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The number of stamps that Kaye and Alberto had were in the

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Re: The number of stamps that Kaye and Alberto had were in the  [#permalink]

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New post 11 Oct 2016, 09:35
2
kilukilam wrote:
The number of stamps that Kaye and Alberto had were in the ration of 5:3 respecctively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto

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


Lets work -
Quote:
The number of stamps that Kaye and Alberto had were in the ration of 5:3 respectively.

Attachment:
1.PNG
1.PNG [ 1.09 KiB | Viewed 1912 times ]

Quote:
After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5.

Attachment:
2.PNG
2.PNG [ 1.48 KiB | Viewed 1911 times ]

So, \(\frac{(5x-10)}{(3x+10)} = \frac{7}{5}\)

Or, \(25x - 50 = 21x + 70\)

Or, \(4x = 120\)

Or, \(x = 30\)

We are asked to find -
Quote:
As a result of the gift, Kaye had how many more stamps than Alberto


Or, (5x-10) - (3x+10) => 2x - 20

Or, 2(30) - 20 =40

Hence answer is (C) 40

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Re: The number of stamps that Kaye and Alberto had were in the  [#permalink]

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New post 11 Oct 2016, 15:37
The number of stamps that Kaye and Alberto had were in the ratio of 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 the gift, Kaye had how many more stamps than Alberto?

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

let x=total stamps
5/8*x-10=7/12*x
x=240
7/12*240=140
5/12*240=100
140-100=40
C.
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Re: The number of stamps that Kaye and Alberto had were in the  [#permalink]

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New post 11 Oct 2016, 16:01
kilukilam wrote:
The number of stamps that Kaye and Alberto had were in the ration of 5:3 respecctively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto

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


We are given that the number of stamps that Kaye and Alberto had were in the ratio 5 : 3. We can represent this as:

K : A = 5x : 3x

We are next given that after Kaye gave Alberto 10 of her stamps, the ratio of the number Kaye had to the number Alberto had was 7 : 5. Using this information we can create the following equation:

(5x – 10)/(3x + 10)= 7/5

5(5x – 10) = 7(3x + 10)

25x – 50 = 21x + 70

4x = 120

x = 30

Kaye now has 5(30) – 10 = 140 stamps and Alberto has 3(30) + 10 = 100 stamps. So Kaye has 140 – 100 = 40 more stamps than Alberto.

Answer: C
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Re: The number of stamps that Kaye and Alberto had were in the  [#permalink]

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New post 28 Mar 2017, 13:44
this is a very very very! tricky question,
to avoid the trick I advise to write down from the beginning what the question asks, and this is: (5x-10)-(3x+10)

let's make up an equation:
(5x-10)/(3x+10)=7/5
we will find that x=30
Let's put it into the required formula above: (5*30-10)-(3*30+10)=40
be careful not to use ration 7:5, because it has no relation to x
this is where the whole trick is

Answer is C
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Re: The number of stamps that Kaye and Alberto had were in the  [#permalink]

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New post 11 May 2017, 05:16
The number of stamps that Kaye and Alberto had were in the ration of 5:3 respecctively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto

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

Solution: Let Kaye has 5x stamps and Alberto has 3x stamps. (5x:3x = 5:3)
When Kaye gives 10 stamps, he is left with (5x - 10) stamps.
and because Alebrto gets 10 stamps, he now has (3x + 10) stamps.
The new ratio is given as 7:5
=> (5x - 10)/((3x + 10) = 7/5
=> 5*(5x - 10) = 7*(3x + 10)
=> 25x - 50 = 21x + 70
=> 25x - 21x = 70 + 50
=> 4x = 120
=> x = 30
Don't be tempted to mark this as your answer. The question is asking something different. The question wants you to find the value of (5x - 10) - (3x + 10)

(5x - 10) - (3x + 10) = 2x - 20 = (2*30) - 20 = 60 - 20 = 40

The answer is (C).
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Re: The number of stamps that Kaye and Alberto had were in the  [#permalink]

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New post 24 Jun 2017, 21:09
kilukilam wrote:
The number of stamps that Kaye and Alberto had were in the ration of 5:3 respecctively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto

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


(5x - 10 )/ (3x + 10) = 7x/5x

(5x - 10)*5 = 7(3x+10)

25x - 50 = 21x + 70
4x = 120
x = 30

Now we need to find the final values after the trade occurs.

