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# The smallest number which, when divided by 4, 6 or 7 leaves a remainde

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Manager
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The smallest number which, when divided by 4, 6 or 7 leaves a remainde [#permalink]

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16 Oct 2010, 23:41
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The smallest number which, when divided by 4, 6 or 7 leaves a remainder of 2, is:

a) 44
b) 62
c) 80
d) 86
e) none of these
[Reveal] Spoiler: OA
Manager
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Re: The smallest number which, when divided by 4, 6 or 7 leaves a remainde [#permalink]

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17 Oct 2010, 00:01
I first find the smallest possible number which is divisible by 4,6 and 7. With a prime factorization you can easily find that this number is 84.

Therefore, 86 (84+2) will be the smallest possible number which when divided by 4, 6 or 7 leaves a remainder of 2. Hence answer should be D.
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Kudos [?]: 84 [0], given: 25

Re: The smallest number which, when divided by 4, 6 or 7 leaves a remainde [#permalink]

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17 Oct 2010, 00:17
The smallest number which, when divided by 4, 6 or 7 leaves a remainder of 2, is:
a) 44
b) 62
c) 80
d) 86
e) none of these

A number will give a remainder only when it is greater than the multiple of the divisors.
In such problems, always start with the greatest divisor. In our case 7.

Test each number with 7. We are left with 44 & 86.
Now test 44 & 86 with 6. We are left with 44 & 86.
Now test 44 & 86 with 4. We are left with 86.

Alternatively after testing with 7 we can easily see that 44 is a multiple of 4. So we only test 86 with the remaining options.

Hope this helps.
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Re: The smallest number which, when divided by 4, 6 or 7 leaves a remainde [#permalink]

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17 Oct 2010, 00:27
feruz77 wrote:
The smallest number which, when divided by 4, 6 or 7 leaves a remainder of 2, is:
a) 44
b) 62
c) 80
d) 86
e) none of these

Pls, help with a solution method!?

Right, the solutions above are correct in their own way. But the way I think about this is the following :

The set of numbers that are divisible by numbers a,b,c are {LCM,LCMx2,LCMx3,...}
So what we need to know is the LCM of 4,6,7
LCM of these numbers is 84.

So the smallest number leaving remainder 2 will be 86

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Re: The smallest number which, when divided by 4, 6 or 7 leaves a remainde   [#permalink] 17 Oct 2010, 00:27
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