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## Comment on

Combining Ratios## HI ADMIN, CAN U PLS EXPLAIN

HI ADMIN, CAN U PLS EXPLAIN ME BELOW QUE.

THE RATIO OF PENCILS' NUMBER TO THE PENS' NUMBER IS 5 TO 3. IF THE PENS' NUMBER EXCEEDS 2/5 THE PENCILS' NUMBER BY 4 , WHAT IS PENS' NUMBER?

## You bet!

You bet!

Let C = # of pencils

Let N = # of pens

"THE RATIO OF PENCILS' NUMBER TO THE PENS' NUMBER IS 5 TO 3"

So, C/N = 5/3

Cross multiply to get: 3C = 5N

"THE PENS' NUMBER EXCEEDS 2/5 THE PENCILS' NUMBER BY 4"

N = (2/5)C + 4

Multiply both sides by 5 to get: 5N = 2C + 20

We now have two equations:

3C = 5N

5N = 2C + 20

Since both equations are set equal to 5N, we can write: 3C = 2C + 20

Solve to get: C = 20

If C = 20, then N = 12

So, there are 12 pens and 20 pencils

## Got You. I often confuse with

## just to add something =)

we could also simplify 24/T=3/4 --> 8/T = 1/4

may help with more hairy problems =)

## Looks good to me!

Looks good to me!

## Hi Brent! Could you please

https://gmatclub.com/forum/the-ratio-by-volume-of-soap-to-alcohol-to-water-in-a-68933.html

## Here's my full solution:

Here's my full solution: https://gmatclub.com/forum/the-ratio-by-volume-of-soap-to-alcohol-to-wat...

Cheers,

Brent

## We can do this right?

P/B*B/T= 5/2*3/4

P/T=15/8

P=60

T=8/15*60=32

## That's a perfectly valid

That's a perfectly valid solution. Nice work!

Cheers,

Brent

## https://gmatclub.com/forum

Hi Brent , for the above question I didn’t understand the part where we have to double and halve the ratios. When I did it I doubled both the ratio terms to have 4/100 (after doubling ) and 1/50 after havle . Can you please explain me this part, why are we only changing one term

## Question link: https:/

Question link: https://gmatclub.com/forum/the-ratio-by-volume-of-soap-to-alcohol-to-wat...

Tricky question!!

Doubling both ratio terms won't double the ratio (we're told that "the ratio of soap to alcohol is doubled")

Initially, the ratio soap/alcohol = 2/50

So, doubling the ratio means the ratio soap/alcohol = 4/50

Notice that 4/50 = 2(2/2/50). That is, the ratio 4/50 is twice the ratio 2/50

In your solution you doubled both ratio terms to get 4/100. However 4/100 and 2/50 are equivalent ratios. So the ratio hasn't been doubled.

Does that help?

## Oh now i get it..if I double

Thanks Brent!!!

## https://gmatclub.com/forum/on

My thinking could possibly be wrong,

So I do get the correct solution but, I was thinking that, since 5+11 is 16, the number (which is less than 30) must divide to an integer, so only 16 would work

## Question link: https:/

Question link: https://gmatclub.com/forum/on-a-certain-sight-seeing-tour-the-ratio-of-t...

That's a good idea, but it's not quite correct.

Statement 1 houses the ratio of children to men was 5 to 11, but statement 2 tells us about the maximum number of WOMEN (which has nothing to do with the number of children and men).