Working from the answer choices is an effective way of going about this problem. The choices for the least of the numbers are 3, 4 and 5. The next greater integer in each case is 4, 5 and 6, respectively, and so the product of interest would be 3*4, 4*5 and 5*6, respectively. We can see that 3*4 is less than 15 and violates our constraint. Thus the least possible number has to be 4. This narrows the answer to C or D.

Next, look at the options for the greatest of the integers: C has 13 and D has 14. In the first case, the product of interest would be 13*14, which is less than 200, whereas in the second case, the product would be 14*15, which is greater than 200. Thus the greatest possible integer is 13, and the correct answer is C.

The approach would be to Identify a perfect square closest to the 2 points.

Between 15 & 200

15 would have the P.S. 16 closest to it (4^2).

Try one number below it - 3 , hence 3*4 = 12. which is out of the range.
4*5 = 20 which is the next consecutive set of consecutive numbers in the range. Hence 4 is is one. (Eliminate answers A,B & E)


200 -
p.s. closest is 196 (14*14)
if you didn't know that you could pick 225 (15*15)

This leaves us with Options as 13 or 14. (If 14*14 is 196 then surely 14*15 is above 200).
HENCE 13 is other end of the range.

Answer C