Data Sufficiency

Carol spends 1/4 of her savings on a stereo and 1/3 less than she spent on the stere for a television. What fraction of her savings did she spend on the stereo and television?

a)1/4
b)2/7
c)5/12
d)1/2
e)7/12

please can anyone help me understand how to break down the process to obtain the answer

Many ways. Pick a smart number.

In this case, pick 12, since lcm of 4 and 3 = 12. You can pick 24, 36, etc. it doesnt matter.

let 12 be savings.

spent 3 on a stereo.
2/3 of stereo = 2 on tv.

stereo + tv = 5

5/total = 5/12.

algebraically you can solve as follows:
x= amount spent.

on stereo = x/4
on tv = (x/4)*(2/3) = 2x/12 = x/6 (note: 1- 1/3 = 2/3)
total spent = x/4 + x/6 = 3x/12 + 2x/12 = 5x/12 = 5/12 *x.

hope that helps.

palvarez wrote:Many ways. Pick a smart number.

In this case, pick 12, since lcm of 4 and 3 = 12. You can pick 24, 36, etc. it doesnt matter.

let 12 be savings.

spent 3 on a stereo.
2/3 of stereo = 2 on tv.

stereo + tv = 5

5/total = 5/12.

Thanks for this. Im still having a bit of difficulty with understanding how you obtain the fraction spent 2/3 of stereo on tv. when the qustion says a 1/3 less?

starz982 wrote:

palvarez wrote:Many ways. Pick a smart number.

In this case, pick 12, since lcm of 4 and 3 = 12. You can pick 24, 36, etc. it doesnt matter.

let 12 be savings.

spent 3 on a stereo.
2/3 of stereo = 2 on tv.

stereo + tv = 5

5/total = 5/12.

Thanks for this. Im still having a bit of difficulty with understanding how you obtain the fraction spent 2/3 of stereo on tv. when the qustion says a 1/3 less?

x is 1/3 less of y ---> x = (1-1/3)y or 2y/3

starz982 wrote:Carol spends 1/4 of her savings on a stereo and 1/3 less than she spent on the stere for a television. What fraction of her savings did she spend on the stereo and television?

a)1/4
b)2/7
c)5/12
d)1/2
e)7/12

please can anyone help me understand how to break down the process to obtain the answer

Hi starz982,

Picking numbers to make the problem less fuzzy is a great approach in word problems. And, if you get good at it, you will also understand the algebra much better.

In word problems involving fractions, picking the lowest common denominator is a great way to go. We see that the two denominators are 3 and 4. The lowest common denominator is 3*4 = 12.

Let her savings be 12.

She spent 1/4 of this on a stereo. What's 1/4 of 12? ...3, of cousre. So she spent 3 bucks on the stereo (what is this, the 70s?). And she spent on the television one-third less than what she spent on the stereo. Well, she spent 3 bucks on the stereo.

What number is 1/3 less than 3?
This can be read as "what number is 3 minus one-third of 3?"
A third of 3 is: 1/3*3 = 1. So, the number that is 1/3 less than 3 is: 3-1 = 2. So she spent 2 bucks on the TV.

She spent 3 + 2 bucks on the stereo and TV, for a total of 5. She started with 12. So the fraction of her savings spent on the TV and stereo is: 5/12, and choose Choice C.

I thought I would paste the IM conversation for others to learn from the questions.

starz982] Thanks for this. Im still having a bit of difficulty with understanding how you obtain the fraction spent 2/3 of stereo on tv. when the qustion says a 1/3 less?[/quote] the information given said that tv was 1/3 less than stereo which is the same thing as saying tv is 2/3 of stereo. try it out with made up numbers - if stereo costs 60 and tv is 1/3 less, this means tv = 60 - (1/3*60) = 40. 40/60 = 2/3 hence tv costs 2/3 of stereo. [quote= wrote: This is how I see it. 1/3 less spent on tv would mean 1/3*60 = 20

yes a '1/3' of 60 = 20 but 'a 1/3 less' than 60 = 40. this is because a 1/3 = 20, total = 60 and so '1/3 less' than 60 = 60-20 = 40

Hope that helps.

Thak you all for your help!!

It makes sense to me now.