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A student took 12 tests. The student's average (arithmetic mean) on  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 36% (02:37) correct 64% (01:59) wrong based on 67 sessions

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A student took 12 tests. The student's average (arithmetic mean) on the first 4 tests was 6/7 of the student's average score on the final 8 tests. What fraction of the total number of points that the student scored on all 12 tests was the total number of points that the student scored on the first 4 tests?

A) $$\frac{3}{20}$$

B) $$\frac{1}{4}$$

C) $$\frac{3}{10}$$

D) $$\frac{1}{3}$$

E) $$\frac{3}{8}$$

Edit: fixed the question...

Originally posted by energetics on 26 Mar 2019, 11:51.
Last edited by energetics on 09 Jun 2019, 09:12, edited 3 times in total.
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Re: A student took 12 tests. The student's average (arithmetic mean) on  [#permalink]

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energetics wrote:
A student took 12 tests. The student's average (arithmetic mean) on the first 4 tests was of the student's average score on the final 8 tests. What fraction of the total number of points that the student scored on all 12 tests was the total number of points that the student scored on the first 4 tests?

A) $$\frac{3}{20}$$

B) $$\frac{1}{4}$$

C) $$\frac{3}{10}$$

D) $$\frac{1}{3}$$

E) $$\frac{3}{8}$$

can someone explain this please, i get 1/4
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Re: A student took 12 tests. The student's average (arithmetic mean) on  [#permalink]

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1
IMO D.

Mean of first four tests = mean of final 8 tests = x

marks scored in first 4 tests = 4x

marks in final 8 tests = 8x

total marks = 12x

so in fraction = 4x/12x
= 1/3

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Re: A student took 12 tests. The student's average (arithmetic mean) on  [#permalink]

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m1033512 wrote:
IMO D.

Mean of first four tests = mean of final 8 tests = x

marks scored in first 4 tests = 4x

marks in final 8 tests = 8x

total marks = 12x

so in fraction = 4x/12x
= 1/3

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I did:

average of first 4: x/4

average of last 8: y/8

from question: x/4=y/8 ---> y=2x

average of all 12 Qs: (x+y)/12

sub y=2x--->(2x+x)/12---> 3x/12---->1/4 x
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Re: A student took 12 tests. The student's average (arithmetic mean) on  [#permalink]

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it was about the total points in first 4 and all 12 tests

So I calculated total points for first 4 and all 12 tests

But this is also not matching the OA .

We need OE for correct understanding

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Re: A student took 12 tests. The student's average (arithmetic mean) on  [#permalink]

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chetan2u

could you help here ....
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Re: A student took 12 tests. The student's average (arithmetic mean) on  [#permalink]

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Hi can someone please explain how the answer is C and not D?
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A student took 12 tests. The student's average (arithmetic mean) on  [#permalink]

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Edit: Fixed the question, sorry for the transcription error.

Originally posted by energetics on 25 Apr 2019, 20:44.
Last edited by energetics on 09 Jun 2019, 09:13, edited 1 time in total.
Intern  Joined: 21 May 2019
Posts: 2
Re: A student took 12 tests. The student's average (arithmetic mean) on  [#permalink]

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Hi,

This question popped up on a Kaplan practice test. The OA is (C) 3/10

The OE is below (copied verbatim)

This question can be solved by Picking Numbers. Because the answer choices are all fractions, we know that no matter what numbers we pick for the test scores, we will arrive at the same fraction for the correct answer. The average formula is Average = sum of the terms / number of terms. We can use this formula in the rearranged form: Sum of the terms = Average × Number of terms.

Since the student's average score on the first 4 tests was 6/7 of the student's average score on the final 8 tests, let's pick a number for the student's average score on the final 8 tests that is divisible by 7. Let's say that the student's average score on the final 8 tests was 70. Then the student's average score on the first 4 tests was 6/7 of 70, which is 60. The total number of points that the student scored on the first 4 tests was 60(4) = 240. The total number of points that the student scored on the final 8 tests was 70(8) = 560. So the total number of points the student scored on all 12 tests was 240 + 560 = 800.

