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C
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Difficulty:
85%
(hard)
Question Stats:
38% (02:23) correct
62%
(02:26)
wrong
based on 78
sessions
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Date
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Not Attempted Yet
3, 5, 10, 7, x.
If x is an integer, is the mean of the five numbers shown greater than the median of these numbers?
(1) x > 3
(2) x < 7
If x is an integer, is the mean of the five numbers shown greater than the median of these numbers?
(1) x > 3
(2) x < 7
15 Feb 2023, 23:32
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TBT
3, 5, 10, 7, x.
If x is an integer, is the mean of the five numbers shown greater than the median of these numbers?
(1) x > 3
(2) x < 7
If x is an integer, is the mean of the five numbers shown greater than the median of these numbers?
(1) x > 3
(2) x < 7
Statement 1
(1) x > 3
Case 1 : Assume x = 10 ⇒ Mean = Median
\(3, \quad 5, \quad 7, \quad 10, \quad 10\)
Case 2 : Assume x = 100 ⇒ Mean > Median
\(3, \quad 5, \quad 7, \quad 10, \quad 100\)
Hence the statement is not sufficient.
Statement 2
(2) x < 7
Case 1 : Assume x = 10 ⇒ Mean = Median
\(0, \quad 3, \quad 5, \quad 7, \quad 10\)
Case 2 : Assume x = -100 ⇒ Mean < Median
\(-100, \quad 3, \quad 5, \quad 7, \quad 10\)
Hence the statement is not sufficient.
Combined
3 < x < 7 ; x = 4, 5, 6
Case 1 : Assume x = 4
\(3, \quad 4, \quad 5, \quad 7, \quad 10\)
Median = 5
Mean = 5.6
Therefore Mean > Median
Case 2 : Assume x = 5
\(3, \quad 5, \quad 5, \quad 7, \quad 10\)
Median = 5
Mean = 6
Therefore Mean > Median
Case 2 : Assume x = 6
\(3, \quad 5, \quad 6, \quad 7, \quad 10\)
Median = 6
Mean = 6.2
Therefore Mean > Median
In all cases, Mean > Median
Option C
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