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# If 30!/10! is written as the product of consecutive integers, the larg

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If 30!/10! is written as the product of consecutive integers, the larg  [#permalink]

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Updated on: 12 Nov 2014, 04:27
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If 30!/10! is written as the product of consecutive integers, the largest of which is 30, what is the smallest of the integers?

A. 1
B. 3
C. 7
D. 11
E. 20

Originally posted by MDK on 12 Oct 2013, 04:01.
Last edited by Bunuel on 12 Nov 2014, 04:27, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: If 30!/10! is written as the product of consecutive integers, the larg  [#permalink]

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12 Oct 2013, 04:22
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Quite straight forward actually. The answer is 11.
30! = 1*2*3......*29*30
10! = 1*2*3......*9*10

So, 1 to 10 gets cancelled out and the remaining series begins with 11. (1 cannot be considered since the series has to be consecutive integers)
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Intern
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Re: If 30!/10! is written as the product of consecutive integers, the larg  [#permalink]

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12 Oct 2013, 04:03
1
lucbesson wrote:
If $$30!/10!$$ is witten as the product of consequtive integers, the largest of which is 30, what is the smallest of the integers?

Once you see the answer, the logic becames clear.
But can anyone suggest how to deal with such kind of problems?

THX!
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Re: If 30!/10! is written as the product of consecutive integers, the larg  [#permalink]

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12 Oct 2013, 04:27
MacFauz wrote:
Quite straight forward actually. The answer is 11.
30! = 1*2*3......*29*30
10! = 1*2*3......*9*10

So, 1 to 10 gets cancelled out and the remaining series begins with 11. (1 cannot be considered since the series has to be consecutive integers)

Yeahhh, you are 100% right!

I accidentally thought that the fraction transforms to 20*21*...*30, so I was looking for some very complicated method to extract 11 from 22 and make another very smart sequence ) Probably I was too tired

But thanks anyway!!!
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Re: If 30!/10! is written as the product of consecutive integers, the larg  [#permalink]

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11 Nov 2014, 16:49
1
Bunuel or WoundedTiger

I have tagged this question as I faced it in the GMAT Prep Exam pack 1, however, the original post is missing the answer choices, Can you please edit the original post to include the answer choices as follows?

A) 1
B) 3
C) 7
D) 11
E) 20

Thanks!
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Re: If 30!/10! is written as the product of consecutive integers, the larg  [#permalink]

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12 Nov 2014, 00:10
1
MDK wrote:
If $$30!/10!$$ is witten as the product of consequtive integers, the largest of which is 30, what is the smallest of the integers?

$$\frac{30!}{10!} = \frac{30 * 29 * 28........... 11 * 10!}{10!}$$

Smallest integer = 11

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Re: If 30!/10! is written as the product of consecutive integers, the larg  [#permalink]

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12 Nov 2014, 04:27
dmmk wrote:
Bunuel or WoundedTiger

I have tagged this question as I faced it in the GMAT Prep Exam pack 1, however, the original post is missing the answer choices, Can you please edit the original post to include the answer choices as follows?

A) 1
B) 3
C) 7
D) 11
E) 20

Thanks!
DmmK

Done. Thank you very much!
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If 30!/10! is written as the product of consecutive integers, the larg  [#permalink]

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18 Aug 2015, 08:25
MacFauz wrote:
Quite straight forward actually. The answer is 11.
30! = 1*2*3......*29*30
10! = 1*2*3......*9*10

So, 1 to 10 gets cancelled out and the remaining series begins with 11. (1 cannot be considered since the series has to be consecutive integers)

Hi,

Just did the GMAT test prep and this question popped up.
Basically, my first answer was the good one, 11, but after double checking, the smallest of the integers, after simplifying the 30*29*28*...*11, is actually 1, because 1*30*29*28... It is possible to breakdown any of the numbers and multiplying them by one.
So I went for 1.
Anyone could tell me from the question, how could I have decided between 11 and 1?
My understanding is that the question specifies "the product of consecutive integer" only to explain what means 30!

Thanks a lot.
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Re: If 30!/10! is written as the product of consecutive integers, the larg  [#permalink]

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29 Aug 2015, 10:31
Hi tsunagaru,

You are right that multiplying the sequence by 1 would still give the same answer. However, including 1 in the sequence would mean that the sequence is not a sequence of consecutive integers any more.

As you have mentioned, the sequence would then become 1*11*12*13.....29*30

As you can see this would not be a valid sequence.
tsunagaru wrote:
MacFauz wrote:
Quite straight forward actually. The answer is 11.
30! = 1*2*3......*29*30
10! = 1*2*3......*9*10

So, 1 to 10 gets cancelled out and the remaining series begins with 11. (1 cannot be considered since the series has to be consecutive integers)

Hi,

Just did the GMAT test prep and this question popped up.
Basically, my first answer was the good one, 11, but after double checking, the smallest of the integers, after simplifying the 30*29*28*...*11, is actually 1, because 1*30*29*28... It is possible to breakdown any of the numbers and multiplying them by one.
So I went for 1.
Anyone could tell me from the question, how could I have decided between 11 and 1?
My understanding is that the question specifies "the product of consecutive integer" only to explain what means 30!

Thanks a lot.

