Problem Solving

Zeppelin. I feel that pre-gmat's solution had was mis-printed. It was supposed to be written the way you have written it.

finally got it...thanks

I don't know why methods don't always work the same.

Consider this problem

A pet shop owner currently has 3 goldfish for every 5 angel fish. If she sells 60 goldfish and buys 300 angelfish, she will have 3 goldfish for every 7 angelfish. How many goldfish does she currently have.

Previously - for the Alberto / Kaye problem - there was an example where the author said to first plug in 5x - 10 / 3x + 10 but if you were to do that in the example above - you would receive the wrong answer.

The method I used for both of these was

First finding that 3K = 5A.

Then K - 10 / A + 10 = 7 / 5

5K - 50 = 7A + 70

5K = 7A + 120

You have the ratio 3K = 5A

So

Multiply everything by 3 in the equation above the 3K = 5A equation

15K = 21A + 360

15K = 25A because 3K = 5A. So 3*5 = 15 and 5*5 = 25

25A = 21A + 360

4A = 360

A = 90

A + 10 = 100

At this point you can just do the ratio

7 / 5 = X / 100.

X = 140.

Please see this link for a good explanation of this question: https://www.gmatpill.com/practice-questi ... m-student/

As for doclkk's question---actually it's not 3K=5A.

If you were trying to translate the first sentence
"A pet shop owner currently has 3 goldfish for every 5 angel fish. "

Then it should be
(Goldfish / Angel Fish) = (3/5)
Cross Multiply:
5G = 3A

So you got it mixed up there. Be careful with these wordings.

Schrute Beets wrote:The number of stamps that Kaye and Alberto had were in the ratio 5:3 respectively. After Kaye gave Alberto 10 of her stamps, the ratio of the number Kaye had to the number Alberto had was 7:5. As a result of this gift, Kaye had how many more stamps than Alberto?

A) 20
B) 30
C) 40
D) 60
E) 90

Thanks!

If you're not so good with ratios, this would be great problem to solve by guessing and checking.

When you're guessing and checking, let the answer choices guide you. Since the answer choices in this problem are all multiples of 10, let's try some multiples of 10 that satisfy K/A = 5/3:

K=50, A=30
K=100, A=60
K=150, A=90

If K gives 10 stamps to Albert, the resulting ratio is (K-10)/(A+10) = 7/5, so K-10 must be a multiple of 7.
Only K=150 works, because 150-10=140.

So let's try K=150, A=90.
K-10 = 150-10 = 140.
A+10 = 90+10 = 100.
140/100 = 14/10 = 7/5. Success!

K-A = 140-100 = 40.

The correct answer is C.

If you let the answer choices guide you, guessing and checking can be a safe and efficient way to solve many tough problems. (And no risk of making an algebraic error!)

Hi Zeppelin,

The main difference between your answer and the others is because you are calculating the number of stamps "before the exchange between Kaye & Alberto"
The clue remains directly in the question:
... As a result of this gift.... (which means that you have to calculate the number of stamps once the transaction settled.

Good luck!

K:A=5:3 ==> 3K-5A=0--------P

(K-10): (A+10)=7:5 ==> 5K-7A=120--------Q

Q- P==> 2K-2A=120

K-A=60

what's wrong with this solution? is there any help?

thank you very much!

hcwz907 wrote:K:A=5:3 ==> 3K-5A=0--------P

(K-10): (A+10)=7:5 ==> 5K-7A=120--------Q

Q- P==> 2K-2A=120

K-A=60

what's wrong with this solution? is there any help?

thank you very much!

The solution up to this point is perfect. But what you have got here is K-A i.e. the difference between Kaye's and Alberto's initial no. of stamps since you took their no. of stamps before the transaction as K & A respectively.

The question being asked is after the transaction has been performed, what is the difference between the no. of stamps..i.e.
(K-10) - (A+10) = K - A - 20

Since you have already correctly arrived at K-A = 60, the answer to the question being asked is 40.


Cheers!

I tried a solution how they usually suggest it in the OG but it doesn't work - I'm not sure why...

1) k/a = 5/3 -> k = (5/3)a
2) (k-10)/(a+10) = 7/5 -> k-10 = 7/5(a+10)
3) then plugged in (5/3)a for k, so: (5/3)a-10=(7/5)a+14
4) Solved for a: (25/3)a - (21/3)a = 24 -> (4/3)a = 24 -> a = 18
5) As I want to know k after the exchange, plugged in 18 in 2): k-10 = (7/5)*28 k = 49.2, but this can be of course not the case....
6) Then in theory substract (k-10)-(a+10)

Does anyone know where I went wrong?

The other algebraic / plug-in solutions didn't seem like something I'd naturally think of doing... Thanks!!

To solve algebraically, I would proceed as follows:

Before the exchange:
Since K:A = 5:3, let K = 5x and A = 3x.

After Kaye gives Alberto 10 stamps:
K = 5x-10, A = 3x+10.
Since the new ratio is 7:5, we get:
(5x-10)/(3x+10) = 7/5
25x - 50 = 21x + 70
4x = 120
x = 30.

Thus:
Kaye's stamps after the exchange = 5x-10 = 5*30 - 10 = 140.
Alberto's stamps after the exchange = 3x+10 = 3*30 + 10 = 100.
Difference = 140-100 = 40.

The correct answer is C.

I posted alternative approaches here:
https://www.beatthegmat.com/ratio-from-g ... 08195.html
https://www.beatthegmat.com/stamps-t85099.html[spoiler][/spoiler]