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# How many integers n satisfy (n – 5) (n – 10) – 3(n – 2) ≤ 0 ?

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Math Expert
Joined: 02 Sep 2009
Posts: 64243
How many integers n satisfy (n – 5) (n – 10) – 3(n – 2) ≤ 0 ?  [#permalink]

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02 Apr 2020, 09:47
00:00

Difficulty:

65% (hard)

Question Stats:

58% (01:35) correct 42% (02:30) wrong based on 19 sessions

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How many integers n satisfy $$(n – 5) (n – 10) – 3(n – 2) ≤ 0$$ ?

A. 8
B. 9
C. 10
D. 11
E. 12

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CEO
Joined: 03 Jun 2019
Posts: 2904
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
Re: How many integers n satisfy (n – 5) (n – 10) – 3(n – 2) ≤ 0 ?  [#permalink]

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02 Apr 2020, 09:54
Bunuel wrote:
How many integers n satisfy $$(n – 5) (n – 10) – 3(n – 2) ≤ 0$$ ?

A. 8
B. 9
C. 10
D. 11
E. 12

Asked: How many integers n satisfy $$(n – 5) (n – 10) – 3(n – 2) ≤ 0$$ ?

(n – 5) (n – 10) – 3(n – 2) ≤ 0
n^2 - 15n + 50 - 3n + 6 ≤ 0
n^2 - 18n + 56 ≤ 0
n^2 - 14n - 4n + 56 ≤ 0
(n-14)(n-4) ≤ 0
4 ≤ n ≤ 14
n = {4,5,6,7,8,9,10,11,12,13,14}: 11 integers

IMO D
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Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
Re: How many integers n satisfy (n – 5) (n – 10) – 3(n – 2) ≤ 0 ?   [#permalink] 02 Apr 2020, 09:54