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The number of distinct factors of 10

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The number of distinct factors of 10 [#permalink] New post 12 Aug 2018, 15:56
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Question Stats:

69% (00:31) correct 30% (00:27) wrong based on 66 sessions
Quantity A
Quantity B
The number of distinct factors of 10
The number of distinct prime factors of 210


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: The number of distinct factors of 10 [#permalink] New post 15 Aug 2018, 05:09
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Explanation

The factors of 10 are 1 & 10, and 2 & 5. Since there are four factors, Quantity A is 4.

The prime factors of 210 are 2, 3, 5, and 7:

Attachment:
Capture.PNG
Capture.PNG [ 63.82 KiB | Viewed 4390 times ]


Because 210 has four prime factors, Quantity B is also 4. The two quantities are equal.
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Re: The number of distinct factors of 10 [#permalink] New post 15 Aug 2018, 17:01
Factorisation is the quickest way to solve it. Since after the factorisation of 10, we'll already have the prime factors of 10, we just need to factorize 21 to get the count for 210.
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Re: The number of distinct factors of 10 [#permalink] New post 30 Jun 2020, 09:55
A doubt regarding this question

why we can't take -1 or -10 as a factor

as per the article -Technically, in the world of mathematics - the answer to this question is yes. There are negative factors and multiples of numbers. For example, -4 and -3 are factors of 12, -24 is a multiple of 3, and the factors of 4 would be -4, -2, -1, 1, 2, 4.

But what exactly does this mean in relation to the GRE and/or the GMAT?

For the GRE: This concept is mentioned in the ETS GRE Math Conventions PDF. You can find it here. The factors of an integer include both the positive and negative integers. This also applies for multiples.

Therefore, technically, if a GRE question were to ask "How many factors does 6 have?" The answer would be 8: (-6, -3, -2, -1, 1, 2, 3, 6). With that said, questions are very likely to specify "positive factors" or "positive integers" on the GRE. We haven't seen an official question before that required knowing that negative factors/multiples exist - but that doesn't mean those questions won't show up at all so you still want to be diligent about this. :)


we should consider them also.

P.S-why there is a restriction
never encountered this issue on GC
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Re: The number of distinct factors of 10 [#permalink] New post 30 Jun 2020, 10:18
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shubham2312 wrote:
A doubt regarding this question

why we can't take -1 or -10 as a factor

as per the article -Technically, in the world of mathematics - the answer to this question is yes. There are negative factors and multiples of numbers. For example, -4 and -3 are factors of 12, -24 is a multiple of 3, and the factors of 4 would be -4, -2, -1, 1, 2, 4.

But what exactly does this mean in relation to the GRE and/or the GMAT?

For the GRE: This concept is mentioned in the ETS GRE Math Conventions PDF. You can find it here. The factors of an integer include both the positive and negative integers. This also applies for multiples.

Therefore, technically, if a GRE question were to ask "How many factors does 6 have?" The answer would be 8: (-6, -3, -2, -1, 1, 2, 3, 6). With that said, questions are very likely to specify "positive factors" or "positive integers" on the GRE. We haven't seen an official question before that required knowing that negative factors/multiples exist - but that doesn't mean those questions won't show up at all so you still want to be diligent about this. :)


we should consider them also.

P.S-why there is a restriction
never encountered this issue on GC


I agree with everything you've said. Here's what the test-makers write:
Image

If this were an official GRE question, there would be some language that would restrict the factors (divisors) to POSITIVE values only.
For example: https://greprepclub.com/forum/the-numbe ... 13805.html

Unfortunately, there are several reputable test prep companies that don't add any kind of restriction (even though that restriction is implied in the official answer)
This has been a pet peeve of mine for quite a while.

Rest assured, the GRE will always have some text that restricts the factors (divisors) to POSITIVE values only.

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
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Re: The number of distinct factors of 10 [#permalink] New post 04 Jul 2020, 12:59
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Prime factors of 10- 1x10, 2x5
Prime factors of 210- 3x5x2x7

Hence Proved
4=4

therefore C

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Re: The number of distinct factors of 10   [#permalink] 04 Jul 2020, 12:59
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