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
[spoiler]OA: C
[/spoiler]
I'm basically interested in a non-algebraic approach! Too much algebra is not good for your GMAT health
Toy Tower
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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
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
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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
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
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Since the number of green bricks decreases by 1/2, the number of green bricks must be EVEN.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 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.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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Succinct and to the point. Thanks a ton for such a great explanation!GMATGuruNY wrote:Since the number of green bricks decreases by 1/2, the number of green bricks must be EVEN.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 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.
....
Regards,
Vivek
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I think you are mixing the color concept with the number of bricks required!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
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.mevicks wrote:I think you are mixing the color concept with the number of bricks required!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
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
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