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Three containers A, B and C have wine concentrations a, b

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Three containers A, B and C have wine concentrations a, b

by BTGmoderatorLU » Tue Jul 31, 2018 2:48 pm

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Three containers A, B and C have concentrations a, b and c, respectively, such that a > b > c. If quantities p, q and r, of wine are taken from the three containers A, B and C, respectively, and mixed, is the concentration of the resulting mixture greater than b?

(1) a − b = b − c
(2) p > q > r

The OA is C.
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Source: — Data Sufficiency |
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by deloitte247 » Sat Aug 18, 2018 1:52 pm

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Question : If quantities p, q, and r of wine are taken from the other 3 containers A , B, C respectively and mixed.
Is the concentration of the resulting mixture greater than b?

Statement 1 : a- b = b- c.
This tells us the difference in concentration is the same but we don't know the ratio in which they are mixed together and hence cannot
tell if the resulting concentration is greater than b, so statement 1 is INSUFFICIENT.

Statement 2 : p > q > r
This tells us that the solution with concentration a has the highest proportion in the
resulting solution but there is no information about concentration b and c so we don't know whether the resulting mixture is greater than b,
so statement 2 is INSUFFICIENT.

Statement 1 and 2 together:
Combining statement 1 and 2 together we know that the concentration of b lies in between middle of concentration a and c. So the resulting solution will depend
on the proportion that is mixed if p is the greatest that means more of concentration a was used and less of concentration c was used,
hence resulting concentration is less than b.
Statement 1 and 2 is SUFFICIENT.
Option C is CORRECT.
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