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

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GeminiHeat
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In a certain deck of cards, each card has a positive integer written [#permalink] New post   30 Apr 2022, 11:38
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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 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
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C
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grenoob28
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Re: In a certain deck of cards, each card has a positive integer written [#permalink] New post   03 May 2022, 23:56
Hi OP. Would love to hear the solution for the problem. Thanks
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Re: In a certain deck of cards, each card has a positive integer written [#permalink] New post   04 May 2022, 02:41
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Given: 15<x(x+1)<200.

Now, it's better to test the answer choices here rather than to solve:

If x=3 then x(x+1)=12<15 --> discard A and B;

If x=4 then x(x+1)=20>15 --> so, the least value is 4, discard E. Test for the largest value: if x=14 then x(x+1)=14*15=210>200 --> discard D.

Answer: C.
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Re: In a certain deck of cards, each card has a positive integer written [#permalink] New post   29 Oct 2023, 09:09
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Use some reasoning:

We know the products are greater than 15, but less than 200.
The lower bound is easy:
If the lowest card were 3, then one of the products would be 12 as 3*4 is 12. Therefore, the lowest card can be 4 - 4*5 is 20, which is over 15.
The upper bound:
Since we know that 15 times 15 is 225, we should try numbers that are near by.
Clearly 15 wont work, since 15*15 is 225, and 15*16 would be larger than that.
14 also does not work as 14*15 is 210, which is greater than 200
So the max card can be 13.

C.
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