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If a number N is divisible by both 2 and 8 then which of the following 12 Aug 2017, 01:33
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A
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68% (00:34) correct 32% (00:34) wrong based on 25 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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A
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If a number N is divisible by both 2 and 8 then which of the following 12 Aug 2017, 02:05
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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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If a number N is divisible by both 2 and 8 then which of the following 13 Aug 2017, 10:09
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I thought C would be correct.. why is it wrong?
can any one explain?
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If a number N is divisible by both 2 and 8 then which of the following 13 Aug 2017, 10:39
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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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If a number N is divisible by both 2 and 8 then which of the following 13 Aug 2017, 12:19
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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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If a number N is divisible by both 2 and 8 then which of the following 14 Aug 2017, 11:59
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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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If a number N is divisible by both 2 and 8 then which of the following 14 Aug 2017, 12:07
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santro789
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.

Answer: A.
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If a number N is divisible by both 2 and 8 then which of the following 14 Aug 2017, 12:10
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Bunuel
santro789
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.

Answer: A.

11. Must or Could be True Questions



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If a number N is divisible by both 2 and 8 then which of the following 14 Aug 2017, 20:12
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Bunuel
santro789
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.

Answer: A.

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



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