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20 Jun 2018, 21:14
Kudos
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
44% (01:42) correct
56%
(01:35)
wrong
based on 392
sessions
History
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Not Attempted Yet
If a,b, and c are positive integers with at least one of the three equal to 7, is the median of the set {a,b,c} greater than 7?
(1) a<7
(2) c>7
New question
(1) a<7
(2) c>7
New question
20 Jun 2018, 23:03
Kudos
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chetan2u
At least one of the three = 7.
(1) a < 7
So at least one integer = 7, and one integer < 7.
If third integer = 7, then since two integers = 7, median of these three = 7
If third integer < 7, then since two integers < 7, median of these three < 7
If third integer > 7, then the median of these three = 7
So the median will either be = 7 or < 7, but never > 7. So this gives NO as an answer to the question asked. Sufficient.
(2) c > 7
So at least one integer = 7, and one integer > 7
If third integer = 7, then since two integers = 7, median of these three = 7
If third integer > 7, then since two integers > 7, median of these three > 7
So the median might be = 7 or greater than 7 also. This doesnt give a definite YES or NO to the question asked. Not Sufficient.
Hence A answer
General Discussion
21 Jun 2018, 04:34
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Solution
Given:
• a, b, and c are positive integers.
• At least one of a, b, and c is 7.
To find:
• Is the median of the set {a,b,c} greater than 7?
Statement-1: “a<7 “
If a is less than 7 then there can be three cases in which numbers will be arranged.
- • a, 7, greater than 7
- o In this case, median is 7.
- • a, (less than 7 and greater than a), 7
- o In this case, median is certainly less than 7.
- • Less than a, a, 7
- o In this case, median is a which is less than 7.
In all the cases median is less than 7.
Hence, Statement 1 alone is sufficient to answer the question.
Statement-2: “c>7 “
If c is greater than 7 then there can be some cases in which numbers will be arranged.
- • 7, c, greater than c
- o In this case, median is c which is greater than 7.
- • Less than 7, ,7 c,
- o In this case, median is 7.
Since we do not have a unique answer from the two cases, we do not need to check for rest of the cases.
Statement 2 alone is not sufficient to answer the question.
Hence, the correct answer is option A.
Answer: A