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Re: If 30!/10! is written as the product of consecutive integers, the larg  [#permalink]

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16 Feb 2017, 08:40
MDK wrote:
If 30!/10! is written as the product of consecutive integers, the largest of which is 30, what is the smallest of the integers?

A. 1
B. 3
C. 7
D. 11
E. 20

30!/10!

$$= \frac{30*29*28...........13*12*11*10!}{10!}$$

Thus we are left with : 30*29*28...........13*12*11

The largest number here is 30 and thus the smallest number will be 11, answer will be (D) 11
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Re: If 30!/10! is written as the product of consecutive integers, the larg  [#permalink]

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21 Feb 2017, 10:21
MDK wrote:
If 30!/10! is written as the product of consecutive integers, the largest of which is 30, what is the smallest of the integers?

A. 1
B. 3
C. 7
D. 11
E. 20

We can simplify 30!/10! to 30 x 29 x 28 x 27 x … x 13 x 12 x 11. Thus, the smallest integer is 11.

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Re: If 30!/10! is written as the product of consecutive integers, the larg  [#permalink]

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22 Feb 2017, 20:42
Hi All,

When a prompt provides you with a 'complex-looking' calculation, it can often help to come up with a much simpler example of the math involved. Here, we're asked to consider 30!/10! - and that might look 'scary' at first glance.

Instead of starting with that example, consider the following - what would 5!/3! look like...?

(5)(4)(3)(2)(1) / (3)(2)(1) = 120/6 = 20

You probably already know that when you simplify a fraction, you divide "top" and "bottom" by the same number, so we can 'cancel out' the 3, 2 and 1 from both the numerator and the denominator. This leaves us with...

(5)(4)/1 = 20

That wasn't too difficult, so now we can apply the same logic to 30!/10!... All of the numbers (10), (9)....(2) and (1) will cancel out, leaving us with...

(30)(29)....(12)(11)/1

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Director Joined: 02 Sep 2016 Posts: 720 Re: If 30!/10! is written as the product of consecutive integers, the larg [#permalink] ### Show Tags 03 Apr 2017, 05:58 30!= 1*2*3*4*5*6*7*8*9*10*11*....................*30 10!=1*2*3*4*5*6*7*8*9*10 Therefore 30!/10!= 11*12*............30 (as all common terms i.e. 10! cancel out). Thus the smallest integer is 11. _________________ Help me make my explanation better by providing a logical feedback. If you liked the post, HIT KUDOS !! Don't quit.............Do it. Intern Joined: 05 Dec 2017 Posts: 15 GMAT 1: 710 Q49 V38 Re: If 30!/10! is written as the product of consecutive integers, the larg [#permalink] ### Show Tags 04 Sep 2018, 12:38 Bunuel wrote: dmmk wrote: Bunuel or WoundedTiger I have tagged this question as I faced it in the GMAT Prep Exam pack 1, however, the original post is missing the answer choices, Can you please edit the original post to include the answer choices as follows? A) 1 B) 3 C) 7 D) 11 E) 20 Thanks! DmmK Done. Thank you very much! Hi Bunuel Can you explain to me why the answer is not 1 please? I was going to choose 11 at first and I get the logic of it as well ; however, I then thought that the smallest integer would always remain to be 1, as anything multiplied by 1 is the number itself. Where is my understanding of the question going wrong? EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12443 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 If 30!/10! is written as the product of consecutive integers, the larg [#permalink] ### Show Tags Updated on: 04 Sep 2018, 13:10 1 Hi sssjav, On Test Day, the GMAT questions that you will face will all be specifically written, so you have to pay careful attention to the details in each prompt. Here, we're told that 30!/10! is to be written as the product of CONSECUTIVE integers and we're asked for the SMALLEST number in that 'string' of integers. If you're comfortable "reducing" the fraction, then you know the result will be: (30)(29)....(12)(11)/1 Remember that we're looking for the smallest integer in the CONSECUTIVE string of those integers. We have to 'work down' from 30...29....28... etc. The number '1' is not included because the numbers 2, 3, 4,....8, 9 and 10 are NOT in that string. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Originally posted by EMPOWERgmatRichC on 04 Sep 2018, 12:58.
Last edited by EMPOWERgmatRichC on 04 Sep 2018, 13:10, edited 1 time in total.
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Re: If 30!/10! is written as the product of consecutive integers, the larg  [#permalink]

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04 Sep 2018, 13:01
EMPOWERgmatRichC wrote:
Hi sssjav,

On Test Day, the GMAT questions that you will face will all be specifically rewritten, so you have to pay careful attention to the details in each prompt. Here, we're told that 30!/10! is to be written as the product of CONSECUTIVE integers and we're asked for the SMALLEST number in that 'string' of integers.

If you're comfortable "reducing" the fraction, then you know the result will be:

(30)(29)....(12)(11)/1

Remember that we're looking for the smallest integer in the CONSECUTIVE string of those integers. We have to 'work down' from 30...29....28... etc. The number '1' is not included because the numbers 2, 3, 4,....8, 9 and 10 are NOT in that string.

GMAT assassins aren't born, they're made,
Rich

Makes sense, thank you.
Re: If 30!/10! is written as the product of consecutive integers, the larg &nbs [#permalink] 04 Sep 2018, 13:01
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