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# A student's average (arithmetic mean) test score on 4 tests

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A student's average (arithmetic mean) test score on 4 tests  [#permalink]

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26 Aug 2012, 03:07
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A student's average (arithmetic mean) test score on 4 tests is 78. What must be the student's score on a 5th test for the student's average score on the 5 tests to be 80?

(A) 80
(B) 82
(C) 84
(D) 86
(E) 88

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Re: A student's average (arithmetic mean) test score on 4 tests  [#permalink]

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12 Apr 2013, 10:42
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Examining the known average can simply things. We need to reach 80. We currently have 78, four times. 78 is -2 away from 80. Having this four times weights our average -8 off what is desires. To 'catch up' to the average in one test, we must make up the full 8 point deficit in one test. We need an 88. 88 - 8 = 80.
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Re: A student's average (arithmetic mean) test score on 4 tests  [#permalink]

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26 Aug 2012, 03:08
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SOLUTION:

A student's average (arithmetic mean) test score on 4 tests is 78. What must be the student's score on a 5th test for the student's average score on the 5 tests to be 80?

(A) 80
(B) 82
(C) 84
(D) 86
(E) 88

Since the student's average test score on 4 tests is 78, then the sum of the first 4 test scores is 4*78=312. We need the sum of ALL 5 scores to be 5*80=400, so if $$x$$ is the 5th test score, then $$312+x=400$$ --> $$x=88$$.

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Re: A student's average (arithmetic mean) test score on 4 tests  [#permalink]

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26 Aug 2012, 08:13
Let the score in the 5th test be x.
The sum of the first 4 tests = 78*4=312
Now it implies 312+x/5=80
Therefore x=88
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Re: A student's average (arithmetic mean) test score on 4 tests  [#permalink]

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27 Aug 2012, 11:15
(sum of x)/4 = 78
So (sum of x) = 312.
Now (sum of x + x5)/5=80
So (312+x5)=400 i.e. x5=88.
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A students average (arithmetic mean) test score on 4 tests  [#permalink]

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15 Dec 2012, 08:28
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I follow Manhattan advice on this one and write the average formula as a first thing:

in order to reach an average of 80 over 5 test the students has to reach 400 points; he now has 78*4= 312.

400-312= 88.

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Re: A students average (arithmetic mean) test score on 4 tests  [#permalink]

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16 Dec 2012, 04:17
Ans:
total score after 4 tests=312 and score needed after 5 tests= 5x80=400 the student scores the difference in the 5th test which is 88 , (E).
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Re: A student's average (arithmetic mean) test score on 4 tests  [#permalink]

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19 Jun 2013, 00:56
(80-78)=2
2*5tests=10

78+10=88
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Re: A student's average (arithmetic mean) test score on 4 tests  [#permalink]

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06 Jun 2014, 02:56
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Let students score be

78..... 78..... 78....... 78

Average after 5th test should be 80

So score in 5th exam should at least be 80 & also it should "cover up the loses" in the earlier tests

Loses earlier = 2 per test = 2 * 4 = 8

80 + 8 = 88

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Re: A student's average (arithmetic mean) test score on 4 tests  [#permalink]

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06 Jun 2014, 06:08
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I will suggest a little different solution (not a very great trick) but very useful for finding averages since it can save your "TIME" at the tests...
Average of 5 tests to be 80 suggests - in each test the student scored 80 (and this can make average 80). SO -
In 5th test the student has to score 80 for sure, plus any deficit to make up for the average. We know in 4 tests his averge was 78, which means he is 2 markes short of average(80 in this case) in previous 4 tests and he has to make up for this deficit in the 5th test. Hence he has to score 2 * 4 (deficit * no of tests) = 8. Remember, he has to score 80 also in the 5th test.
Hence in total - 80 + 8 = 88. Choice E

Here is how I would approach - 80 in the 5th test, and 2 *4 = 8 totl 88 n the 5th tests. SO it took few seconds to do the ques... Practise this kind of technique while solving questions n averages has been very handy for m... All the best!!
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Re: A student's average (arithmetic mean) test score on 4 tests  [#permalink]

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05 Jul 2014, 08:04
zerosleep wrote:
I will suggest a little different solution (not a very great trick) but very useful for finding averages since it can save your "TIME" at the tests...
Average of 5 tests to be 80 suggests - in each test the student scored 80 (and this can make average 80). SO -
In 5th test the student has to score 80 for sure, plus any deficit to make up for the average. We know in 4 tests his averge was 78, which means he is 2 markes short of average(80 in this case) in previous 4 tests and he has to make up for this deficit in the 5th test. Hence he has to score 2 * 4 (deficit * no of tests) = 8. Remember, he has to score 80 also in the 5th test.
Hence in total - 80 + 8 = 88. Choice E

Here is how I would approach - 80 in the 5th test, and 2 *4 = 8 totl 88 n the 5th tests. SO it took few seconds to do the ques... Practise this kind of technique while solving questions n averages has been very handy for m... All the best!!

