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- akhilsuhag
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Look for values that satisfy both statements.x, 3, 1, 12, 8
If x is an integer, is the median of the 5 numbers shown greater than the average of the 5 numbers?
1) x>6
2) x is greater than the median of the 5 numbers
Be sure to try extreme values.
If x=9:
The numbers are 1, 3, 8, x=9, 12.
Average = (1+3+8+9+12)/5 = 33/5.
Median = 8.
Average < median.
If x=100:
The numbers are 1, 3, 8, 12, x=100.
Average = (1+3+8+12+100)/5 = 124/5.
Median = 8.
Average > median.
Since in the first case the average is less than the median, and in the second case the average is greater than the median, the two statements combined are INSUFFICIENT.
The correct answer is E.
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- Brent@GMATPrepNow
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Target question: Is the median greater than the average?x,3,1,12,8
If x is an integer, is the median of the 5 numbers shown greater than the average (AM) of 5 numbers?
1. x >6
2. x is greater than the median of 5 numbers
Given: We have the set {1, 3, 8, 12, x}
Notice that there are 3 possible scenarios we need to consider:
Scenario #1: x is less than 3, in which case the median is 3
Scenario #2: 3 < x < 8, in which case the median is x
Scenario #3: x is greater than 8, in which case the median is 8
The average of this set will be (24+x)/5.
Okay, now onto the statements
Statement 1: x > 6
This rules our scenario #1, but we must still consider scenarios #2 and #3
Here are two possible values of x that yield conflicting answers to the target question:
Case a: x = 7 (median = 7 and average = 31/5), in which case, the median is greater than the average
Case b: x = 21 (median = 8 and average = 9), in which case, the median is NOT greater than the average
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x is greater than the median of the 5 numbers
This rules our scenarios #1 and #2, which leaves scenario #3
Here are two possible values of x that yield conflicting answers to the target question:
Case a: x = 11 (median = 8 and average = 7), in which case, the median is greater than the average
Case b: x = 21 (median = 8 and average = 9), in which case, the median is NOT greater than the average
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
IMPORTANT: Notice that the x-values we used to show that statement 2 is not sufficient ALSO satisfy statement 1. So, we know immediately that the combined statements are NOT SUFFICIENT.
To see what I mean, here are the two conflicting cases:
Case a: x = 11 (median = 8 and average = 7), in which case, the median is greater than the average
Case b: x = 21 (median = 8 and average = 9), in which case, the median is NOT greater than the average
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT.
Answer = E
Cheers,
Brent