Problem Solving

BTGModeratorVI wrote: ↑

Wed Oct 07, 2020 7:16 am

If 45% of z is 120% of y and y is 75% of x, what percent of x is z?

A. 200
B. 160
C. 100
D. 65
E. 50

Answer: a
Source Cole and Princeton Review

One approach is to find values that satisfy the given information.

y is 75% of x
So it could it be the case x = 400 and y = 300

45% of z is (equals) 120% of y
120% of y = (1.2)(300) = 360
So, 45% of z = 360
In other words, 0.45z = 360
Divide both sides by 0.45 to get: z = 800

What percent of x is z?
In other words: What percent of 400 is 800?
Another way to phrase this is: 800 is what percent of 400?
Since 800 is TWICE 400, we can also conclude that 800 is 200 percent of 400

Answer: A

Cheers,
Brent

BTGModeratorVI wrote: ↑

Wed Oct 07, 2020 7:16 am

If 45% of z is 120% of y and y is 75% of x, what percent of x is z?

A. 200
B. 160
C. 100
D. 65
E. 50

Answer: a

Solution:

We can create the equations:

0.45z = 1.2y

and

y = 0.75x

We need to determine the value of z/x * 100.

Solving the first equation, we have:

y = 0.45z/1.2 = 4.5z/12 = 9z/24 = 3z/8

Substituting y = 3z/8 into the second equation, we have:

3z/8 = 0.75x

3z/8 = 3x/4

z/x = 3/4 * 8/3

z/x = 2

Therefore, z/x * 100 = 2 * 100 = 200.

Answer: A