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Is positive integer x divisible by 70?

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Is positive integer x divisible by 70? [#permalink]

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New post 06 Feb 2018, 04:52
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Is positive integer x divisible by 70? [#permalink]

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New post 06 Feb 2018, 09:00
Bunuel wrote:
Is positive integer x divisible by 70?

(1) x is divisible by 2 and 5.

(2) x is divisible by 2 and 7.


\(70=2*5*7\)

for \(x\) to be divisible by \(70\) it must have all \(2\), \(5\) & \(7\) as factors

Statement 1: nothing mentioned about \(7\). Insufficient

Statement 2: Nothing mentioned about \(5\). Insufficient

Combining 1 & 2: we know \(x\) is divisible by \(2\), \(5\) & \(7\), hence \(x\) must be divisible by \(70\). Sufficient

Option C
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Re: Is positive integer x divisible by 70? [#permalink]

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New post 06 Feb 2018, 09:04
Bunuel wrote:
Is positive integer x divisible by 70?

(1) x is divisible by 2 and 5.

(2) x is divisible by 2 and 7.


70 when prime-factorized gives us 2*5*7.
So we need to check if the number is divisible by 2,5, and 7.

1. x being divisible by 2 and 5 is not enough, since
we don't know if x is divisible by 7 (Insufficient)

2. x being divisible by 2 and 7 is not enough, since
we don't know if x is divisible by 5 (Insufficient)

On combining the information given in both the statements,
we can clearly tell that x is divisible by 70 (Sufficient - Option C)
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Re: Is positive integer x divisible by 70?   [#permalink] 06 Feb 2018, 09:04
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Is positive integer x divisible by 70?

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