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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] New post 26 Aug 2012, 02:07
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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] New post 26 Aug 2012, 02:08
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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.

Answer: E.
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Re: A student's average (arithmetic mean) test score on 4 tests [#permalink] New post 26 Aug 2012, 07:13
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] New post 27 Aug 2012, 10:15
(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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Re: A student's average (arithmetic mean) test score on 4 tests [#permalink] New post 31 Aug 2012, 01:11
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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.

Answer: E.
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A students average (arithmetic mean) test score on 4 tests [#permalink] New post 15 Dec 2012, 07:28
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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.

Answer E
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Re: A students average (arithmetic mean) test score on 4 tests [#permalink] New post 16 Dec 2012, 03:17
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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] New post 12 Apr 2013, 09:42
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] New post 18 Jun 2013, 23:56
(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] New post 06 Jun 2014, 01:56
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

Answer = E
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Re: A student's average (arithmetic mean) test score on 4 tests [#permalink] New post 06 Jun 2014, 05:08
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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] New post 05 Jul 2014, 07:04
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
Re: A student's average (arithmetic mean) test score on 4 tests   [#permalink] 05 Jul 2014, 07:04
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