K: 5(30) - 10 = 150-10 = 140

A: 3(30) + 10 = 100

140 - 100 = 40.
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Re: The number of stamps that Kaye and Alberto had were in the  [#permalink]

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New post 24 Jul 2017, 05:59
Bunuel, could you explain whats wrong with the the following method?

x/y =3/5. x-10/y+10 = 7/5. Hence on solving we get x as 50 and y as 30, which clearly does not tell us the answer. Can you please provide some conceptual clarity?
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Re: The number of stamps that Kaye and Alberto had were in the  [#permalink]

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New post 24 Jul 2017, 06:15
kilukilam wrote:
The number of stamps that Kaye and Alberto had were in the ration of 5:3 respecctively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto

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


\(\frac{K}{A} = \frac{5x}{3x}\)

\(\frac{5x-10}{3x+10} = \frac{7}{5}\)

\(25x - 50 = 21x + 70\)
\(4x = 120\)
\(x = 30\)

\(A = 3(30)+10 = 100\)
\(K = 5(30)-10 = 140\)

\(K-A = 40\). Ans - C.
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Re: The number of stamps that Kaye and Alberto had were in the  [#permalink]

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New post 24 Jul 2017, 06:28
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OreoShake wrote:
Bunuel, could you explain whats wrong with the the following method?

x/y =3/5. x-10/y+10 = 7/5. Hence on solving we get x as 50 and y as 30, which clearly does not tell us the answer. Can you please provide some conceptual clarity?


Hi, there are a couple of things to note here.

I'm assuming that you assigned the variables x and y as: Alberto = x, Kaye = y. First off, when two things are in a ratio they must be represented using a common variable, if there were no relationship mentioned, for instance if it says that Kaye and Alberto had some stamps, then you may assign two separate variables to each since we don't know in what way they are related, if at all.

Secondly, Kaye gave Alberto 10 stamps, so it must be x+10/y-10 = 7/5. This equation cannot be solved for x and y, one value has to be represented using the other, since there are 2 variables involved.
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Re: The number of stamps that Kaye and Alberto had were in the  [#permalink]

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New post 06 Apr 2018, 08:52
kilukilam wrote:
The number of stamps that Kaye and Alberto had were in the ration of 5:3 respecctively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto

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


We are given that the number of stamps that Kaye and Alberto had was in the ratio 5 : 3. We can represent this as:

K : A = 5x : 3x

We are next given that after Kaye gave Alberto 10 of her stamps, the ratio of the number Kaye had to the number Alberto had was 7 : 5. Using this information, we can create the following equation:

(5x – 10)/(3x + 10) = 7/5

5(5x – 10) = 7(3x + 10)

25x – 50 = 21x + 70

4x = 120

x = 30

Kaye now has 5(30) – 10 = 140 stamps, and Alberto has 3(30) + 10 = 100 stamps. So Kaye has 140 – 100 = 40 more stamps than Alberto has.

Answer: C
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Re: The number of stamps that Kaye and Alberto had were in the  [#permalink]

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New post 13 Oct 2019, 05:19
This is a fairly easy question on ratios, but with a big trap in terms of language. The most common answer that a lot of students get on this question is 60 i.e. option D. However, this is the trap answer.

Questions like these on ratios test your knowledge of mutliples of numbers. As such, although the conventional approach of assuming the stamps as 5x and 3x and then building an equation followed by solving the equation yields you the answer, it’s always good to approach ratio questions using numbers.

We know that the number of stamps that Kaye and Alberto had are multiples of 5 and 3 respectively. So, what do we do? Do we start with 5 and 3? The answer is a bigg no. Observe the options, all the options are bigger numbers than 5 and 3. And remember that we are trying to find the difference between the number of stamps. We need to take bigger multiples of 5 and 3, which are multiples of 10 as well (preferably).

Let’s try 50 and 30, then. After gifting 10 stamps to Alberto, the respective numbers with Kaye and Alberto would be 40 and 40. This is not in the ratio of 7:5. So, 50 and 30 are not the number of stamps.

If we try 100 and 60, we obtain the numbers 90 and 70 after the gifting process. This is in the ratio of 9:7, NOT 7:5.

When we try 150 and 90, we see that the resultant numbers after Kaye gifts alberto would be 140 and 100 which are in the ratio of 7:5. Therefore, Kaye must have started off with 150 stamps and Alberto with 90 stamps. So, Kaye had 60 more stamps than Alberto?? No, that’s not correct.

Observe that the question mentions “As a result of the gift…”. This means, we need to find out how much more Kaye had AFTER gifting 10 stamps to Alberto. AFTER gifting 10 stamps to Alberto, Kaye had 140 and Alberto had 100, so Kaye had 40 more stamps.

The correct answer option is C.

Every word, every phrase and every sentence in a GMAT question is valuable. If you rush through the questions without paying due attention, you run the risk of falling for the trap answers. If required, after you compute an answer, re-read the question statement and satisfy yourselves that you have indeed answered the actual question and NOT what you thought the question was.

Hope that helps!
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Re: The number of stamps that Kaye and Alberto had were in the   [#permalink] 13 Oct 2019, 05:19

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