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The expression n! is defined as the product of the integers from 1 thr

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The expression n! is defined as the product of the integers from 1 thr  [#permalink]

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New post 30 Jul 2018, 21:52
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The expression n! is defined as the product of the integers from 1 through n. If p is the product of the integers from 100 through 299 and q is the product of the integers from 200 through 299, which of the following is equal to p/q?

A. 99!
B. 199!
C. 199!/99!
D. 299!/99!
E. 299!/199!

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(PS01656)

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Re: The expression n! is defined as the product of the integers from 1 thr  [#permalink]

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New post 30 Jul 2018, 22:15
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Bunuel wrote:
The expression n! is defined as the product of the integers from 1 through n. If p is the product of the integers from 100 through 299 and q is the product of the integers from 200 through 299, which of the following is equal to p/q?

A. 99!
B. 199!
C. 199!/99!
D. 299!/99!
E. 299!/199!

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(PS01656)


OA:C

\(p =\frac{{299!}}{{99!}}\)

\(q =\frac{{299!}}{{199!}}\)

\(\frac{p}{q}=\frac{\frac{{299!}}{{99!}}}{\frac{{299!}}{{199!}}}\)

\(\frac{p}{q}=\frac{{299!}}{{99!}}*\frac{{199!}}{{299!}}=\frac{{199!}}{{99!}}\)
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Re: The expression n! is defined as the product of the integers from 1 thr  [#permalink]

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New post 30 Jul 2018, 21:59
200 through 299 will cancel out leaving 100 through 199.
It can be written as 199!/99!.
C should be the ans.

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Re: The expression n! is defined as the product of the integers from 1 thr  [#permalink]

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New post 03 Aug 2018, 15:01
1
Bunuel wrote:
The expression n! is defined as the product of the integers from 1 through n. If p is the product of the integers from 100 through 299 and q is the product of the integers from 200 through 299, which of the following is equal to p/q?

A. 99!
B. 199!
C. 199!/99!
D. 299!/99!
E. 299!/199!


The quotient p/q is the product of the integers from 100 to 199, inclusive, since the product of the integers from 200 to 299, inclusive, appears in both p and q and thus it gets canceled out.

We can consider the product of the integers from 100 to 199, inclusive, as the product of the integers from 1 to 199, inclusive, divided by the product of the integers from 1 to 99, inclusive. That is,

p/q = the product of the integers from 100 to 199, inclusive = 199!/99!

Answer: C
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Re: The expression n! is defined as the product of the integers from 1 thr  [#permalink]

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New post 05 Aug 2018, 05:37
Bunuel wrote:
The expression n! is defined as the product of the integers from 1 through n. If p is the product of the integers from 100 through 299 and q is the product of the integers from 200 through 299, which of the following is equal to p/q?

A. 99!
B. 199!
C. 199!/99!
D. 299!/99!
E. 299!/199!

NEW question from GMAT® Quantitative Review 2019


(PS01656)


Given,
p=100*101*102*.......................*298*299 and
q=200*201*202*.......................*298*299
Thus, \(\frac{p}{q}\)=\(\frac{101*102*103*.......................*298*299}{200*201*202*.......................*298*299}\)=100*101*102*--------------*198*199=\(\frac{1*2*3*.................*198*199}{1*2*3*...............*98*99}\)=\(\frac{199!}{99!}\)

Ans. (C)
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Re: The expression n! is defined as the product of the integers from 1 thr &nbs [#permalink] 05 Aug 2018, 05:37
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