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# At a certain stage of a soccer tournament, the score ratio of teams A,

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Intern
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At a certain stage of a soccer tournament, the score ratio of teams A, [#permalink]

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01 Dec 2012, 06:28
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Question Stats:

81% (01:27) correct 19% (01:30) wrong based on 98 sessions

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At a certain stage of a soccer tournament, the score ratio of teams A, B and C was 3:4:5. Eventually, the score ratio of A to B has doubled while the score ratio of A to C has halved. If the final score of team C was 40, what was the final score of team B?

A. 8
B. 10
C. 20
D. 40
E. 80

[Reveal] Spoiler:
I tried this as below:

a:b:c = 3:4:5

a:b= 3:4

doubled:
a:b = 2* 3:4 = 3:2

halved
a:c = (1/2)*3:5 = 3:10

a:c/a:b = (3/10)/ (3/2) = 6/30

given c =40

substituting, we get b = 8.

Pls let me know the basic approach on this.
[Reveal] Spoiler: OA

Last edited by Bunuel on 07 Oct 2017, 02:30, edited 1 time in total.
Renamed the topic and edited the question.

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Re: At a certain stage of a soccer tournament, the score ratio of teams A, [#permalink]

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01 Dec 2012, 06:44
2
KUDOS
manukumar wrote:
At a certain stage of a soccer tournament, the score ratio of teams A, B and C was 3:4:5. Eventually, the score ratio of A to B has doubled while the score ratio of A to C has halved. If the final score of team C was 40, what was the final score of team B?

1)8
2)10
3)20
4)40
5)80

I tried this as below:

a:b:c = 3:4:5

a:b= 3:4

doubled:
a:b = 2* 3:4 = 3:2

halved
a:c = (1/2)*3:5 = 3:10

a:c/a:b = (3/10)/ (3/2) = 6/30

given c =40

substituting, we get b = 8.

Pls let me know the basic approach on this.

A to B = 3 : 4

So, on doubling we get 6 : 4

A to C = 3 : 5

So, on halving we get 1.5 : 5 or 3 : 10 or 6 : 20

So final ratio = 6 : 4 : 20.

If 20x = 40

4x = 8

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Re: At a certain stage of a soccer tournament, the score ratio of teams A, [#permalink]

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17 Feb 2017, 11:26
Ratio of A:B is originally 3:4. Then this ratio is doubled and we have $$\frac{3}{2}$$ * 2 = $$\frac{6}{4}$$
Ratio of A:C is originally 3:5. Then this ratio is halved so we have $$\frac{3}{5}$$ * $$\frac{1}{2}$$ = $$\frac{3}{10}$$.

In order to compare the two ratio we must express the common term (in this case A) in the same quantity. Thus we multiply the second ratio ($$\frac{3}{10}$$) for 2 and we get $$\frac{6}{20}$$

So now the new score ratio of team A, B and C is 6:4:20. If we divide the score of team C by the ratio for team C we get the multiplier (in this case is 2).
Finally by applying the multiplier to B we get 8.

Hope it is clear.

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Re: At a certain stage of a soccer tournament, the score ratio of teams A, [#permalink]

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17 Feb 2017, 21:24

A : B : C Initially:
3 : 4 : 5

6 : 4 (ratio A:B is doubled )

3 : __ : 10 (ratio is A: C is halved)
6 : __ : 20

6 : 4 : 20 Finally,
12 : 8 : 40 (since C has to become 40)

Therefore, B = 8
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Re: At a certain stage of a soccer tournament, the score ratio of teams A, [#permalink]

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12 Mar 2017, 10:49
I like making it in a table:

A:B:C
3:4:5 then A:B doubled
6:4:? then A:C halved
3:?:10 let's make a common ration for all 3:
6:4:20 and since C earned 40 points:
12:8:40 B is 8

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Re: At a certain stage of a soccer tournament, the score ratio of teams A, [#permalink]

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15 Mar 2017, 16:52
1
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Expert's post
manukumar wrote:
At a certain stage of a soccer tournament, the score ratio of teams A, B and C was 3:4:5. Eventually, the score ratio of A to B has doubled while the score ratio of A to C has halved. If the final score of team C was 40, what was the final score of team B?

