Good one

A
let set be all nos from 10 .... 20
range = 10

if we add 10, range no change



let set be all nos from 100 .... 110
range = 10

if we add 10, range will change

so A insuff




B [we can use negative nos also to invalidate this point but let me try with +ve ones]
mean is smaller
means added no is less than prev mean

Example
let set be all nos from 10 ... 20
range = 10
mean = 15

added no = 5 [range will change]
added no = 14[range will not change]

so insufficient



A+B
The example of point B still holds



so IMO ans is E

whats the OA??

I agree with @stop800...E should be the ans..whats the OA?

stop@800 wrote:Good one

A
let set be all nos from 10 .... 20
range = 10

if we add 10, range no change



let set be all nos from 100 .... 110
range = 10

if we add 10, range will change

so A insuff




B [we can use negative nos also to invalidate this point but let me try with +ve ones]
mean is smaller
means added no is less than prev mean

Example
let set be all nos from 10 ... 20
range = 10
mean = 15

added no = 5 [range will change]
added no = 14[range will not change]

so insufficient



A+B
The example of point B still holds



so IMO ans is E

whats the OA??

I did exactly same way and got E but OA is A and it is not wrong.

I'm not sure how A would suffice.

As long as the Largest number in the set is smaller than twice the shortest number, the range will increase.

2 2 2 => add 0 and the new range is 2. range of original set was 0.

2 3 => add 1 and the new range is 2. range of original set was 1

2 2 6 => add 4 and the new range is equal to the old range -- 4.

In both the cases all the numbers are positive and you get a Yes and a No.

How can it be A?

stop@800 wrote:Good one
mean is smaller
means added no is less than prev mean

Example
let set be all nos from 10 ... 20
range = 10
mean = 15

added no = 5 [range will change]
added no = 14[range will not change]

There are few flaws in stop@800 solution.
The problem says “mean is smaller than R” and not “the mean is smaller”
You cannot add 5 nor 14, because they are not the range. Than range in that case is 10.

My answer is C.
“The mean of the new set is smaller than R.” means that R is actually bigger than the mean of the new set. We need to know though if R is in the set or has a value bigger than any element of the set. For later, it means that R will be bigger than the initial range since all elements are positive (and we know from the stem that R equals the range).
We are left with “mean"<R<biggest element of the set which means the range will not change.

Please provide me with an example that proves me wrong.

youngwolf wrote:

stop@800 wrote:Good one
mean is smaller
means added no is less than prev mean

Example
let set be all nos from 10 ... 20
range = 10
mean = 15

added no = 5 [range will change]
added no = 14[range will not change]

There are few flaws in stop@800 solution.
The problem says “mean is smaller than R” and not “the mean is smaller”

Good Catch. Thanks

You cannot add 5 nor 14, because they are not the range. Than range in that case is 10.

My answer is C.
“The mean of the new set is smaller than R.” means that R is actually bigger than the mean of the new set. We need to know though if R is in the set or has a value bigger than any element of the set. For later, it means that R will be bigger than the initial range since all elements are positive (and we know from the stem that R equals the range).
We are left with “mean"<R<biggest element of the set which means the range will not change.

Please provide me with an example that proves me wrong.