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# For a positive inteer n, if p is the product of all the integers from

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Manager
Joined: 01 Nov 2017
Posts: 82
GMAT 1: 700 Q50 V35
GMAT 2: 640 Q49 V28
GMAT 3: 680 Q47 V36
GMAT 4: 700 Q50 V35
For a positive inteer n, if p is the product of all the integers from  [#permalink]

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01 Jul 2018, 02:38
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25% (medium)

Question Stats:

77% (01:05) correct 23% (01:31) wrong based on 61 sessions

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For a positive inteer n, if p is the product of all the integers from 1 to n, inclusive, and is divisible by 1,560, what is the least possible value of n?

A. 9

B. 10

C. 11

D. 12

E. 13

I was able to find out that n at least must be a 13 to have a product that is divisible by 1560 but then the question what is the LEAST possible value made me understand that they are asking for the n that is unlikely to get us such number. I was completely lost because all ABCD are correct answers. I just picked the smallest and looked at the answer which indicated the answer as E.

If answer is E, then the question probably should have sounded like "What is the smallest possible value of n"

Am I right? Please advise.

Alex
Senior Manager
Joined: 04 Aug 2010
Posts: 271
Schools: Dartmouth College
Re: For a positive inteer n, if p is the product of all the integers from  [#permalink]

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01 Jul 2018, 03:34
2
alexlearning17 wrote:
Hi everyone,

I came across the following question from Math Revolution.

For a positive inteer n, if p is the product of all the integers from 1 to n, inclusive, and is divisible by 1,560, what is the least possible value of n?

A. 9

B. 10

C. 11

D. 12

E. 13

$$p = n!$$
$$1560 = 2^3 * 3 * 5 * 13$$

For $$p$$ to be divisible by 1560, $$n!$$ must include 13.
A, B, C and D imply that n! = 9!, 10!, 11! or 12!.
Since none of these options for n! will include 13, eliminate A, B, C and D.

Quote:
I was able to find out that n at least must be a 13 to have a product that is divisible by 1560 but then the question what is the LEAST possible value made me understand that they are asking for the n that is unlikely to get us such number. I was completely lost because all ABCD are correct answers. I just picked the smallest and looked at the answer which indicated the answer as E.

If answer is E, then the question probably should have sounded like "What is the smallest possible value of n"

Am I right? Please advise.

Alex

least possible value is common wording and conveys the same meaning as smallest possible value.
An OG problem that asks for the least possible value:
https://gmatclub.com/forum/if-y-is-an-i ... 39867.html
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Manager
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Posts: 135
Re: For a positive inteer n, if p is the product of all the integers from  [#permalink]

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01 Jul 2018, 08:15
$$1560 = 2^3*3^1*5^1*13^1$$
That means that p should include all primes mentioned above
P should be >= 13 to satisfy equation above

answer P = 13
Manager
Joined: 01 Nov 2017
Posts: 82
GMAT 1: 700 Q50 V35
GMAT 2: 640 Q49 V28
GMAT 3: 680 Q47 V36
GMAT 4: 700 Q50 V35
Re: For a positive inteer n, if p is the product of all the integers from  [#permalink]

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02 Jul 2018, 02:30
Yeah, I completely understand how to do the question. The only problem I had is "least" vs "smallest"... that's weird when they consider these two words to be the same.
Re: For a positive inteer n, if p is the product of all the integers from &nbs [#permalink] 02 Jul 2018, 02:30
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# For a positive inteer n, if p is the product of all the integers from

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