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Math Expert V
Joined: 02 Sep 2009
Posts: 59587
The sum of three numbers is 20. The first is four times the sum of the  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 79% (02:22) correct 21% (03:08) wrong based on 34 sessions

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The sum of three numbers is 20. The first is four times the sum of the other two. The second is seven times the third. What is the product of all three?

(A) 28
(B) 40
(C) 100
(D) 400
(E) 800

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Posts: 1489
Concentration: Accounting, Finance
GPA: 3.68
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Re: The sum of three numbers is 20. The first is four times the sum of the  [#permalink]

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Bunuel wrote:
The sum of three numbers is 20. The first is four times the sum of the other two. The second is seven times the third. What is the product of all three?

(A) 28
(B) 40
(C) 100
(D) 400
(E) 800

3rd = x

2 nd = 7x

1 st = 4(x + 7x ) = 32x.

x + 7x + 32x = 20

x = 1/2.

we are looking for product = x*7x*32x = 1/2 * 7 * 1/2 * 32*1/2 = 1/2 * 1/2 * 1/2 * 32 * 7 = 28.

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Concentration: Sustainability, Marketing
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Re: The sum of three numbers is 20. The first is four times the sum of the  [#permalink]

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Bunuel wrote:
The sum of three numbers is 20. The first is four times the sum of the other two. The second is seven times the third. What is the product of all three?

(A) 28
(B) 40
(C) 100
(D) 400
(E) 800

a+b+c=20
a=4*(b+c)
b=7c
so
4b+4c+7c+c=20
40c=20
c=1/2
b= 7/2
a= 16
so a*b*c = 16*7/4 = 28
IMO A
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Re: The sum of three numbers is 20. The first is four times the sum of the  [#permalink]

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Bunuel wrote:
The sum of three numbers is 20. The first is four times the sum of the other two. The second is seven times the third. What is the product of all three?

(A) 28
(B) 40
(C) 100
(D) 400
(E) 800

We can let the numbers be a, b, and c; thus:

a + b + c = 20

and

a = 4(b + c)

a = 4b + 4c

and

b = 7c

Substituting, we have:

a = 4(7c) + 4c

a = 32c

Substituting again, we have:

32c + 7c + c = 20

40c = 20

c = 1/2, so b = 7/2, and a = 4(7/2 + 1/2) = 4(4) = 16.

The product of all 3 numbers is:

16 x 7/2 x 1/2 = 16 x 7/4 = 28.

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GMAT 1: 680 Q49 V34 The sum of three numbers is 20. The first is four times the sum of the  [#permalink]

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Bunuel wrote:
The sum of three numbers is 20. The first is four times the sum of the other two. The second is seven times the third. What is the product of all three?

(A) 28
(B) 40
(C) 100
(D) 400
(E) 800

Given
a+b+c=20
a=4*(b+c)
b=7c

=> 40c=20
=> c=1/2 and b= 7/2
=> a= 16

a*b*c = 16*1/2*7/2
=> 28

Option A is the correct choice The sum of three numbers is 20. The first is four times the sum of the   [#permalink] 24 Mar 2019, 07:16
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