Problem Solving

First, i want to say that this is a great site. This is my first post. I just got the kaplan math workbook to brush up on my math. And wouldn't you know it, i am stumped on one of the problems in the quizes. I just can't understand the explanation. I will type out the problem and the corrct answer. Could someone please tell me how the arrived at the answer?

If x, and y, and z are all positive and 0.04x=5y=2z, then which of the following is true?

x<y<z
x<z<y
y<x<z this was my answer
y<z<x this is the correct answer
z<y<x

The explanation is that since all the terms are positive, we know that it takes more y's than z's to equal one x. Therefore, x is the biggest, followed by z, and y is the smallest.

Wouldn't y be the largest? Followed by z and then ending in x? If anyone has the same book, the question is on page 23 and the answer is on page 77. Thanks for the help.

If x, and y, and z are all positive and 0.04x=5y=2z, then which of the following is true?

x<y<z
x<z<y
y<x<z this was my answer
y<z<x this is the correct answer
z<y<x

One of the easiest ways to solve this type of question is by picking numbers.

Since 0.04x is the weirdest of the terms, let's let x=100. Therefore, 0.04x = (.04)100 = 4

So, we have 0.04x = 5y = 2z, which becomes 4 = 5y = 2z

if 5y = 4, then y = 4/5. If 2z =4, then z = 4/2 = 2

Therefore, x=100, z =2, y = 4/5. The order is x > z > y. Flip that around to get (d).

If you want to compare the variables without picking numbers, then it's easiest if you get rid of the decimal first.

Since 0.04 = 4/100 = 1/25, we can just multiply all 3 terms by 25 to get:

x = 125y = 50z

so, it takes 125 y's to make 50 z's or 1 x. Therefore, x is the biggest, followed by z, followed by y.

edit: forgot to turn of html, messed up my first post, sorry!

Wouldn't y be the largest? Followed by z and then ending in x?

With this reasoning you should have picked answer B, why did you pick D ?

basically if 5x = 2y, then one of the possible solution is x = 2 and y = 5.... and 2 is greater than 5. and if we look back at the equation, variable with bigger multiplier is smaller

DarNoor wrote:First, i want to say that this is a great site. This is my first post. I just got the kaplan math workbook to brush up on my math. And wouldn't you know it, i am stumped on one of the problems in the quizes. I just can't understand the explanation. I will type out the problem and the corrct answer. Could someone please tell me how the arrived at the answer?

If x, and y, and z are all positive and 0.04x=5y=2z, then which of the following is true?

x<y<z
x<z<y
y<x<z this was my answer
y<z<x this is the correct answer
z<y<x

The explanation is that since all the terms are positive, we know that it takes more y's than z's to equal one x. Therefore, x is the biggest, followed by z, and y is the smallest.

Wouldn't y be the largest? Followed by z and then ending in x? If anyone has the same book, the question is on page 23 and the answer is on page 77. Thanks for the help.

multiply everything by 100
4x=500y=200z
x=125y=50z
so definitely x is the largest of all
Now for y and z, we have 5y=2z
or z=2.5y
So, z is greater than y
so we got x>z>y or y<z<x