Anurag@Gurome wrote:

Ashujain wrote:Set A has 20 numbers and Set B has 40 numbers. Is the range of B greater than 45?

1) The range of sets A and B combined exceeds 50.
2) The range of B > range of A

I'm going to solve this by plugging numbers.

My intuition says, the statements do not provide any solid pointer to answer the question. Hence, I'm making a guess that both of them together are not sufficient. And accordingly I'll pick numbers and try to show that. If I fail at that, I'll try otherwise.

Take the following to cases...
Case 1:

• A = {0, 0, ..., 25}, i.e. nineteen zeroes and 25
  B ={0, 0, ..., 50}, i.e. 39 zeroes and 50
  Range of A = (25 - 0) = 25
  Range of B = (50 - 0) = 50

Case 2:

• A = {0, 0, ..., 25}, i.e. nineteen zeroes and 25
  B ={0, 0, ..., 30}, i.e. 39 zeroes and 30
  Range of A = (25 - 0) = 25
  Range of B = (30 - 0) = 30

Both the above cases satisfy both the statements, but in the first case range of B is greater than 45 but not in the second case.

The correct answer is E.

@Anurag

I am not sure but i guess you have misunderstood statement 1.

You have taken it as Range of set A + Range of set B > 50 but Statement 1 is 'the range of a set which is made by combining sets A and B exceeds 50'.

Will it make any difference to the answer anyway?

I guess we can then solve it by considering both the statements together. Below is my explanation:

Case1:
A = {0, 0, ..., 25}, i.e. nineteen zeroes and 25
B ={0, 0, ..., 51}, i.e. 39 zeroes and 50
Range of A = (25 - 0) = 25
Range of B = (51 - 0) = 51
Range of combined set = 51 - 0 = 51

Case2:
A = {51, 51, ..., 52}, i.e. nineteen 51s and 52
B ={0, 0, ..., 51}, i.e. 39 zeroes and 50
Range of A = (52 - 51) = 1
Range of B = (51 - 0) = 51
Range of combined set = 52 - 0 = 52

Hence, we can say that Range of set B will always be greater than 45 when we combine statements 1 and 2.

Kindly correct me if I am wrong.

Anurag@Gurome wrote:

Ashujain wrote:@Anurag

I am not sure but i guess you have misunderstood statement 1.

You have taken it as Range of set A + Range of set B > 50 but Statement 1 is 'the range of a set which is made by combining sets A and B exceeds 50'.

If that is the case, consider the following two cases...
Case 1:

• A = {0, 0, ..., 25}, i.e. nineteen zeroes and 25
  B ={0, 0, ..., 60}, i.e. 39 zeroes and 60
  Range of A = (25 - 0) = 25
  Range of B = (60 - 0) = 60
  Range of the combined set = (60 - 0) = 60 > 50

Case 2:

• A = {-25, 0, 0, ...}, i.e. nineteen zeroes and -25
  B ={0, 0, ..., 30}, i.e. 39 zeroes and 30
  Range of A = (0 - (-25)) = 25
  Range of B = (30 - 0) = 30
  Range of the combined set = (30 - (-25)) = 55 > 50

Both the above cases satisfy both the statements, but in the first case range of B is greater than 45 but not in the second case.

The correct answer is E.

Thanks Anurag! Got it now...