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# A student’s average (arithmetic mean) test score on four tests is 78.

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Math Expert
Joined: 02 Sep 2009
Posts: 49968
A student’s average (arithmetic mean) test score on four tests is 78.  [#permalink]

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25 Sep 2018, 04:57
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Difficulty:

25% (medium)

Question Stats:

74% (01:31) correct 26% (01:47) wrong based on 19 sessions

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A student’s average (arithmetic mean) test score on four tests is 78. If each test is scored out of 100, which of the following can be the student’s score on the fifth test so that the student’s average score on the five tests increases by an integer value?

(A) 82
(B) 87
(C) 89
(D) 93
(E) 95

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Math Expert
Joined: 02 Aug 2009
Posts: 6956
Re: A student’s average (arithmetic mean) test score on four tests is 78.  [#permalink]

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26 Sep 2018, 00:06
Bunuel wrote:
A student’s average (arithmetic mean) test score on four tests is 78. If each test is scored out of 100, which of the following can be the student’s score on the fifth test so that the student’s average score on the five tests increases by an integer value?

(A) 82
(B) 87
(C) 89
(D) 93
(E) 95

total score in four tests = $$4*78 = 312$$
now the average after 5 tests should be an integer, let the marks in 5th be x
so total = 312+x and average = $$\frac{(312+x)}{5}$$= an integer
so $$312+x$$ must be divisible by 5, meaning units digit of 312+x must be 5 or 0
so units digit of x can be
1) 5-2=3, or
2) 10-2=8

in the given choices, D has a 3 in units digit
so marks are $$312+93=405$$ and average = $$\frac{405}{5}=81$$

D
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: A student’s average (arithmetic mean) test score on four tests is 78. &nbs [#permalink] 26 Sep 2018, 00:06
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