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# If n=(81!  − 80!  + 79!)/(79!), which of the following could be subtr

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Math Expert
Joined: 02 Sep 2009
Posts: 50617
If n=(81!  − 80!  + 79!)/(79!), which of the following could be subtr  [#permalink]

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05 Apr 2016, 06:49
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Difficulty:

15% (low)

Question Stats:

87% (01:40) correct 13% (03:08) wrong based on 39 sessions

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If n=(81!  − 80!  + 79!)/(79!), which of the following could be subtracted from n so that √n is an integer?

A. 1
B. 2
C. 3
D. 4
E. 5

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Math Expert
Joined: 02 Aug 2009
Posts: 7035
If n=(81!  − 80!  + 79!)/(79!), which of the following could be subtr  [#permalink]

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05 Apr 2016, 07:02
Bunuel wrote:
If n=(81!  − 80!  + 79!)/(79!), which of the following could be subtracted from n so that √n is an integer?

A. 1
B. 2
C. 3
D. 4
E. 5

hi,

first lets find n..
$$n=\frac{(81! − 80! + 79!)}{(79!)}$$..
$$n=\frac{81! }{79!} − \frac{80!}{79!} + \frac{79!}{79!}$$..
$$n=81*80 - 80 + 1 = 80(81-1) +1 = 80^2 +1$$
so what should be subtracted from$$80^2+1$$, so that it becomes a perfect square ..
ans is 1, as $$80^2-1+1=80^2$$

A
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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If n=(81!  − 80!  + 79!)/(79!), which of the following could be subtr &nbs [#permalink] 05 Apr 2016, 07:02
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