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# If a, b, and c are integers such that the product of a, b and c is 20

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If a, b, and c are integers such that the product of a, b and c is 20 [#permalink]
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Bunuel wrote:
If a, b, and c are integers such that the product of a, b and c is 20 and $$c > 4 > a \geq b$$. Which of the following could be the value of b + a?

A. 11
B. 10
C. 8
D. 2
E. –10

$$abc=20 \implies ab > 0$$.
Hence, $$c>4 \implies ab>5$$ $$\implies (a+b)^2 \geq 4ab>20 > 16 = 4^2$$ $$\implies -4 \leq a+b \leq 4$$

It's clear that the remain choice is D.
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Re: If a, b, and c are integers such that the product of a, b and c is 20 [#permalink]
Given,
abc=20
20 can be written as,
20=1x20
=2x10
=4x5
=5x4
=10x2
=20x1
abc=(c)x(ab)
Since c>4,c can be 5,10,20.This means ab can be 4,2,1
Case1:ab=4
(a,b)=((1,4),(2,2),(4,1)).This means a+b can be 5,4
Case2:ab=2
(a,b)=((2,1),(1,2)).This means a+b can be 3
Case3:ab=1
(a,b)=((1,1)).This means a+b can be 2
Also,c>b,a
So,a+b can be 2,3
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Re: If a, b, and c are integers such that the product of a, b and c is 20 [#permalink]
Bunuel wrote:
If a, b, and c are integers such that the product of a, b and c is 20 and $$c > 4 > a \geq b$$. Which of the following could be the value of b + a?

A. 11
B. 10
C. 8
D. 2
E. –10

We are given that a, b, and c are integers such that the product of a, b, and c is 20 and c > 4 > a ≥ b.

We see that c must be greater than 4, and that a and b must be less than 4 but could also equal each other.

Let’s list out some possible options for the values of a, b, and c, noting that their product must be 20.

a = 1, b = 1, c = 20

We see that in this case a + b = 1 + 1 = 2, which is answer D.

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Re: If a, b, and c are integers such that the product of a, b and c is 20 [#permalink]
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Re: If a, b, and c are integers such that the product of a, b and c is 20 [#permalink]
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