Simple Math Problem involving ratios. Tell me how to solve it.

[TommyVercetti]

This is not homework, I am not even in school. I am studying for the GMAT, and this is one of the questions in the book. They just give you a small hint saying "Not all problems use the Ratio box" and that is all.

Tell me how to solve this problem, explain me the method, and any other helpful tips you use to solve ratios.

If the ratio of X to Y is 3 to 2, and the ratio of Y to Z is 5 to 4, then the ratio of X to Z is

A) 15/6

B) 15/8

C) 4/5

D) 8/15

E) 1/2

 

[pillage2001]

B and I'm a lousy teacher so no teaching. I might be wrong too.

 

[Stojakapimp]

um...i'm not sure how to do it mathematically, but you can multiply Y to Z by 2 to get 10 to 8...so now X to Y is something to 10....to get 10 from 2 you have to multiply by 5, so multiply the 3 by five to get 15. So X to Z is 15 to 8

 

[silverpig]

X/Y = 3/2
Y/Z = 5/4

Y = 2X/3 from the first one
Y = 5Z/4 from the second one

Y = Y so

2X/3 = 5Z/4

8X = 15Z

X/Z = 15/8

 

[dman]

I'm guessing B,using rusty algebra, but I'm probably not doing something right.

Rusty Algebra:

x/y = 3/2

y/z = 5/4

then:
y=(5/4)z

Then substitute Y into first equation

x/[(5/4)*z]=3/2

Do the math... to simplify multiply both sides by (5/4):

x/z=(3/2)(5/4)

x/z=15/8

or x:z = 15:8

But because I haven't done this in like 10yrs I'm not postive I did it right. I'm happy knowing others came up with the same answer though.

 

[nd]

X/Y = 3/2

Y/Z = 5/4

Problem: Find X/Z

Rewrite equations to get substitution for X and Z since we want X/Z:
X = Y*(3/2)
Z = Y/(5/4) = Y*(4/5)

X/Z = Y*(3/2) / Y*(4/5)
X/Z = (3/2) / (4/5) = (3/2) * (5/4) = 15/8

 

[screw3d]

As explained by the previous three posts, yes. It's a simple question..

 

[OulOat]

This is just unit conversion.

miles per hour * hours per min = miles per min.
60 miles/ 1 hour * 1 hour/ 60 mins = 1 mile/ 1 min

X per Y * Y per Z = X per Z.
(3X/ 2Y) * (5Y/ 4Z) = 15X/ 8Z.

No need to make it more complex by subsitution and stuff, just multiply the ratios since Y cancels out (its in both the numerator and denominator).

 

[ohtwell]

I think it's B!

X to Y = 3 to 2
Y to Z = 5 to 4

I found a common denominator between the two values of Y, and then multiplied the other part of the ratio by the LCD of the two Ys. In this instance the LCD was 10

X to Y = 15 to 10
Y to Z = 10 to 8

Therefor,

X to Z = 15 to 8

You can't reduce that so that's your final answer. I think that's right!


: ) Amanda

 

[chowderhead]

for me this is TOO much math ... look for patterns.
X is bigger than Y, Y is bigger than Z therefore X is bigger than Z. Eliminate answers C, D, E.
It's hard to explain the thought process but if you want speed you don't really have time to write all these formulas or write all this math down ... so do it mentally.
I have to have x=15 (from the remaining choices) so I mutiple 3x5 for X for 15 and 2x5 for Y. Y becomes 10. Well to balance the ratios, 10 is twice as much as 5 so I assume you mutiple Z by 2 which will give you eight.
I think you should go with whatever thought process will give you accurate/reliable answers quickly. Eliminate wrong choices as sometimes it may be faster to work "backwards" from the various answers (i.e. plugging in the various answers) than forwards to get the answers. Good luck in your prep work.