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A group of adults took a quiz that was scored from 10 to 40.

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A group of adults took a quiz that was scored from 10 to 40.  [#permalink]

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New post Updated on: 22 Oct 2019, 23:18
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EMPOWERgmat DS Series:
Pack 3, Question 2

A group of adults took a quiz that was scored from 10 to 40. If the highest score was 6 points higher than the next-highest score, what was the highest score?

(1) No one taking the test got a score lower than 32.
(2) No one taking the test got an even-numbered score.



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Originally posted by EMPOWERgmatRichC on 15 Oct 2019, 22:44.
Last edited by EMPOWERgmatRichC on 22 Oct 2019, 23:18, edited 1 time in total.
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Re: A group of adults took a quiz that was scored from 10 to 40.  [#permalink]

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New post 17 Oct 2019, 01:27
EMPOWERgmatRichC wrote:
EMPOWERgmat DS Series:
Pack 3, Question 2

A group of adults took a quiz that was scored from 10 to 40. If the highest score was 6 points higher than the next-highest score, what was the highest score?

(1) No one taking the test got a score lower than 32.
(2) No one taking the test got an even-numbered score.


Lets assume that the highest score is x.
So, as per the given information, we know that:
A. \(x\leq{40}\)
B. Second highest score will be (x-6)

We have to find the highest score, x, so if we can find value of either x or (x-6), we can arrive at our answer.

(1) This statement suggests that the possible scores are 32,33,34,35,36,37,38,39, and 40.
Since highest score, x, is 6 more than the second highest score and \(x\leq{40}\), only possible values of (x-6) are 32,33, and 34, and therefore only possible values of x are 38,39, and 40.
So, from the above information, we don't get a unique value of x.
Thus, this statement is insufficient.

(2) This statement suggests that possible scores are all odd numbers between 1 and 39, both the limits included.
Hence, if the second highest score is 5, the highest score will be 11, and if the second highest score is 33, the highest score will be 39.
So, from the information in this statement, we don't get a unique value of x.
Thus, this statement is insufficient.

From statement (1) and (2) together, we know that:
a. Possible values of highest score are 38,39, and 40
b. Possible scores are odd numbers
So, from (1) and (2) combined, we get that value of x is 39.
Thus, this statement is sufficient.

Therefore, the correct answer is option C.
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Re: A group of adults took a quiz that was scored from 10 to 40.   [#permalink] 17 Oct 2019, 01:27
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