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10 May 2017, 02:39
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C
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Difficulty:
5%
(low)
Question Stats:
90% (00:31) correct
10%
(01:06)
wrong
based on 92
sessions
History
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Time
Result
Not Attempted Yet
Is the average (arithmetic mean) of a and b positive?
(1) a is positive.
(2) b is larger than a.
(1) a is positive.
(2) b is larger than a.
10 May 2017, 03:00
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Using statement 1 alone, we cannot infer anything about the value of b.
Using statement 2 alone, multiple cases can be created for the values of both a and b and nothing concrete can be concluded about the nature of the arithmetic mean.
Using both the statements together, we can say that both a and b are positive and hence, their mean would be positive as well.
Hence, Option C should be the correct answer.
Using statement 2 alone, multiple cases can be created for the values of both a and b and nothing concrete can be concluded about the nature of the arithmetic mean.
Using both the statements together, we can say that both a and b are positive and hence, their mean would be positive as well.
Hence, Option C should be the correct answer.
10 May 2017, 05:53
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Bunuel
Target question: Is the average (arithmetic mean) of a and b positive?
Statement 1: a is positive.
There are several values of a and b that satisfy statement 1. Here are two:
Case a: a = 1 and b = 1, in which case the average of a and b is 1, which is POSITIVE
Case b: a = 1 and b = -3, in which case the average of a and b is -1, which is NEGATIVE
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: b is larger than a
There are several values of a and b that satisfy statement 1. Here are two:
Case a: a = 1 and b = 3, in which case the average of a and b is 2, which is POSITIVE
Case b: a = -3 and b = -1, in which case the average of a and b is -2, which is NEGATIVE
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that a is positive
Statement 2 tells us that b is larger than a, which means b is positive.
If a and b are both POSITIVE then the average of a and b must be POSITIVE
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer:
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