Thanks zerosleep.. I always followed traditional approach.. now i would try your way when encountered with question on averages
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Re: A student's average (arithmetic mean) test score on 4 tests  [#permalink]

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10 Sep 2014, 03:39
Bunuel wrote:
A student's average (arithmetic mean) test score on 4 tests is 78. What must be the student's score on a 5th test for the student's average score on the 5 tests to be 80?

(A) 80
(B) 82
(C) 84
(D) 86
(E) 88

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total of 4 test = 4*78 = 312
if the mean of 5 test has to be 80 then total has to be 400.

400-312=88.

so in the fifth test the score should be 88 for the mean to become 80
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Re: A student's average (arithmetic mean) test score on 4 tests  [#permalink]

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16 Nov 2014, 08:40
(4*78+x)/5=80
x=(5*80)-(4*78) ok so 5*78-4*78= 78,
x= 5*(80-78) + 78 --> 5*2+78
total score required 78+10=88
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Re: A student's average (arithmetic mean) test score on 4 tests  [#permalink]

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23 Nov 2015, 11:51
Alternative approach : (New data - Old avg)/New number of items in the set = change in average
(New - 78) /5 = 2
New = 88
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Re: A student's average (arithmetic mean) test score on 4 tests  [#permalink]

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25 May 2016, 07:18
Bunuel wrote:
A student's average (arithmetic mean) test score on 4 tests is 78. What must be the student's score on a 5th test for the student's average score on the 5 tests to be 80?

(A) 80
(B) 82
(C) 84
(D) 86
(E) 88

To solve, we use the average equation:

average = sum/quantity

We don't know the individual scores for each of the first 4 tests, but because their average is 78, we can think of the first 4 scores as 4 scores of 78 each. We then multiply 78 by 4 to get the sum of those four tests:

78 x 4 = 312

Let's let n = the score on the 5th test. Thus, the sum of the 5 tests is 312 + 5th test score, or 312 + n. Also, because the new average will be 80, we substitute 80 for the new average. We can now solve for n.

Average = sum/quantity

80 = (312 + n)/5

400 = 312 + n

88 = n

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Re: A student's average (arithmetic mean) test score on 4 tests  [#permalink]

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25 May 2016, 08:46
Bunuel wrote:
A student's average (arithmetic mean) test score on 4 tests is 78. What must be the student's score on a 5th test for the student's average score on the 5 tests to be 80?

(A) 80
(B) 82
(C) 84
(D) 86
(E) 88

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To have avg score of 80 implies that student needs 80 marks in all 5 tests.

That means 2 marks increase in all 4 tests= 4*2= 8 total marks increase in 4 tests + 80 marks in 5th tests= 88 marks

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Re: A student's average (arithmetic mean) test score on 4 tests  [#permalink]

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10 Dec 2016, 11:26
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Re: A student's average (arithmetic mean) test score on 4 tests  [#permalink]

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01 Apr 2017, 09:12
Total score in 4 tests= 4*78=312
The average of 5 tests is 80. Therefore the total score of 5 tests= 5*80=400

Therefore in the 5th test, the student must score 88 (400-312).
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Re: A student's average (arithmetic mean) test score on 4 tests  [#permalink]

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14 Sep 2017, 00:16
average is 78 from 4 tests
required average is 80
-2*4 need to be covered from the 5th test
so 80+8 = 88 he should get
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Re: A student's average (arithmetic mean) test score on 4 tests  [#permalink]

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29 Jan 2018, 16:02
Hi All,

The standard average formula 'approach' is likely the easiest for most Test Takers to use on these types of prompts. However, there is another way to think about this prompt - since the average of the first 4 tests is 78, we can think of those tests as four 78s. For a 5th exam to raise the overall average to 80, that exam has to score 80 points on its own AND raise each of the other 4 tests to 80. Those 4 tests would require an extra 2 points apiece...

80 + 4(2) = 88 points

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Re: A student's average (arithmetic mean) test score on 4 tests &nbs [#permalink] 29 Jan 2018, 16:02

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