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If m and z are integers, is z divisible by 11 ? [#permalink]
 06 Feb 2012, 09:11
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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]
06 Feb 2012, 09:24
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.
Ans=E
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Re: Divisibility by 11 [#permalink]
06 Feb 2012, 09:37
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]
06 Feb 2012, 09:37
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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]
06 Feb 2012, 12:27
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]
06 Feb 2012, 14:05
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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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
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