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Kali builds a tower using only red, green, and blue toy bric

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Joined: 24 Aug 2016
Posts: 29
Re: Kali builds a tower using only red, green, and blue toy bric  [#permalink]

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New post 04 Sep 2016, 12:55
1
I found it more intuitive to solve like this:

R : G : B
4 : 3 : 1

G = 3B
(1/3)B - (1/2)G = -14
(1/3)B - (1/2)3B = -14
B = 12

R : G : B
48 : 36 : 12 = 96

96 - (1/2)G + (1/3)B =
96 - 18 + 4 = 82

96 x 2 = 192 - 82 = 110



Though I will concede the method above is probably quicker and uses (arguably) simpler math.
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Location: United States (CA)
GMAT 1: 710 Q45 V41
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Re: Kali builds a tower using only red, green, and blue toy bric  [#permalink]

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New post 28 May 2017, 12:24
Bunuel wrote:
Kali builds a tower using only red, green, and blue toy bricks in a ratio of 4:3:1. She then removes 1/2 of the green bricks and adds 1/3 more blue bricks, reducing the size of the tower by 14 bricks. How many red bricks will she need to add in order to double the total number of bricks used to build the original tower?

A. 82
B. 96
C. 110
D. 120
E. 192


First use the hidden multipliers to set up the ratios to the problem:

R:G:B:total
4x:3x:1x = 8x total

Now we know that 14 bricks were removed, so the new total is 8x - 14

Re-doing the ratios gives you 4x:3x/2:4/3x

The sum of these parts is 41x/6, a quantity equal to 8x - 14
We then determine x = 12

So to double the original tower of 8x, we need 16x bricks, all of which will be red.

The incremental value is 16x - (8x - 14) or 16x - 41x/6. Substituting x = 12 we find the total number of new bricks = 110.
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Re: Kali builds a tower using only red, green, and blue toy bric  [#permalink]

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New post 27 Jul 2018, 21:52
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Re: Kali builds a tower using only red, green, and blue toy bric &nbs [#permalink] 27 Jul 2018, 21:52

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