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# If a number N is divisible by both 2 and 8 then which of the following

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If a number N is divisible by both 2 and 8 then which of the following  [#permalink]

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12 Aug 2017, 01:33
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25% (medium)

Question Stats:

66% (00:23) correct 34% (00:21) wrong based on 38 sessions

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If a number N is divisible by both 2 and 8, then which of the following statements must be true?

I. N is divisible by 4
II. N is divisible by 6
III. N is divisible by 16

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

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Re: If a number N is divisible by both 2 and 8 then which of the following  [#permalink]

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12 Aug 2017, 02:05
Imo 1 only . A is the answer.
Suppose if not=8.
Then it's divisible by 4 but not by 6 or 16.

Thus A wins

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Re: If a number N is divisible by both 2 and 8 then which of the following  [#permalink]

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13 Aug 2017, 10:09
I thought C would be correct.. why is it wrong?
can any one explain?
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Re: If a number N is divisible by both 2 and 8 then which of the following  [#permalink]

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13 Aug 2017, 10:39
pclawong wrote:
I thought C would be correct.. why is it wrong?
can any one explain?

Suppose we chose the number 8. It's divisible by both 4 ad 8 but not by 16. So it cannot be C .

Hope it helps.

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Re: If a number N is divisible by both 2 and 8 then which of the following  [#permalink]

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13 Aug 2017, 12:19
When N is divisible by 2 and 8 means, N has at least 3 2s in it (because 8 = 2x2x2). With this information given, look at the options:
1. Is N divisible by 4 --- Yes, because 4 = 2x2
2. Is N divisible by 6 --- Don't know for sure, because 6 = 2x3. From the given information, we don't know if N has a 3 in it.
3. Is N divisible by 8 --- Don't know again, because 8 = 2x2x2x2. From the given information again, we don't know if N has 4 2s in it.

Because this is a "Must" question, we know for sure that N is divisible by 4.
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Re: If a number N is divisible by both 2 and 8 then which of the following  [#permalink]

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14 Aug 2017, 11:59
Am not sure If I got the correctly. If we assume N=48. Then It would be divisible by 4, 6 and 16. Then options dont make sense. Please help me understand the question. where am going wrong?
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Re: If a number N is divisible by both 2 and 8 then which of the following  [#permalink]

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14 Aug 2017, 12:07
santro789 wrote:
Am not sure If I got the correctly. If we assume N=48. Then It would be divisible by 4, 6 and 16. Then options dont make sense. Please help me understand the question. where am going wrong?

If a number N is divisible by both 2 and 8, then which of the following statements must be true?

I. N is divisible by 4
II. N is divisible by 6
III. N is divisible by 16

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

Notice that the question asks "which of the following statements must be true", not "which of the following statements could be true". While N could be divisible by any number, it must be divisible only by some of the numbers.

Generally if a positive integer x is divisible by positive integers a and b, then it will be divisible by the least common multiple of a and b. Thus since N is divisible by both 2 and 8, then it will be divisible by the LCM(2, 8), which is 8. If N is divisible by 8, then it's divisible by every factor of 8: 1, 2, 4, and 8. Therefore, only option A MUST be true.

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Re: If a number N is divisible by both 2 and 8 then which of the following  [#permalink]

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14 Aug 2017, 12:10
Bunuel wrote:
santro789 wrote:
Am not sure If I got the correctly. If we assume N=48. Then It would be divisible by 4, 6 and 16. Then options dont make sense. Please help me understand the question. where am going wrong?

If a number N is divisible by both 2 and 8, then which of the following statements must be true?

I. N is divisible by 4
II. N is divisible by 6
III. N is divisible by 16

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

Notice that the question asks "which of the following statements must be true", not "which of the following statements could be true". While N could be divisible by any number, it must be divisible only by some of the numbers.

Generally if a positive integer x is divisible by positive integers a and b, then it will be divisible by the least common multiple of a and b. Thus since N is divisible by both 2 and 8, then it will be divisible by the LCM(2, 8), which is 8. If N is divisible by 8, then it's divisible by every factor of 8: 1, 2, 4, and 8. Therefore, only option A MUST be true.

11. Must or Could be True Questions

For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
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If a number N is divisible by both 2 and 8 then which of the following  [#permalink]

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14 Aug 2017, 20:12
Bunuel wrote:
santro789 wrote:
Am not sure If I got the correctly. If we assume N=48. Then It would be divisible by 4, 6 and 16. Then options dont make sense. Please help me understand the question. where am going wrong?

If a number N is divisible by both 2 and 8, then which of the following statements must be true?

I. N is divisible by 4
II. N is divisible by 6
III. N is divisible by 16

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

Notice that the question asks "which of the following statements must be true", not "which of the following statements could be true". While N could be divisible by any number, it must be divisible only by some of the numbers.

Generally if a positive integer x is divisible by positive integers a and b, then it will be divisible by the least common multiple of a and b. Thus since N is divisible by both 2 and 8, then it will be divisible by the LCM(2, 8), which is 8. If N is divisible by 8, then it's divisible by every factor of 8: 1, 2, 4, and 8. Therefore, only option A MUST be true.

Adding on to what Bunuel explained, we can write $$N = 8K$$

Now, $$\frac{N}{4} = \frac{8k}{4} =$$ Always an Integer

$$\frac{N}{6} = \frac{8k}{6} =$$ May or may not be an integer, depending upon the value of k (if $$k=1$$, $$\frac{N}{6}$$ is not an integer, but if $$k=3$$, $$\frac{N}{6}$$ is an integer)

$$\frac{N}{16} = \frac{8k}{16} =$$ May or may not be an integer, depending upon the value of k (if $$k=1$$, $$\frac{N}{16}$$ is not an integer, but if $$k=2$$, $$\frac{N}{16}$$ is an integer)

Hence only I must be true . Option A

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
If a number N is divisible by both 2 and 8 then which of the following   [#permalink] 14 Aug 2017, 20:12
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