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# In a certain deck of cards, each card has a positive integer

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In a certain deck of cards, each card has a positive integer [#permalink]

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15 Sep 2006, 15:40
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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 largest 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
VP
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15 Sep 2006, 16:15
D. 4 and 14

Given product > 15 and < 200

Starting with smallest first product of consecutive integers > 15 is 4x5 = 20.

Largest consecutive integers with product < 200 = 13 x14 (as 14x15 = 210)

For this I just picked numbers.
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15 Sep 2006, 16:48
My thoughts as well, but OA is different...
VP
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15 Sep 2006, 21:46
Oh #%(#, I picked C initially .. I know my mistake....

If it were 14 then the product would be 14 x 15 > 200...

STUPID STUPID MISTAKE!!!!

eazyb81 wrote:
My thoughts as well, but OA is different...
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16 Sep 2006, 01:47
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 largest 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

15 < x(x+1)<200

equivelant to

15<x(x+1)

the smallest to consecutive intigers that can make this true is (4,5) and 4<5 thus the least intiger is 4

x(x+1) < 200

the largest to consecutive intigers that can make this true is (13,14) and 13<14 thus the largest intiger is 13 because

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16 Sep 2006, 02:47
Given the least value is 15 and max value is 200

From the options it's clear that answer is C.
4x5 =20 >15
13X14 = 182 <200

So the min and max no's on the cards must be 4 and 13

Regards,
_________________

Last edited by cicerone on 25 Sep 2008, 01:09, edited 1 time in total.
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16 Sep 2006, 08:56
OA is C....thanks guys!
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