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

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

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New post 25 Sep 2018, 04:57
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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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Re: A student’s average (arithmetic mean) test score on four tests is 78.  [#permalink]

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New post 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 = \(\frac{405}{5}=81\)

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
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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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