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The sum of three numbers is 20. The first is four times the sum of the

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The sum of three numbers is 20. The first is four times the sum of the  [#permalink]

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New post 19 Mar 2019, 02:28
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A
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E

Difficulty:

  25% (medium)

Question Stats:

80% (02:23) correct 20% (03:17) wrong based on 30 sessions

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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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New post 19 Mar 2019, 03:27
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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.

A is the correct answer.
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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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New post 19 Mar 2019, 06:37
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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New post 21 Mar 2019, 17:52
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.

Answer: A
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The sum of three numbers is 20. The first is four times the sum of the  [#permalink]

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New post 24 Mar 2019, 07:16
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
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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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