Answer [spoiler]{C}[/spoiler]
Let total be x

14 = (3/8)(1/2)x - (1/3)(1/8)x
x = 96

Bricks after decrease = 96 - 14 = 82

Number of bricks to be added = 2*96 - 82 = 110

Shorter trick:

Let the total number of bricks be 8x.. So,

After Reduction: 8x - 14

The number of balls to be increased = 2(8x) - ( 8x -14) ==> 8x + 14

We need answer which is 14 more than 8 divisible

82 - 14 = 68 NOT POSSIBLE
96 - 14 = 82 NOT POSSIBLE
110 - 14 = 96 POSSIBLE
120 - 14 = 106 NOT POSSIBLE
192 - 14 = 178 NOT POSSIBLE

mevicks 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

Since the number of green bricks decreases by 1/2, the number of green bricks must be EVEN.
Since the number of blue bricks increases by 1/3, the number of blue bricks must be a MULTIPLE OF 3.
Thus, the MULTIPLIER for the ratio must be an EVEN MULTIPLE OF 3 -- in other words, a MULTIPLE OF 6.

Multiplying R:G:B = 4:3:1 by 6, we get:
R=24, G=18, B=6.
Here, if 1/2 of the green bricks are removed, and the number of blue bricks increases by 1/3, the net change = -(1/2 * 18) + (1/3 * 6) = -9 + 2 = -7.

To double the net change to -14, all of the values in the ratio must also DOUBLE:
R=48, G=36, B=12.
Thus:
T = 48+36+12 = 96 bricks.

After 14 bricks are removed, the remaining number of bricks = 96-14 = 82.
To increase this value to double the original number of bricks -- 192 -- the number of additional bricks needed = 192-82 = 110.

The correct answer is C.

GMATGuruNY wrote:

mevicks 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

Since the number of green bricks decreases by 1/2, the number of green bricks must be EVEN.
Since the number of blue bricks increases by 1/3, the number of blue bricks must be a MULTIPLE OF 3.
Thus, the MULTIPLIER for the ratio must be an EVEN MULTIPLE OF 3 -- in other words, a MULTIPLE OF 6.
....

Succinct and to the point. Thanks a ton for such a great explanation!

Regards,
Vivek

Thanks for your good discussion.
My problem with this question is that it asked number of RED bricks that are needed to be add, not green or blue!
why they are the same?

Thanks in advance

monadona wrote:Thanks for your good discussion.
My problem with this question is that it asked number of RED bricks that are needed to be add, not green or blue!
why they are the same?

Thanks in advance

I think you are mixing the color concept with the number of bricks required!

Consider this:

BIGGERTOWER - SMALLERTOWER = 14 Bricks (Color is irrelevant now)

BIGGERTOWER = 96
SMALLERTOWER = 82

Now we just need to make the SMALLERTOWER double of the BIGGERTOWER (which is the original tower) by adding ONLY A FEW BRICKS OF ONE SINGLE COLOR.
96 * 2 = 192
To make 82 reach the height of 192 we need to add 110 Bricks.
The stem says that the additional bricks are all red, so the 110 bricks are all red.

Hope it helps.

Regards,
Vivek

mevicks wrote:

monadona wrote:Thanks for your good discussion.
My problem with this question is that it asked number of RED bricks that are needed to be add, not green or blue!
why they are the same?

Thanks in advance

I think you are mixing the color concept with the number of bricks required!

Consider this:

BIGGERTOWER - SMALLERTOWER = 14 Bricks (Color is irrelevant now)

BIGGERTOWER = 96
SMALLERTOWER = 82

Now we just need to make the SMALLERTOWER double of the BIGGERTOWER (which is the original tower) by adding ONLY A FEW BRICKS OF ONE SINGLE COLOR.
96 * 2 = 192
To make 82 reach the height of 192 we need to add 110 Bricks.
The stem says that the additional bricks are all red, so the 110 bricks are all red.

Hope it helps.

Regards,
Vivek

Oh I got it.
i usually tend to make questions more complex than they really are. In the end of this question, I applied proportions again to the 110!!!!
Thank u so much