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# DIVISIBILITY

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Intern
Joined: 08 Apr 2014
Posts: 2
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09 Apr 2014, 11:09

Is X divisible by 119

1) x is divisible by 17
2) x is divisible by 7

Is X divisible by 96

1)x is divisible by 6
2)x is divisible by 16

My question is that how in the first the answer is together SUFFICIENT and in the second both INSUFFICIENT?

Thank you.
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09 Apr 2014, 11:46
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Let x = 48.
Then x is not divisible by 96, but is divisible by 6 and 16.
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10 Apr 2014, 01:27
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Expert's post
nikolas7 wrote:

Is X divisible by 119

1) x is divisible by 17
2) x is divisible by 7

Is X divisible by 96

1)x is divisible by 6
2)x is divisible by 16

My question is that how in the first the answer is together SUFFICIENT and in the second both INSUFFICIENT?

Thank you.

In the first problem, you are given that 17 and 7 are factors of x. Both are prime numbers hence you cannot make them using any other numbers. So 17*7 = 119 must be a factor of x.

In the second question, first statement tells you that 2 and 3 are factors of X.
The second statement tell you that four 2s are factors of X.
Together, you know that four 2s and a 3 are factors of X. That is 48 is a factor of X. But is 96? We don't know. Note that 6 and 16 have a common 2. Hence we cannot say that x must be divisible by 6*16 = 96.
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17 Apr 2014, 11:51
nikolas7 wrote:

Is X divisible by 119

1) x is divisible by 17
2) x is divisible by 7

Is X divisible by 96

1)x is divisible by 6
2)x is divisible by 16

My question is that how in the first the answer is together SUFFICIENT and in the second both INSUFFICIENT?

Thank you.

Hey

One way of solving such problems is to find Least common multiple of the two numbers.
In first problem - LCM of 17 and 7 is 119. So X will definitely be divisible by 119
In second problem - LCM of 16 and 6 is 48. So X will definitely be divisible by 48. But may or may not be divisible by 96.
Re: DIVISIBILITY   [#permalink] 17 Apr 2014, 11:51
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