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If m and z are integers, is z divisible by 11 ?

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If m and z are integers, is z divisible by 11 ? [#permalink] New post 06 Feb 2012, 08:11
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If m and z are integers, is z divisible by 11 ?

(1) m is a 2 digit number with equal units and tens digits
(2) m - z is divisible by 11
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Re: Divisibility by 11 [#permalink] New post 06 Feb 2012, 08:24
Statement 1: Tells nothing about Z. Not enough info
Statement 2: Lots of number combination will work. Not enough info

1+2= m= [99,88,77,66,55,44,33,22,11,00,-11....] Z could be the same numbers. If Z = 11,22,33 then it is divisible, but if Z was 0 then it's not divisible. Not enough info.

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Re: Divisibility by 11 [#permalink] New post 06 Feb 2012, 08:37
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If m and z are integers, is z divisible by 11?

(1) m is a 2 digit number with equal units and tens digits --> m is of a type 11, 22, ..., 99 so basically we are told that m is divisible by 11. Though still insufficient, as no info about z.

(2) m - z is divisible by 11. Clearly insufficient.

(1)+(2) {multiple of 11}-z={multiple of 11} --> z={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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Re: Divisibility by 11 [#permalink] New post 06 Feb 2012, 08:37
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kys123 wrote:
Statement 1: Tells nothing about Z. Not enough info
Statement 2: Lots of number combination will work. Not enough info

1+2= m= [99,88,77,66,55,44,33,22,11,00,-11....] Z could be the same numbers. If Z = 11,22,33 then it is divisible, but if Z was 0 then it's not divisible. Not enough info.

Ans=E


Zero is divisible by every integer except zero itself: 0/integer=0.
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Re: Divisibility by 11 [#permalink] New post 06 Feb 2012, 11:27
Thanks Bunuel. I had no idea that 0 has that type of property where is divisible by any number. I am assuming any number with no remainder after being divided is divisible. Also another question, so let's say the question was, is Z a multiple of 11 instead of divisible by 11 then the answer will be E
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Re: Divisibility by 11 [#permalink] New post 06 Feb 2012, 13:05
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kys123 wrote:
Thanks Bunuel. I had no idea that 0 has that type of property where is divisible by any number. I am assuming any number with no remainder after being divided is divisible. Also another question, so let's say the question was, is Z a multiple of 11 instead of divisible by 11 then the answer will be E


a is a multiple of b means that a=kb, for some integer k;
a is divisible by b means that a/b=integer;

Which means that a is a multiple of b is the same as a is divisible by b (just remember that 0/0 is undefined).

So, there is no difference between saying "z is divisible by 11" and "z is a multiple of 11".
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DS [#permalink] New post 07 Jun 2012, 09:55
If m and z are integers, is z divisible by 11 ?
(1) m is a two-digit number with equal tens and units digits.
(2) m - z is divisible by 11.

can anyone explain the question in a better way

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Re: DS [#permalink] New post 07 Jun 2012, 09:58
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alchemist009 wrote:
If m and z are integers, is z divisible by 11 ?
(1) m is a two-digit number with equal tens and units digits.
(2) m - z is divisible by 11.

can anyone explain the question in a better way

regards


Merging similar topics. Please ask if anything remains unclear.
_________________

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: DS   [#permalink] 07 Jun 2012, 09:58
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