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# How many of the integers that satisfy the inequality (a+1)(a+2)(a+4)

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Current Student
Joined: 27 May 2014
Posts: 524
GMAT 1: 730 Q49 V41
How many of the integers that satisfy the inequality (a+1)(a+2)(a+4)  [#permalink]

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29 Mar 2017, 01:24
1
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Difficulty:

65% (hard)

Question Stats:

45% (01:37) correct 55% (01:43) wrong based on 97 sessions

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How many of the integers that satisfy the inequality (a+1)(a+2)(a+4) ≥ 0 are less than 4?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

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Posts: 274
Location: India
GMAT 1: 570 Q48 V22
GMAT 2: 640 Q49 V28
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Re: How many of the integers that satisfy the inequality (a+1)(a+2)(a+4)  [#permalink]

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29 Mar 2017, 01:32
1
saswata4s wrote:
How many of the integers that satisfy the inequality (a+1)(a+2)(a+4) ≥ 0 are less than 4?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

(a+1)(a+2)(a+4) ≥ 0 means when a={-1,-2,-4} the value of (a+1)(a+2)(a+4) = 0

But
when a=0 (a+1)(a+2)(a+4) = 1*2*4 > 0
when a=1 (a+1)(a+2)(a+4) = 2*3*5 > 0
when a=2 (a+1)(a+2)(a+4) = 3*4*6 > 0
when a=3 (a+1)(a+2)(a+4) = 4*5*7 > 0
and when a=-3 (a+1)(a+2)(a+4) = (-2)*(-1)*1 > 0

So 8 integers that satisfy the inequality (a+1)(a+2)(a+4) ≥ 0 which are less than 4

Hence option E is correct
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How many of the integers that satisfy the inequality (a+1)(a+2)(a+4)  [#permalink]

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29 Mar 2017, 01:50
1
saswata4s wrote:
How many of the integers that satisfy the inequality (a+1)(a+2)(a+4) ≥ 0 are less than 4?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

Solve for the inequality $$(a+1)(a+2)(a+4) ≥ 0$$ using factor table with sign, we have $$a \in [-4, -2] \cup [-1, +\infty)$$

Since $$a$$ is integer and $$a<4$$, we have $$a \in \{-4,-3,-2,-1,0,1,2,3\}$$

The answer is E.
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Re: How many of the integers that satisfy the inequality (a+1)(a+2)(a+4)  [#permalink]

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14 Apr 2017, 16:58
Hello,

Here is a short video to explain a smart way of solving this question. If you get the concept explained in the video, the question can be solved in 60 seconds or less.

https://youtu.be/ZIgKyR7oN88

I have covered this concept in detail on my conceptual post today-
https://gmatclub.com/forum/gmat-quant-o ... l#p1836874

All the best!
Maxximus
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Re: How many of the integers that satisfy the inequality (a+1)(a+2)(a+4)  [#permalink]

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04 Feb 2019, 04:06
saswata4s wrote:
How many of the integers that satisfy the inequality (a+1)(a+2)(a+4) ≥ 0 are less than 4?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

The range to satisfy above inequality will be between

-4 <= 0 <= 3

E
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Re: How many of the integers that satisfy the inequality (a+1)(a+2)(a+4)   [#permalink] 04 Feb 2019, 04:06
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# How many of the integers that satisfy the inequality (a+1)(a+2)(a+4)

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