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Jim had an average (arithmetic mean) of 86 on four tests, each grade

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Jim had an average (arithmetic mean) of 86 on four tests, each grade  [#permalink]

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New post 28 Dec 2017, 00:50
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Jim had an average (arithmetic mean) of 86 on four tests, each grade being an integer. Did Jim score 100 on any test?

(1) Jim scored 4 points higher on each consecutive test.
(2) Jim never scored below a 70.

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Re: Jim had an average (arithmetic mean) of 86 on four tests, each grade  [#permalink]

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New post 28 Dec 2017, 03:05
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Bunuel wrote:
Jim had an average (arithmetic mean) of 86 on four tests, each grade being an integer. Did Jim score 100 on any test?

(1) Jim scored 4 points higher on each consecutive test.
(2) Jim never scored below a 70.


Jim had an average (arithmetic mean) of 86 on four tests = 86*4 = 344 (Total Marks)

(1) Jim scored 4 points higher on each consecutive test.

Let x be first test marks next three consecutive test will be x+4, x+8, x+12

Sum = 4x+24 =344

x=>80

hence highest would be 92, which gives us NO

(2) Jim never scored below a 70

Scenario 1) Let all test be 86 which gives NO

Scenario 2) Let two test be 70, 70 and other two test will be 100 & 104

Gives us Yes

Hence A
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Jim had an average (arithmetic mean) of 86 on four tests, each grade  [#permalink]

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New post 28 Dec 2017, 17:28
Bunuel wrote:
Jim had an average (arithmetic mean) of 86 on four tests, each grade being an integer. Did Jim score 100 on any test?

(1) Jim scored 4 points higher on each consecutive test.
(2) Jim never scored below a 70.


(1) Jim scored 4 points higher on each consecutive test.

The average of a set of consecutive integers is the median in an odd set and the average for an even set is the average of the two middle numbers.
So, an even set of 4 numbers each +4 points higher with an average of 86 must have two middle numbers equal to:
\(86=\frac{(n+4)+(n+8)}{2}\), \(172=(2n+12)\), \(n=80\), then \((n+4)=84\) and \((n+8)=88\) and the other two in the set are 80 and 92; none of which are 100; sufficient.

(2) Jim never scored below a 70. But we cannot determine if Jim scored 100 or not; insufficient.

(A) is the answer.
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Jim had an average (arithmetic mean) of 86 on four tests, each grade &nbs [#permalink] 28 Dec 2017, 17:28
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