We now have that the student scored a total of 240 points on the first 4 tests and a total of 800 points on all 12 tests. The fraction that 240 is of 800 is 3/10 , or Answer Choice (C).
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Re: A student took 12 tests. The student's average (arithmetic mean) on  [#permalink]

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pratu27 wrote:
Hi,

This question popped up on a Kaplan practice test. The OA is (C) 3/10

The OE is below (copied verbatim)

This question can be solved by Picking Numbers. Because the answer choices are all fractions, we know that no matter what numbers we pick for the test scores, we will arrive at the same fraction for the correct answer. The average formula is Average = sum of the terms / number of terms. We can use this formula in the rearranged form: Sum of the terms = Average × Number of terms.

Since the student's average score on the first 4 tests was 6/7 of the student's average score on the final 8 tests, let's pick a number for the student's average score on the final 8 tests that is divisible by 7. Let's say that the student's average score on the final 8 tests was 70. Then the student's average score on the first 4 tests was 6/7 of 70, which is 60. The total number of points that the student scored on the first 4 tests was 60(4) = 240. The total number of points that the student scored on the final 8 tests was 70(8) = 560. So the total number of points the student scored on all 12 tests was 240 + 560 = 800.

We now have that the student scored a total of 240 points on the first 4 tests and a total of 800 points on all 12 tests. The fraction that 240 is of 800 is 3/10 , or Answer Choice (C).

In this case, the question here is flawed as it does not mention 6/7 and so it appears as though the average in the first 4 tests was the same as the average in the last 8 tests.

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Re: A student took 12 tests. The student's average (arithmetic mean) on  [#permalink]

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firas92 wrote:
pratu27 wrote:
Hi,

This question popped up on a Kaplan practice test. The OA is (C) 3/10

The OE is below (copied verbatim)

This question can be solved by Picking Numbers. Because the answer choices are all fractions, we know that no matter what numbers we pick for the test scores, we will arrive at the same fraction for the correct answer. The average formula is Average = sum of the terms / number of terms. We can use this formula in the rearranged form: Sum of the terms = Average × Number of terms.

Since the student's average score on the first 4 tests was 6/7 of the student's average score on the final 8 tests, let's pick a number for the student's average score on the final 8 tests that is divisible by 7. Let's say that the student's average score on the final 8 tests was 70. Then the student's average score on the first 4 tests was 6/7 of 70, which is 60. The total number of points that the student scored on the first 4 tests was 60(4) = 240. The total number of points that the student scored on the final 8 tests was 70(8) = 560. So the total number of points the student scored on all 12 tests was 240 + 560 = 800.

We now have that the student scored a total of 240 points on the first 4 tests and a total of 800 points on all 12 tests. The fraction that 240 is of 800 is 3/10 , or Answer Choice (C).

In this case, the question here is flawed as it does not mention 6/7 and so it appears as though the average in the first 4 tests was the same as the average in the last 8 tests.

Posted from my mobile device

I think the OP copied the question from Kaplan, but did not check to see if it was copied correctly. Kaplan depicts fractions as images, which do not render with a paste command.

The original question is as follows: A student took 12 tests. The student's average (arithmetic mean) on the first 4 tests was 6/7 of the student's average score on the final 8 tests. What fraction of the total number of points that the student scored on all 12 tests was the total number of points that the student scored on the first 4 tests?
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Re: A student took 12 tests. The student's average (arithmetic mean) on  [#permalink]

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(x1+x2+x3+x4)/4 = 6/7((x5+........+x12)/8)
(x1+x2+x3+x4) = 6/14(x5+........+x12)

Fraction
(x1+x2+x3+x4)/(x1+........+x12)
6/14(x5+........+x12)/6/14((x5+........+x12) +(x5+........+x12)
6/14(x5+........+x12)/20/14(x5+........+x12)
(6/14) /(20/14)
3/10

C
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A student took 12 tests. The student's average (arithmetic mean) on  [#permalink]

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2
As we are looking for ratio, we can take any value for the average and still end up with same ratio.

Let’s say, average on last 8 tests is 7
So, the average on first 4 tests is 7*6/7 = 6

Total: 8*7 + 4*6 = 80
Required ratio = 4*6/80 = 3/10

Option C

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Re: A student took 12 tests. The student's average (arithmetic mean) on  [#permalink]

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Just take any multiple of 6 and 7...for simplicity let us take 6 marks in first 4 test and 7 marks in last 8 tests

Sum in first 4 =6*4=24
Total sum=24+56=80

Required ratio= 24/80=3/10.

Hence ,C

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