CAT 4 Question #22 " Kali builds a tower using only red, gre

[briant851]

"Kali builds a tower using only red, green, and blue toy bricks in a ratio of 4:3:1. She then removes of the green bricks and adds 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?"

**I am not sure how they were able to get (41/6)x for the new total of bricks. Can anyone please explain?***

Kali builds a tower using only red, green, and blue toy bricks in a ratio of 4:3:1. She then removes of the green bricks and adds 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?

[RonPurewal]

"Kali builds a tower using only red, green, and blue toy bricks in a ratio of 4:3:1. She then removes of the green bricks and adds 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?"

presumably there's supposed to be a fraction between the red words?

there should definitely be something there.

please double-check. thanks.

[briant851]

"she removes 1/2 of the green bricks. and adds 1/3 of the blue bricks"

[tim]

I'm going to post the correct text of the question here, since the original poster has now incorrectly transcribed it twice:

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?

Since this is a ratios question, we will use an unknown multiplier:
Original numbers - 4x red bricks, 3x green bricks, x blue bricks
After the adjustment - 4x red bricks, 3/2 x green bricks, 4/3 x blue bricks

Add these together and you get:

4 + 3/2 + 4/3 = 24/6 + 9/6 + 8/6 = 41/6

Does that help?

[briant851]

Yes thank You

[tim]

You're welcome!

[RonPurewal]

Yes thank You

you're welcome.

[JohannaH678]

Is there any alternate strategies that can be used on this problem? I was thinking we can't use smart numbers because 14 bricks is given. Perhaps working backwards or estimation? I understand how to do it with algebra but was hoping to get better at using alternate strategies especially on the harder 700-800 level questions.

[RonPurewal]

presumably the problem has multiple-choice options -- so it should (at least theoretically) be possible to backsolve from those options.
that may not be any easier than solving the problem "forward"—but, as always, the point is just to develop as many techniques as possible.

as per the forum rules, we need the ENTIRE problem AS ORIGINALLY PROVIDED, INCLUDING ALL ANSWER CHOICES, before we can continue the discussion. (in fact, the existing discussion shouldn't even have happened without the answer choices.)
thanks.

[JohannaH678]

Kali builds a tower using only red, green, and blue toy bricks in a ratio of 4:3:1. She then removes of the green bricks and adds 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

[RonPurewal]

She then removes of the green bricks...

^^ you're definitely missing something there...

[JohannaH678]

The fractions didn't copy over:

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

[RonPurewal]

yeah, this problem is going to be extremely annoying to backsolve, because the question contains a reference to the number of bricks in the original tower.

honestly, it's not worth posting the backsolving solution here, since (1) it's MUCH more complicated than the "forward" solution, and (2) it requires the same skill set anyway—in other words, anyone who understands how to backsolve this problem would also be able to solve it in the "forward" direction.
if you are at the very top of the quant scoring scale, it could be a "fun activity" to try to figure out how to backsolve this problem, but... otherwise, no real pedagogical value there.