A. 30

B. 25

C. 55

D. 27

E. 52

Correct Answer is Choice E. 52.

Explanatory Answer

Let the smallest of the 10 numbers be X_{1} and the largest be X_{10}.

The range for the 10 numbers is maximized when the smallest number is X_{1} is minimized and the largest number X_{10} is maximized.

Let us assume X_{1} to be 1.

The range of the first 7 numbers is 25. So, X_{7} = X_{1} + 25 = 1 + 25 = 26.

The range of the last 7 numbers is 30.

i.e., X_{10} = X_{4} + 30.

Our objective is to maximize X_{10}.

X_{10} is 30 more than X_{4}.

Therefore, if X_{4} is maximized, X_{10} will also be simultaneously maximized.

These 10 numbers are distinct integers.

Now let us find out what is the maximum value that X_{4} can take.

We know X_{7} is 26.

Hence, X_{6} cannot be more than 25; X_{5} cannot be more than 24 and X_{4} cannot be more than 23.

So, X_{4} can take a maximum value of 23.

So, max X_{10} = 23 + 30 = 53.

The range of the 10 numbers is X_{10} – X_{1} = 53 – 1 = 52.

David John says

shud we also consider neg integers..? distinct neg integers…