Data Sufficiency

The range of set A is R. A number having a value equal to R is added to set A. Will the range of set A increase?
(1) All the numbers in set A are positive.
(2) The mean of the new set is smaller than R.

the range is the difference between the highest and lowest number in the set. and the question is basically asking if the range is higher than the highest number - because that is the only way the range can increase.

1) if we know all the numbers are positive then it is impossible for H-L to be greater than H (any time you subtract a positive number from a positive number the result is less than the original). Therefore this is sufficient to say that the range will not change - thus you have only answers A and D left.

2) the mean is the average of the numbers - I did this by picking some numbers and checking for sets with all positives vs. sets with some negatives:

if the set is (1234) then the range is 3 and the new set would be 1, 2, 3, 3, 4 - the average is 13/5 which is less than 3 BUT you can also get this with a set including negative numbers. If the set is (-1, 2, 3) then the range is 4 and the new set is -1, 2, 3, 4 with an average of 2. Thus the new average is less than R. Knowing this you can have either type of set so it is insufficient to answer the question.

The answer is A.

A can't be the answer. Range can be increased if new number added is smaller than smallest number.
e.g. 10, 11, 12.
Range is 12-10 = 2.

New set, 2, 10, 11, 12
New Range is 12-2 = 10(which is > 2).

If set is 1, 2, 3
Range is 3-1 = 2

New set 1, 2, 2, 3
New Range remains same i.e 2.

Nice caught crackthegmat2011

Please post OA

IMO C.

opponent wrote:The range of set A is R. A number having a value equal to R is added to set A. Will the range of set A increase?
(1) All the numbers in set A are positive.
(2) The mean of the new set is smaller than R.

IMO C

Let set A = {a,b,c}

Statement 1 - In sufficient
By testing Numbers
{2,6,8} ---> Range = 6 ---> New Set {2,6,6,8} ---> New Range 6 ---> No change
{5,7,8} ---> Range = 3 ---> New Set {3,5,7,8} ---> New Range 5 ---> Changed


Statement 2 - In sufficient
Statement 2 says ---> The mean of the new set is smaller than R.
In set A {a,b,c} ---> Range (c-a) ---> New Mean (a+b+c+c-a)/4 = (2c+b)/4
Implying, (2c+b)/4 < (c-a)
2c+b < 4c-4a
4a<2c-b
a<(2c-b)/4

Now using above equation in set A {a, 4, 10)
a<(20-4)/4 ---> a<4

Case 1 - when a is positive
A {2,4,10} ---> Range = 8 ---> New Set {2,4,8,10} ---> New Range 8 ---> No change
A {0.5,4,10}--> Range = 9.5 ---> New Set {0.5,4,9.5,10} ---> New Range 9.5 ---> No change

Case 2 - when a is Negative
A {-2,4,10} ---> Range = 12 ---> New Set {-2,4,10,12} ---> New Range 14 ---> Changed
A {-0.5,4,10}--> Range = 10.5 ---> New Set {-0.5,4,10,10.5} ---> New Range 11 ---> Changed
A {-300,4,10}--> Range = 310 ---> New Set {-300,4,10,310} ---> New Range 610 ---> Changed


Statement 1 & 2 - Sufficient
Case 1 - when a is positive
A {2,4,10} ---> Range = 8 ---> New Set {2,4,8,10} ---> New Range 8 ---> No change
A {0.5,4,10}--> Range = 9.5 ---> New Set {0.5,4,9.5,10} ---> New Range 9.5 ---> No change

I'm getting E as answer.

Let Set A = {1,2,3}

=> Range = 2

If we add x = R = 2, then the range remain the same

Let Set A = {1,1,1}

Range = 0

If we add x = R = 0 in this set, then the range become 1-0 = 1

So (1) is Insufficient

(2)


In case 2 above, if we add x = 0, then mean is lesser and the Range increases.

Again, let A = {1,1,2} then if we add x = 1, the new mean = 5/4 < original mean = 4/3, but the range remains same.

So Insufficient

(1) + (2) includes all cases above

Answer - E

In case 2 above, if we add x = 0, then mean is lesser and the Range increases.

Condition 1 says all the numbers in set A are positive. therefore this case is not applicable when using both statements 1 & 2 together.