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# Is positive integer x divisible by 70?

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Math Expert
Joined: 02 Sep 2009
Posts: 50708
Is positive integer x divisible by 70?  [#permalink]

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06 Feb 2018, 04:52
00:00

Difficulty:

15% (low)

Question Stats:

88% (00:30) correct 12% (00:30) wrong based on 34 sessions

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Is positive integer x divisible by 70?

(1) x is divisible by 2 and 5.

(2) x is divisible by 2 and 7.

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

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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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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? &nbs [#permalink] 06 Feb 2018, 09:04
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