In a certain deck of cards, each card has a positive 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
a) 3 and 15
b) 3 and 20
c) 4 and 13
d) 4 and 14
e) 5 and 14

trial and error is the way to go here.
the # on the card is orange.

1 x 2 = 2
2 x 3 = 6
3 x 4 = 12
4 x 5 = 20 (so 4 is the smallest possible card number)
5 x 6 = 30
.
.
.
12 x 13 = 156
13 x 14 = 182
14 x 15 = 210 (so 13 is the smallest possible card number)

answer = c
notice that just finding the upper bound of 13 is good enough, because only one of the answer choices features that number.
auxiliary lesson: don't just pick numbers that appear more than other numbers do. specifically, don't assume that the upper bound is 14 just because 14 is the only number that appears more than once in the answer choices.

the q is greatest num here ??
when we multiply 13 * 14 the ans shud be 182 here .....so the greatest integer is 14 ??? not thirteen ??

and also u have mentioned 13 as the smallest num ???
Plz explain

* first, please type complete words in your posts. the extra time required to type "should" instead of "shud" is negligible, and doing so makes your posts MUCH easier for everyone to read.

* if you're multiplying 13 x 14, then the number ON THE CARD is 13. remember, the directions are to multiply the integer on the card by the next LARGER integer. this means that the smaller of the two numbers is the one on the card.
if 14 is on the card, you'd have 14 x 15, which is too big.

* i don't understand the final question (13 was never mentioned as the smallest number; it's the biggest one). check out the post above, which shows that 4 is the smallest possible number on the card.