A set of 1522 numbers has a single mode. If the mode repeats 12 times

Given: Single mode and it occurs 12 times. 1522 - 12 = 1510 numbers whose mode we don't know.

To find the RANGE(max-min) of number of unique numbers, we'll take two cases:

Case 1: Where the number of unique numbers is Maximum:

Since we already know that one number is occurring 12 times, we'll keep that aside and look at the remaining 1510 numbers.
1510/2 = 755.

Divided by 2 because every number is repeated atleast twice as stated in the question.
So there are 755 numbers that occurs twice in this series.
(1,1,2,2,3,3,4,4,..... 755 numbers like this, and, 123,123,123,123(12 times))


So total unique numbers = 755 + 1 = 756.

Case 2: For the Unique numbers to be minimum.

1510/11 = 137 + 3 remainder

Divided by 11 because we have a single mode that occurs 12 times. So the other numbers can repeat 11 times. And the remainder 3 can be of a same number.

So the total unique numbers in this set is 137 + 1 + 1 = 139

Range = 756 -139 = 617

OA - D.