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

Question

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

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

Bunuel · Accepted Answer

Original ratio = R:G:B = 4x:3x:x.
Original total = 4x + 3x + x = 8x.

The new number of bricks: 4x, 3x/2, 4x/3.
New total = 4x + 3x/2 + 4x/3 = 41x/6.

We are told that {Original total} - {New total} = 14 --> 8x - 41x/6 = 14 --> x = 12.

Original total = 8x = 96;
New total = 41x/6 = 82.

To double the original number of bricks, or simply to have 2*96 = 192 bricks, she need to add 192 - 82 = 110.

Answer: C.

Autoboat · Answer

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.

bekerman · Answer

Isn't the question asking for the total 'red bricks' to build the tower? In the sense, wouldn't it be 8x (target) - 4x (current), which would be 48? I know that wasn't among the answers choices so that is why I was confused when I was doing this one. Thanks!

Bunuel · Answer

The question asks how many red bricks will she need   to add   in order  to double  the total number of bricks used to build the  original tower   ?

bekerman · Answer

Sorry, I still don't follow this. If there were 4x red bricks in the original tower and we want to double that, it would be 8x red bricks (+ however many green and blue bricks but that seems to be irrelevant). So why is it not 4x?

MalfuriousP · Answer

They want to double the original amount of blocks, not just the red blocks

the original tower had 96 bricks, the new tower has 82 bricks and the question is asking how many extra red blocks are needed to build a tower of 192 bricks (double the original: 96*2).

192-82 = 110

so 110 bricks need to be added to the new 82 brick tower to double the original.

They worded the question as  how many red bricks need to be added  but really it could be any colour just that 110 more bricks need to be there to equal 192

PareshGmat · Answer

Red ............ Green .......... Blue ........... Total

4x ................ 3x .............. x .................... 8x

After addition / removal of bricks   (No need to solve as 8x gets cancelled)

4x ................  3x - \frac{3x}{2}  ......  x+ \frac{x}{2}  ........... 8x-14

Setting up the equation:

4x + 3x - \frac{3x}{2} + x+ \frac{x}{2} = 8x - 14

\frac{3x}{2} - \frac{x}{2} = 14

x = 12

Double of initial bricks used = 16 * x = 192

Bricks after addition / removal = 8x-14 = 82

Additional bricks required = 192 - 82 = 110 (Colour should not matter)

Answer = C

MathRevolution · Answer

Let the total number of bricks = 96 (4:3:1 happens to be 8 parts, so considered multiple of 8 close to 100.Also, keep in mind that the units obtained should be divisible by 2 and 3 i.e. divisible by 6)

Red: 48 units
Green: 36 units
Blue: 12 units

Removes 1/2 of the green bricks: 36 - 18 = 18 left
Adds 1/3 more blue bricks: 12 + 4 = 16.

Total bricks now : 48 + 18 + 16 = 82.

Reduced size = 96 - 14 = 82 units.

We need length to be 96 * 2 = 192 units.

We need 192 - 82 = 110 units more (Only red).

Answer C

RajatJ79 · Answer

Bunuel  ,  MathRevolution  - Would the following be a correct way of solving the question:

Original ratio = R:G:B = 4x:3x:x. Hence, Original total = 4x + 3x + x = 8x. (multiple of 8)
Size of the tower has been reduced by 14 bricks.

Hence, the number of red bricks to be added to double the size of original tower would be in the form  14 + original total , written as:  14 + multiple of 8

Only option C correctly fits the above condition.  110 = 14 + 96 
Hence, answer is Option C.

Kinshook · Answer

Given: 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.

Asked: How many red bricks will she need to add in order to double the total number of bricks used to build the original tower?

Let the red, green and blue toy bricks used be 4k, 3k & k respectively.

Green bricks removed = 3k/2
Blue bricks added = k/3

Change = 3k/2 - k/3 = 14
7k/6 = 14
k = 12

Bricks used in original tower = 4k + 3k + k = 8k = 96
Green bricks removed = 3k/2 = 18
Blue bricks added = k/3 = 4

Red bricks to be added = 96 + 14 = 110

IMO C

A2D2 · Answer

How to know where to take different variables and where same, I tried taking x,y,z and got stuck

Bunuel · Answer

Notice that if we reduce x we get the given ratio of 4:3:1. If you use x, y, and z instead, you don't get the original ratio.

x there is a positive multiple (1, 2, 3, ...), which shows that the number of red, green, and blue bricks could be:

4*1 = 4, 3*1 = 3, and 1*1 = 1, for x = 1; 
4*2 = 8, 3*2 = 6, and 1*2 = 2, for x = 2; 
4*3 = 12, 3*3 = 9, and 1*3 = 3, for x = 3; 
...

Generally, if we are told that say the number of boys to girls in a certain class is 2 to 1, then this could be expressed as B:G = 2x:x, where x is a positive multiple.

btsaami · Answer

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

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

We use options to find the correct answer. Given R:G:B= 4:3:1 Total bricks used= 8x
When G is reduced by half we and 1/3 more blue is added, the size is reduced by 14Therefore becomes 8X-14.

To this, we will add extra red to achieve the height (2*8x)
= 16x.
No. of red bricks added = 16x-(8x-14) = 8x+14

Verify from options, 8x+14=110 --> 8x=110-14 = 96. i.e. 96 is divisible by 8 hence 110 is the answer.

Other options don't fulfill the condition as above. Hence, C

nikita.nanda1810 · Answer

Bunuel Is the original ratio given in this question just to help find 'k', since adding 110 will change the original ratio. I reached the point where 110 extra bricks are required but didn't tally why only 110 red extra are required since the ratio would not be maintained.

Appreciate your explanation.

Thanks!

Appreciate your explanation.

Thanks!

Bunuel · Answer

The original ratio is just to find 'x'. After that the ratio is no longer a concern.

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=87465 --- Harsha GMAT-Club-Forum-7byps07z.png

Sarvam · Answer

“How many red bricks will she need to add in order to double the total number of bricks used to build the original tower?”

What it does NOT say:

It does NOT say: add bricks of any color

It does NOT say: restore the original ratio

It does NOT say: ignore color

It specifically says: red bricks

So color absolutely matters.

hence the answer should be 96 option B anyone can confirm?

shivani1351 · Answer

Let the number of red, green, and blue bricks that Kali uses initially be 4x, 3x, and x respectively.
Let the size of this initial tower be 't'. Thus, t = 8x

After removing 1/2 of the green bricks and adds 1/3 more blue bricks: the number of bricks becomes = 4x+(3x-1.5x)+(x+x/3) = 41x/6
As it is given that the size of the tower gets reduced by 14 bricks:

41x/6 = t-14

We can write this as: 41x/6 = 8x-14 (as t = 8x)

Solving this, we get the value of x = 12. Thus, t = 96 (original tower size) and the size of the new tower is 82 (i.e. 96-14).
We need to double the total number of bricks used to build the original tower, hence, we need to make the size of the tower as 192. Thus, the total number of red bricks to be added = 192-82 = 110

Hence, the correct option is Option (C) 110 (Answer)

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

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