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

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Re: If 30!/10! is written as the product of consecutive integers, the larg [#permalink]
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MDK wrote:
If $$\frac{30!}{10!}$$ 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

$$\frac{30!}{10!} = \frac{(30)(29)(28)(27)(26). . . . . (13)(12)(11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)}{(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)}$$

$$= (30)(29)(28)(27)(26). . . . . (13)(12)(11)$$

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

GMAT assassins aren't born, they're made,
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Re: If 30!/10! is written as the product of consecutive integers, the larg [#permalink]
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.
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Re: If 30!/10! is written as the product of consecutive integers, the larg [#permalink]
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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?
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If 30!/10! is written as the product of consecutive integers, the larg [#permalink]
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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

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]
This question confused me cuz it's too easy.. I spent unnecessary extra time to think that there might be a trap...
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Re: If 30!/10! is written as the product of consecutive integers, the larg [#permalink]
30!= 30 * 29 * 28 ...... *13*12*11*10*9.........3*2*1

10! = 10*9.........3*2*1

$$\frac{30! }{ 10!}$$ = $$\frac{30 * 29 * 28 ...... *13*12*11*10*9.........3*2*1}{ 10*9.........3*2*1}$$

=> 30*29*28......*13*12*11

=> 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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Bunuel, looks like this Q misses the Gmatprep tag, please add. Thanks!
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Re: If 30!/10! is written as the product of consecutive integers, the larg [#permalink]
nhatanh811 wrote:
Bunuel, looks like this Q misses the Gmatprep tag, please add. Thanks!

_____________________
Added the tag. Thank you.
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