Data Sufficiency

I misread the ques as the median of the numbers is greater than 2 and came to a conclusion that the answer is A...

its a day of making silly mistakes.....

A series of 5 numbers is 3, 4, 5, 5, x, is the range greater than 2?
1> the median of the numbers is greater than the mean

Median> mean

3+4+5+5+x/5

median = 5

Then its sufficient

but if its 6 range will vary.



2> the median is 4

meadian= 4

x has to be less than 3

range not clear

Combining statement 1 and 2...range can be clear

Hence C

ern5231 wrote:A series of 5 numbers is 3, 4, 5, 5, x, is the range greater than 2?
1> the median of the numbers is greater than the mean
2> the median is 4

What needs to be concluded: Is x<3 to answer if Range >2.

A. Not sufficient
x=0, Mean = 3.2, median = 4, Range >2? Yes
x=2, Mean = 3.8, Median =4, Range >2? Yes
x=3, Mean = 4, Median =4, Range >2? No
x=5, Mean = 4.4, Median =5, Range >2? No
x=6, Mean = 4.6, Median = 5, Range >2? Yes
It satisfies requirement of x<3, but it also satisfies x>5

B. Not Sufficient
So plug in x=2 and x=6
x=2, Median =4, Range>2? Yes
x=6, Median = 5, Range >2? Yes
But, x=3, Median =4, Mean = 4, Range >2? No.

So A&B together shows when x<3, it satisfies all the conditions as below:
1. Range>2
2. Median > Mean
3. Median =4

So Answer is C

I hope this is right way of solving!

deleted

A series of 5 numbers is 3, 4, 5, 5, x, is the range greater than 2?
1> the median of the numbers is greater than the mean
2> the median is 4

We need to determine if 3 <= x <= 5 (range = 2), or not (range > 2).

You should recognize that:
if x <= 4, the median is 4
if 4 <= x <= 5, the median is x
if x >= 5, the median is 5

Statement 1: Median > Mean
Plugging in is one approach, but many people have done this, so instead I will take the approach of figuring out when this is true.

The median is either 4, 5, or x
The mean is (17 + x)/5 = 3.4 + x/5

So, the mean and median are equal in three places:
3.4 + x/5 = 4
x/5 = 0.6
x = 3

3.4 + x/5 = x
3.4 = 0.8x
x = 3.4/0.8 = 34/8 = 17/4 = 4.25

3.4 + x/5 = 5
x/5 = 1.6
x = 8

So, those are the three boundary points, which create 4 regions
When x < 3, the median is 4 but the mean is smaller: MEDIAN > MEAN
When 3 < x < 4.25, the median is 4 or x, and the mean is slightly bigger: MEDIAN < MEAN (if you're not sure about this region, you can just plug in x = 4, which gives you median = 4, mean = 4.2)
When 4.25 < x < 8, the median is x or 5, and the mean is slightly smaller: MEDIAN > MEAN (if you're not sure about this region, you can just plug in x = 6, which gives you median = 5, mean = 4.6)
When x > 8, the median is 5 but the mean is larger: MEDIAN < MEAN

So, MEDIAN > MEAN means either x < 3 (in which case the range is > 2) OR 4.25 < x < 8 (in which case the range might be 2 or it might be bigger). Insufficient.

Statement 2: Median = 4
This is true whenever x <= 4. So, the range may or may not be > 2. Insufficient.

Combined:
St 1 tells us that x < 3 OR 4.25 < x < 8
St 2 tells us that x <= 4
Combined: x < 3. Range > 2. Sufficient.

i was able to conclude that the answer cannot be derived from the two statements individually but chose the wrong option E and did not think of combining them.next time ill try to keep this in mind.

Answer: B

Fell for trap answer B

ern5231 wrote:A series of 5 numbers is 3, 4, 5, 5, x, is the range greater than 2?
1> the median of the numbers is greater than the mean
2> the median is 4

Nas A

when x = 3 Median = 4 and mean > 4

only if x < 3 median is > mean so ans is A

*Not sure though

1) median >mean
x can take diff values
not sufficient

2) x=4,3,2,1
not sufficient

together, yes, range will be greater than 2!

ans: [C]

A in Answer.

3,3,4,5,5 gives Median = Mean = 4.

x,3,4,5,5 where, x < 3 will give Median(4) > Mean

Hence, Range (5-x) > 2

OA C.

in the string!
Median > mean.
that mean max number + x/2 > mean.

so (5+x)/2> (3+4+5+5+x)/5
...
x>3.
2. median is 4. for this string is sufficient.

so both of them are fine.

1) Median > Mean
x=2 => Median = 4, mean = 19/5<4, range = 3>2
x=5 => median = 5, mean = 22/5<5, range = 2

=> 1) is IS

2) Median = 4
=> x<=4
x=2 and x=4 will yield different results in term of range.

=> 2) is IS

Combine 2 stats: 4>mean or 20>x+17 or x<3 => range>2

Choose C

1)Mean = (17+x)/5 < median

There are 2 ways to maximise the range:

a) x>5,x = 5 + t, median = 5 (where t >= 0)
so (17+5+t)/5 < 5
so t < 3 (this works)

b) x<3,x = 3 - t median = 4 (where t >= 0)
so (17+3-t)/5 < 4
so t > 0 (this works)

Now let's try range = 2, x = median = 4.5:
so (17+4.5)/5 < 4.5
21.5 < 22.5 (this works too)
INSUFFICIENT

2)Median = 4
(17+x)/5 < 4
x < 3 (this works)
However, if 3<x<4 then it will not work.
INSUFFICIENT.

Combined:
As shown above, b) x<3,x = 3 - t median = 4 (where t >= 0)
so (17+3-t)/5 < 4
so t > 0 (SUFFICIENT)

Answer C.

A series of 5 numbers is 3, 4, 5, 5, x, is the range greater than 2?
1> the median of the numbers is greater than the mean
2> the median is 4
My answer is C.
Explanation:
1) Mean = (17+x)/5 and median depends on 'what number is x?' NS
2) Median = 4, it tells x must be on LHS, but it may be 2, 3, or 4. NS
1) & 2) together
If x=2; mean is 3.8 < median 4
If x =3; mean is 4 = median
If x =4; mean is 4.2 >median
Hence, range is greater than 2. And answer is c.