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# Jim had four tests, with each grade being an integer. Did Jim score 10

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Math Expert
Joined: 02 Sep 2009
Posts: 52153

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25 Dec 2017, 23:14
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Difficulty:

25% (medium)

Question Stats:

96% (01:37) correct 4% (01:11) wrong based on 31 sessions

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Jim had four tests, with each grade being an integer. Did Jim score 100 on any test?

(1) Jim got a 46 on one of the tests.
(2) Jim's highest grade was twice the average (arithmetic mean) of his three lowest grades.

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Joined: 07 Dec 2017
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26 Dec 2017, 00:15
Bunuel wrote:
Jim had four tests, with each grade being an integer. Did Jim score 100 on any test?

(1) Jim got a 46 on one of the tests.
(2) Jim's highest grade was twice the average (arithmetic mean) of his three lowest grades.

We'll solve this question by using the underlying logic of averages (without calculating).
This is a Logical approach.

(1) This gives information on only one test. What about the others?
Insufficient.

(2) This gives an equation with only variables in it - infinite solutions!
Insufficient.

Combined - We substitute 46 into our equation from (2) but this still gives an equation with 3 variables in it.
Infinite solutions --> Insufficient!

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26 Dec 2017, 16:50
Bunuel wrote:
Jim had four tests, with each grade being an integer. Did Jim score 100 on any test?

(1) Jim got a 46 on one of the tests.
(2) Jim's highest grade was twice the average (arithmetic mean) of his three lowest grades.

(1) Jim got a 46 on one of the tests. Ok so one of the four tests he had a score of 46, but we don't know the other scores; insufficient.

(2) Jim's highest grade was twice the average (arithmetic mean) of his three lowest grades. So, $$Highest=2*\frac{Lowest}{3}$$, nothing about the score values; insufficient.

(1)+(2).All we know is that the highest is twice the average of the three lowest scores and 46 could be the highest or one of the lowest; insufficient.

Re: Jim had four tests, with each grade being an integer. Did Jim score 10 &nbs [#permalink] 26 Dec 2017, 16:50
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