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# Richard took two tests. Did he score equal marks in both the tests?

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Manager
Joined: 11 Aug 2016
Posts: 196
Richard took two tests. Did he score equal marks in both the tests?  [#permalink]

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05 Sep 2018, 12:53
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Difficulty:

55% (hard)

Question Stats:

38% (01:11) correct 62% (01:17) wrong based on 29 sessions

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Richard took two tests. Did he score equal marks in both the tests?

(1) The standard deviation and the variance of the marks scored by Richard in the two tests are equal.
(2) The mean and the median of the marks scored by Richard in the two tests are equal.

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Math Expert
Joined: 02 Aug 2009
Posts: 6795
Re: Richard took two tests. Did he score equal marks in both the tests?  [#permalink]

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05 Sep 2018, 20:15
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Richard took two tests. Did he score equal marks in both the tests?

Most important info- there are only two numbers

(1) The standard deviation and the variance of the marks scored by Richard in the two tests are equal.
so SD and variance of two numbers is same..
what is the relation between SD and variance?
: $$SD=\sqrt{V}$$
let SD be x, so $$x=\sqrt{x}.......x^2=x........x^2-x=0.........x(x-1)=0$$
so x can be 0 or 1
If SD is 0, both numbers are same. example 40,40
If SD is 1, both number differ by 2, example 40,42
insuff

(2) The mean and the median of the marks scored by Richard in the two tests are equal.
Mean and median will always be SAME when we have two numbers
example
40,40 mean=median=40
40,42, mean=median=41
insuff

combined..
both cases still remain..
(40,40) and (40,42)
insuff

E
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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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##### General Discussion
Manager
Joined: 09 Aug 2017
Posts: 194
Richard took two tests. Did he score equal marks in both the tests?  [#permalink]

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05 Sep 2018, 17:13
I just marked answer by guess and fortunately answer was correct. But I didn't understand the problem.
For a test, Richard will score certain marks that will be mean and median itself.
Could you elaborate the question and answer?
Richard took two tests. Did he score equal marks in both the tests? &nbs [#permalink] 05 Sep 2018, 17:13
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