A student took 12 tests. The student's average (arithmetic mean) on

Question

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...

Show Answer

Official Answer

C

A)  \frac{3}{20}

B)  \frac{1}{4}

C)  \frac{3}{10}

D)  \frac{1}{3}

E)  \frac{3}{8}

Edit: fixed the question...

Ish1996 · Answer

can someone explain this please, i get 1/4

m1033512 · Answer

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

Posted from my mobile device

Ish1996 · Answer

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

m1033512 · Answer

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

Posted from my mobile device

m1033512 · Answer

chetan2u

could you help here ....

devavrat · Answer

Hi can someone please explain how the answer is C and not D?

energetics · Answer

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

MBAPU27 · Answer

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).

firas92 · Answer

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

MBAPU27 · Answer

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?

ManjariMishra · Answer

(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

Vinit800HBS · Answer

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

Posted from my mobile device

saukrit · Answer

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

Posted from my mobile device

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

A student took 12 tests. The student's average (arithmetic mean) on

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A student took 12 tests. The student's average (arithmetic mean) on

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards