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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.