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Newbie | Next Rank: 10 Posts
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by sahaldar » Mon Jul 16, 2007 2:34 am
Q) In a certain deck of card has a positive integers written on it. In a multiplication game, a child draw a card and multiplies the integer on the card by the next large integer. If each possible product is between 15 and 200, then the least and greates integers on the card could be.

a) 3 and 15
b) 3 and 20
c) 4 and 13
d) 4 and 14
e) 5 and 14

ans) C
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Junior | Next Rank: 30 Posts
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by blah45 » Mon Jul 16, 2007 5:27 am
15 < product < 200
Let's start with the upper limit of 200. How do we get the product? By multiplying two consecutive numbers (i.e., the number that was picked and the next larger number which would be the very next number after the one that was picked).

So, n_max * (n_max + 1) < 200
we know 13 * 13 = 169 (if you don't remeber this then you can always start @ 10 *11 = 110 and work your way up). 13* 13 is not valid b/c both numbers have to be different. So, we can try 13* 14 and then 14* 15.

13 * 14 = 182
14 * 15 = 210.

so, n_max = 13. At this point we already know that the answer is (C).

Just to complete the problem ...
Similarly, n_min * (n_min + 1) > 15. We know that 4 * 4 = 16 (again, this is not valid b/c both numbers have to be different). so, 4 * 5 = 20. That meets the requirement.
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