Data Sufficiency

x,3,1,12,8

If x is an integer, is the median of the 5 numbers shown greater than the average (arithmetic mean) of the 5 numbers?

1. x>6
2. x is greater than the median of the 5 numbers


oa tba

I get E)

OA,please?

Hi Ch,
Friendly request: If you could post the OA wiht the spoiler function going forward it would be much appreciated!

cramya wrote:I get E)

OA,please?

Hi Ch,
Friendly request: If you could post the OA wiht the spoiler function going forward it would be much appreciated!

I agree both with your spoiler request and E choice.

1) Insuf X can be 1000000000000 and the mean can;t be greater than the AV

2) Insuf - it only tells us that x > 12 and with the same logic in (1) it can be 10000000000000 and mean can't be greater than AV

Yes E is correct

Sry I didn't know how to do the spoiler thing at first, now I do

Sir, what is "AV"?

tkhalid wrote:Sir, what is "AV"?

average (arithmetic mean)

logitech wrote:

cramya wrote:I get E)

OA,please?

Hi Ch,
Friendly request: If you could post the OA wiht the spoiler function going forward it would be much appreciated!

I agree both with your spoiler request and E choice.

1) Insuf X can be 1000000000000 and the mean can;t be greater than the AV

2) Insuf - it only tells us that x > 12 and with the same logic in (1) it can be 10000000000000 and mean can't be greater than AV

Agree with the answer but the reasoning has to rule out a definite "No" to the question, as a definite "No" would make the statements sufficient as well.

To rule out a definite No:

From statement two, we basically know that if X is higher than the median, which implies that the median has to be 8. Since the sum of the four numbers given is 24, if X is 9 then the arithmetic average is 33/5 = less than 8 (the median), however if X is instead something large like 21, the arithmetic average is 45/5 = 9 (greater than 8 - the median). Therefore a definite "No" is not possible in this case.

Therefore answer is E.

[quote="praneeth]Agree with the answer but the reasoning has to rule out a definite "No" to the question, as a definite "No" would make the statements sufficient as well.

To rule out a definite No:

From statement two, we basically know that if X is higher than the median, which implies that the median has to be 8. Since the sum of the four numbers given is 24, if X is 9 then the arithmetic average is 33/5 = less than 8 (the median), however if X is instead something large like 21, the arithmetic average is 45/5 = 9 (greater than 8 - the median). Therefore a definite "No" is not possible in this case.

Therefore answer is E.[/quote]

hi,

can u pls explain how the median is 8?

logitech wrote:

2) Insuf - it only tells us that x > 12 and with the same logic in (1) it can be 10000000000000 and mean can't be greater than AV

Logitech,

Shouldnt stmt 2 give us x>8 instead of x>12? Am i missing something here?

jimmiejaz wrote:[quote="praneeth]Agree with the answer but the reasoning has to rule out a definite "No" to the question, as a definite "No" would make the statements sufficient as well.

To rule out a definite No:

From statement two, we basically know that if X is higher than the median, which implies that the median has to be 8. Since the sum of the four numbers given is 24, if X is 9 then the arithmetic average is 33/5 = less than 8 (the median), however if X is instead something large like 21, the arithmetic average is 45/5 = 9 (greater than 8 - the median). Therefore a definite "No" is not possible in this case.

Therefore answer is E.

hi,

can u pls explain how the median is 8?[/quote]

If X is smaller than 8 and larger than the median the numbers would look something like:

1, 3, X, 8 12

since there are only two numbers smaller than X, and two numbers greater than X no other number can be the median, i.e. X has to be the median which doesn't satisfy our assumption that X is greater than the median.

There are only two numbers smaller than 8 in the data set, therefore for X to be greater than the median X has to be greater than 8.

hi praneeth,

thanks for the explanation. Actually, i got confused. In the post above yours, i had deduced the same that x>8 for x to be greater than the median. I asked x>8 and you wrote median = 8. both are different interpretations for the same thing.
cheers!!!!!