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## Comment on

Hockey versus Football## Alternately we can solve it

Since we are dealing with ratios we can eliminate choices B and D as they are not divided by both 5 (2+3) and 8 (5+3).

Working with 40 we can see that it can be divided in ratio of 2:3 (25,15) but taking 18 from 25 to 15 doesn't give us a ratio of 3:5. Similarly 120 can be eliminated. In fact we would have got the answer 80 if we started working with option C as we usually do.

## Great approach - I love it!

Great approach - I love it!

The great/interesting thing about GMAT math questions is that they can typically be solved using more than one approach.

## Hi Sandy

Can I please request you to explain how you arrived at 5(2+3) and 8(5+3)

Thanks

## Dear JSN

On Friday the ratio is 2:3, therefore, the total number of fans has to be divisible by 5 (2+3). That means our answer cannot be 72 or 108 because these numbers cannot be split into ratio of 2:3 without using fractions. Next day the ratio becomes 5:3 when 18 fans switch over side (from football to hockey). It means that if we split our number into ratio of 2:3 (hockey:football) and then move 18 from football to hockey, the ratio of hockey to football must become 5:3. for example, if number of fans is 40 then on Friday the ratio is 16:24 (2:3) but if we move 18 from football to hockey it will become 34:6 which is not equal to (5:3). Similarly we can eliminate 120. In case of 80 the ratio on Friday will be 32:48 and on Saturday 50(32+18):30(48-18) which is equal to 5:3, hence the answer.

## Thank you Sandy :)

## Alternately it could be :

Since, 3H = 2F. We could just substitute it in the second eq. to get the value of F directly and hence find H.

## Hey!

I solved this in another way. I gave the ratios variables.

So Fri - 2x:3x and Sat - 5y:3y.

So the two equations are - 3x-18=3y and 2x+18=5y.

Now in this way, I need solve only for one variable. I solve for y, get it as 10 and add 5(10)+3(10)=80.

Is this a valid approach?

## Perfectly valid!

Perfectly valid!

## and alternatively - just plug

## Perfect!

Perfect!

## Can this be solved with 1

## You bet.

You bet.

GIVEN: On Friday, the ratio of hockey fans to football fans was 2/3

Let 2x = number of hockey fans

So, 3x = number of football fans

(notice that these values ensure that the ratio = 2/3)

GIVEN: On Saturday, 18 football fans became hockey fans

So, 2x + 18 = number of hockey fans on SATURDAY

And 3x - 18 = number of football fans on SATURDAY

GIVEN: the ratio of hockey fans to football fans became 5/3

So: (2x + 18)/(3x - 18) = 5/3

Cross multiply: 3(2x + 18) = 5(3x - 18)

Expand: 6x + 54 = 15x - 90

Solve: x = 16

So, the number of hockey fans on Friday = 2(16) = 32

So, the number of football fans on Friday = 3(16) = 48

TOTAL number of fans = 32 + 48 = 80

Cheers,

Brent

## You guys are awesome. Thanks

## Like more people suggested in

80/ 5 (because the ratio is 2:3) = 16

Hockey players: 2 * 16 = 32 | Football players 3 * 16 = 48 -> (32 + 48 = 80)

Hockey players: 32 + 18 = 50 | Football players 48 - 18 = 30 -> 50 + 30 = 80 as well

I do understand that the algebraic equations need to be practiced for questions where the tactic of checking answer choices is less convenient ;).

Cheers,

Glenn

## That's a perfectly valid

That's a perfectly valid approach, especially when you start with the correct answer :-)

It's hard to say whether testing the answer choices would be the fastest approach if one had to test 3 or 4 answer choices.

Cheers,

Brent

## Hi, what is the level of this

## I'd say this is a medium

I'd say this is a medium-difficulty question (between 500 and 600).

## can i write 2f-3h = 0 ?

## Absolutely.

Absolutely.

Since the ratio of hockey fans to football fans is 2 to 3, we can write: H/F = 2/3

Cross multiply to get: 2F = 3H

Subtract 3H from both sides to get: 2F - 3H

## Hi Brent,

I tried using this method but could not get the answer:

Since 18 members increased the ratio from (1) 2:3 to (2) 5:3. I thought that would make sense that ratio 5-2 = 3 mean 3 ratio = 18 members. Thus, 1 ratio = 6 members. If there is a total if 8 ratios (5+3), then total number of fans is 8*6 = 48.

May I know what is wrong with this?

## That method will work, but

That method will work, but for a slightly different question type.

Your solution would work if the question told us that 18 NEW hockey fans were added to the group, and the ratio changed to 5 to 3.

However, in the given question, 18 people stopped being football fans and switched to being hockey fans.