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Set X of has an average of 61. If the largest element is 7 greater tha
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29 Jan 2017, 05:50
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18
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C
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Difficulty:
95% (hard)
Question Stats:
35% (02:31) correct 65% (02:36) wrong based on 198 sessions
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Set \(X\) of has an average of \(61\). If the largest element is 7 greater than 6 times the smallest element, how many values out of \({2,3,5,8,9,11,53,102,123,178,210,267,283,311,376,383,399,401}\) can be a part of Set \(X\)?
Re: Set X of has an average of 61. If the largest element is 7 greater tha
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29 Jan 2017, 08:53
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ziyuenlau wrote:
Set \(X\) of has an average of \(61\). If the largest element is 7 greater than 6 times the smallest element, how many values out of \({2,3,5,8,9,11,53,102,123,178,210,267,283,311,376,383,399,401}\) can be a part of Set \(X\)?
I think this Q has already been discussed earlier. I hope you have searched for it before posting. Average is 61..find the max and min values possible, you will get the answer
_________________
Set X of has an average of 61. If the largest element is 7 greater tha
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29 Jan 2017, 13:32
Answer (C) is right.
2,3,5,8, can not be a part of X. Even if one of them is a min element of X then the max element is not greater 61 and the average of X cannot be 61. 376,383,399,401 can not be a part of X. Even if one of them is a max element of X then the min element is not less than 61 and the average of X cannot be 61.
Set X of has an average of 61. If the largest element is 7 greater tha
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Updated on: 15 May 2018, 21:31
Given average \(61\) and \(max\) = \(min * 6 + 7\), so set must have alteast two different integers (meaning it is not a set of all same integers)
in a set of different integers, min value can't be equal to average, so \(min\) < \(61\) => \(max\) < \(61 * 6 + 7\), so \(max\) < \(373\) similarly, max value can't be equal to average, so \(max\) > \(61\) => \(61\) < \(max\) < \(373\)
now we found, \(max\) > \(61\)=> \(min * 6 + 7\) > \(61\) => \(min\) > \(9\).
all the elements in the set must be between \(9 < S < 373\), only 9 integers of the given falls within the range => Answer (C)
Originally posted by hellosanthosh2k2 on 03 Jan 2018, 01:42.
Last edited by hellosanthosh2k2 on 15 May 2018, 21:31, edited 1 time in total.
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35% (02:31) correct 
