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Re: An integer X is a multiple of 8 [#permalink]
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snowbrood wrote:
why did u omit option A 16 is also correct along with option B and option C as 16 means 2*2*2*2 and the multiples are 8 14 33 which have factors 2*2*2*(2*7)*(3*11) or am i missing something


No 16 is not a factor.

We can rewrite the numbers in terms of factors:

\(8 = 2^3\)

\(14 = 2\times 7\)

\(33 = 3^11\)

So X must have = 2^3 \times 3 \times 7 \times 11.

\(16= 2^4\) This may not be a factor. For example, 1848 is a possible value of X but \(\frac{1848}{16}=115.5\)
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Re: An integer X is a multiple of 8 [#permalink]
sandy wrote:
snowbrood wrote:
why did u omit option A 16 is also correct along with option B and option C as 16 means 2*2*2*2 and the multiples are 8 14 33 which have factors 2*2*2*(2*7)*(3*11) or am i missing something


No 16 is not a factor.

We can rewrite the numbers in terms of factors:

\(8 = 2^3\)

\(14 = 2\times 7\)

\(33 = 3^11\)

So X must have = 2^3 \times 3 \times 7 \times 11.

\(16= 2^4\) This may not be a factor. For example, 1848 is a possible value of X but \(\frac{1848}{16}=115.5\)




But, 8*14*33 is 3696, which is a factor of 16. So why not option A?
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Re: An integer X is a multiple of 8 [#permalink]
Preetham wrote:
sandy wrote:
snowbrood wrote:
why did u omit option A 16 is also correct along with option B and option C as 16 means 2*2*2*2 and the multiples are 8 14 33 which have factors 2*2*2*(2*7)*(3*11) or am i missing something


No 16 is not a factor.

We can rewrite the numbers in terms of factors:

\(8 = 2^3\)

\(14 = 2\times 7\)

\(33 = 3^11\)

So X must have = 2^3 \times 3 \times 7 \times 11.


\(16= 2^4\) This may not be a factor. For example, 1848 is a possible value of X but \(\frac{1848}{16}=115.5\)




But, 8*14*33 is 3696, which is a factor of 16. So why not option A?


As shown above, 16 does not satisfy the condition all times, For instance, when divided by 3696, it gives us a factor, but in case of 1848 it doesn't. Similarly, the other two numbers (24,77) always satisfy the condition.
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Re: An integer X is a multiple of 8 [#permalink]
BUT HOW ARE WE SUPPOSED TO KNOW THAT 16 WILL NOT BE INCLUDED
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Re: An integer X is a multiple of 8 [#permalink]
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akkaur0310 wrote:
BUT HOW ARE WE SUPPOSED TO KNOW THAT 16 WILL NOT BE INCLUDED


Sir, this is a hard question due to the fact that it has a trap in it. We need to crosscheck each and every option before selecting the answer. In this case, if one does not crosscheck for other numbers which have same multiples (like 1848), then they've fallen for the trap.
You're not supposed to know everything, such questions check how aware you're of the fact that there are other multiples of the given number other than 3696.
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Re: An integer X is a multiple of 8 [#permalink]
Can anyone explain elaborately.
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Re: An integer X is a multiple of 8 [#permalink]
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sukrut96 wrote:
akkaur0310 wrote:
BUT HOW ARE WE SUPPOSED TO KNOW THAT 16 WILL NOT BE INCLUDED


Sir, this is a hard question due to the fact that it has a trap in it. We need to crosscheck each and every option before selecting the answer. In this case, if one does not crosscheck for other numbers which have same multiples (like 1848), then they've fallen for the trap.
You're not supposed to know everything, such questions check how aware you're of the fact that there are other multiples of the given number other than 3696.



I see one simple way of doing this. just take the LCM of all the multiple and then check for factors
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Re: An integer X is a multiple of 8 [#permalink]
Hey, I have a problem understanding the formulation of this question.

'An integer X is a multiple of 8, 14 and 33. WHich of the following is a factor of X.'

Answers B and C are definitely correct.
But why A and D cannot also be a factor?
It doesn't mention that 8, 14, and 33 are the only multiple factors of X. I would understand it if at some way,
the question would limit it to 'only'.
I think this is also what other people here had a problem with.
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Re: An integer X is a multiple of 8 [#permalink]
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When a number is a multiple of other numbers X,Y,and Z it must be at the intersection of those numbers that has all the factors that in the end X will contain.

It is like a building block of a wall: you take a brick here and there and when you complete the puzzle you will have X

To have x you nee the 2,3,7, and 11 or a combination of these

A and D does not have

A has one the two
D has only the three

Please refer to the following https://gre.myprepclub.com/forum/gre-ma ... tml#p95905
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Re: An integer X is a multiple of 8 [#permalink]
why is a 4th 2 not included in X = (2)(2)..... when considering the prime factorization of 14?

for example, why is X not (2)(2)(2)(2)(7)(3)(11)
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Re: An integer X is a multiple of 8 [#permalink]
Shouldn't this question contain the word 'MUST'?

"An integer X is a multiple of 8, 14 and 33. Which of the following 'MUST BE' a factor of X."

Otherwise all answers can be correct.
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Re: An integer X is a multiple of 8 [#permalink]
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