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While analyzing my scores across 8 mock CATs that I had taken, I reali

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cfc198
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While analyzing my scores across 8 mock CATs that I had taken, I reali [#permalink] New post   Updated on: 29 Apr 2019, 05:19
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While analyzing my scores across 8 mock CATs that I had taken, I realized that the average marks when the worst seven scores are considered is 5 less than the average marks when the best seven scores are considered. What is the difference between the highest and the lowest scores?

1. 20
2. 25
3. 30
4. 35
5. 40
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Official Answer
D

Originally posted by cfc198 on 28 Apr 2019, 11:27.
Last edited by Bunuel on 29 Apr 2019, 05:19, edited 1 time in total.
Edited the OA.
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briantoth6
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Re: While analyzing my scores across 8 mock CATs that I had taken, I reali [#permalink] New post   28 Apr 2019, 19:45
Relatively confident that the answer is wrong and should be D:

Construct 8 blank spaces:

_ _ _ _ _ _ _ _

Let the middle 6 be equal to x:

_ x _

let the lowscore be equal to A, and the highscore be equal to B:

A x B

Introduce low score variable: L, then:

A + x = 7*L
x + B = 7*(L+5) ----> x + B - 35 = 7L

substitute:

A + x = x + B - 35

eliminate x:

A = B - 35 ...... or ...... A + 35 = B

therefore, the highscore is 35 greater than the lowscore
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Re: While analyzing my scores across 8 mock CATs that I had taken, I reali [#permalink] New post   29 Apr 2019, 05:14
Expert Reply
Yes, the answer is definitely 35, and the OA reported in the OP is not correct. Suppose the sum of the six middle scores is S, the highest score is H, and the lowest score is L. Then the average of the seven highest scores is (S + H)/7 and the average of the seven lowest scores is (S + L)/7. These differ by 5:

(S + H)/7 - (S + L)/7 = 5
S + H - S - L = 35
H - L = 35
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firas92
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Re: While analyzing my scores across 8 mock CATs that I had taken, I reali [#permalink] New post   29 Apr 2019, 05:47
Let's arrange the 8 scores in ascending order.

Assign x = average of first 7 scores (These will be the lowest 7 scores since we have arranged the scores in ascending order)

x = 1st term + 2nd term +.... 7th term

Then sum of the first 7 terms will be 7x


Assign y = average of last 7 scores
(These will be the highest 7 scores since we have arranged the scores in ascending order)

y = 2nd term + 3rd term +.... 8th term

Then sum of last 7 terms will be 7y

Now we are given

y-x = 5

We need to find 7y-7x (2nd to 7th terms will be cancelled out)

Just multiply the equation above by 7

7y-7x=35

(D)

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Re: While analyzing my scores across 8 mock CATs that I had taken, I reali [#permalink]
29 Apr 2019, 05:47
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