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09 Jan 2018, 23:38
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E
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Difficulty:
45%
(medium)
Question Stats:
63% (02:10) correct
37%
(01:56)
wrong
based on 146
sessions
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If 6 positive integers have a sum less than 10, what is the value of the greatest of the integers?
(1) The average (arithmetic mean) of the 6 integers is 3/2.
(2) The median of the integers is 1.
(1) The average (arithmetic mean) of the 6 integers is 3/2.
(2) The median of the integers is 1.
09 Jan 2018, 23:53
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Bunuel
Let the integers in ascending order be a, b, c, d, e, f. We are given that a+b+c+d+e+f < 10. WE have to find 'f'.
(1) Avg = 3/2. So sum = 3/2 * 6 = 9. This means
a+b+c+d+e+f = 9. So there is a possibility that a=b=c=d=e=1, and then f=4. Or we could have a=b=c=1, and d=e=f=2. Multiple possibilities for 'f'. So Insufficient.
(2) Median is 1. So the average of middle two integers (c &d) is 1. Which means c+d = 2. This is only possible when c=d=1. And since they are in ascending order, this also means that a=b=1 too (no integer can be 0 since they are all positive integers). So a=b=c=d=1. This means e+f < 6 (total sum has to be less than 10). But we could have e=1, f=4 Or we could have e=2, f=3. Multiple possibilities for 'f'. Insufficient.
Combining the statements, we get that a=b=c=d=1. And now e+f=5. But again if e=1, f=4 and if e=2, f=3. WE cant uniquely determine value of 'f'. Insufficient.
Hence E answer
rahul16singh28
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11 Jan 2018, 08:18
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amanvermagmat
Hi amanvermagmat, chetan2u
The question asks for the greatest value of the integer which can be only one value i.e. 4. Other possibilities are there but of all the possibilities greatest is 4. Can you please let me know if I am missing something.
