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

Question

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

kumarparitosh123 · Answer

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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pclawong · Answer

I thought C would be correct.. why is it wrong?
can any one explain?

kumarparitosh123 · Answer

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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Blackbox · Answer

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.

santro789 · Answer

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?

Bunuel · Answer

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.

Answer: A.

Bunuel · Answer

11. Must or Could be True Questions 
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For more check  Ultimate GMAT Quantitative Megathread

Hope it helps.

niks18 · Answer

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

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

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