word problem

[teejaycrown]

In a certain deck of cards, each card has a particular integer written on it. In a multiplication game, a child draws a card and multiplies the integer on the card by the next larger integer. If each possible product is between 15 and 200, then the least and greatest integers on the cards could be
3&15, 3&20, 4&13, 4&14, 5&14

[bursal]

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.

[eaakbari]

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