 is always a multiple of 11. Thus answer is C

Hope this clarifies

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Re: If m and n are both two digit numbers and m-n = 11x, is x an   [#permalink] 16 Feb 2014, 08:52
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