1)8
2)10
3)20
4)40
5)80

We are given that the original ratio of A : B : C = 3x : 4x : 5x.

After the ratio of A to B doubles and the ratio of A to C is halved, we have:

A/B = 6x/4x

AND

A/C = 3x/10x

Since we need term A to be the same in both ratios, we can multiply our second ratio by 2/2 and we have:

A/C = 6x/20x

Now the ratio of A : B : C = 6x : 4x : 20x

Since team C had a final of 40 points, we have:

20x = 40

x = 2

So, the final score of team B was 4 x 2 = 8.

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Re: At a certain stage of a soccer tournament, the score ratio of teams A, [#permalink]

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07 Oct 2017, 02:28
1
KUDOS
Hello Moderators,

I got this question as a part of daily practice questions from my workbook. Do you think it would be a good Idea to hide the highlighted portion of the question? The highlighted text is giving away a possible approach that can be taken to solve the question. Hiding this will help users when they attempt it using Timer.

manukumar wrote:
At a certain stage of a soccer tournament, the score ratio of teams A, B and C was 3:4:5. Eventually, the score ratio of A to B has doubled while the score ratio of A to C has halved. If the final score of team C was 40, what was the final score of team B?

1)8
2)10
3)20
4)40
5)80

I tried this as below:

a:b:c = 3:4:5

a:b= 3:4

doubled:
a:b = 2* 3:4 = 3:2

halved
a:c = (1/2)*3:5 = 3:10

a:c/a:b = (3/10)/ (3/2) = 6/30

given c =40

substituting, we get b = 8.

Pls let me know the basic approach on this.

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Re: At a certain stage of a soccer tournament, the score ratio of teams A, [#permalink]

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07 Oct 2017, 02:31
susheelh wrote:
Hello Moderators,

I got this question as a part of daily practice questions from my workbook. Do you think it would be a good Idea to hide the highlighted portion of the question? The highlighted text is giving away a possible approach that can be taken to solve the question. Hiding this will help users when they attempt it using Timer.

manukumar wrote:
At a certain stage of a soccer tournament, the score ratio of teams A, B and C was 3:4:5. Eventually, the score ratio of A to B has doubled while the score ratio of A to C has halved. If the final score of team C was 40, what was the final score of team B?

1)8
2)10
3)20
4)40
5)80

I tried this as below:

a:b:c = 3:4:5

a:b= 3:4

doubled:
a:b = 2* 3:4 = 3:2

halved
a:c = (1/2)*3:5 = 3:10

a:c/a:b = (3/10)/ (3/2) = 6/30

given c =40

substituting, we get b = 8.

Pls let me know the basic approach on this.

_______________
Edited. Thank you.
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Re: At a certain stage of a soccer tournament, the score ratio of teams A, [#permalink]

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07 Oct 2017, 03:21
manukumar wrote:
At a certain stage of a soccer tournament, the score ratio of teams A, B and C was 3:4:5. Eventually, the score ratio of A to B has doubled while the score ratio of A to C has halved. If the final score of team C was 40, what was the final score of team B?

A. 8
B. 10
C. 20
D. 40
E. 80

[Reveal] Spoiler:
I tried this as below:

a:b:c = 3:4:5

a:b= 3:4

doubled:
a:b = 2* 3:4 = 3:2

halved
a:c = (1/2)*3:5 = 3:10

a:c/a:b = (3/10)/ (3/2) = 6/30

given c =40

substituting, we get b = 8.

Pls let me know the basic approach on this.

Initially A:B:C = 3:4:5

Finally, A: B = 6:4 = 3:2
and, A:C = 3: 10
So, A: B: C = 3: 2: 10

Also final score of C = 40
So , A: B: C = 12 : 8 : 40

So, B = 8

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Re: At a certain stage of a soccer tournament, the score ratio of teams A,   [#permalink] 07 Oct 2017, 03:21
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