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In a certain deck of cards, each card has a positive integer [#permalink]
11 Apr 2012, 01:34

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64% (01:50) correct
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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 with the next large integer. If the each possible product is between 15 and 200, then the least and greatest integer on the card would be

A. 3 and 15 B. 3 and 20 C. 4 and 13 D. 4 and 14 E. 5 and 14

Re: In a certain deck of cards, each card has a positive integer [#permalink]
11 Apr 2012, 02:14

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sapna44 wrote:

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 with the next large integer. If the each possible product is between 15 and 200, then the least and greatest integer on the card would be

A. 3 and 15 B. 3 and 20 C. 4 and 13 D. 4 and 14 E. 5 and 14

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.

Else you could find that the greatest value is 13 and since only C offers it, then it must be correct. _________________

Re: In a certain deck of cards, each card has a positive integer [#permalink]
05 Aug 2014, 11:39

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Re: In a certain deck of cards, each card has a positive integer [#permalink]
16 Apr 2015, 14:56

The part that was confusing to me was the wording, "If each possible product is between 15 and 200..." I took that to mean it had to be 15 at the lowest and 200 at the highest. Since there aren't any perimeters that fit those integers, it burnt up my time and left me frustrated. Learned and moved forward though.

Re: In a certain deck of cards, each card has a positive integer [#permalink]
16 Apr 2015, 18:28

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Expert's post

Hi All,

Since the answers to this question are numbers, I'm going to TEST THE ANSWERS.

We're told that, after drawing a card, you must multiply the number on the card by the next larger integer and end up with a number between 15 and 200. We're asked for the smallest and largest possible numbers on the cards.

IF the number was 3, then… 3(4) = 12, which is NOT between 15 and 200. Eliminate A and B.

IF the number was 4, then… 4(5) = 20, which IS between 15 and 200. Eliminate E.

Now, on to the biggest number:

IF the number was 13, then… 13(14) = 182 IF the number was 14, then… 14(15) = 210

Re: In a certain deck of cards, each card has a positive integer [#permalink]
17 Apr 2015, 00:38

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Expert's post

Quote:

I found the wording a bit confusing, the child draws a card and multiplies it with the next large integer.

I didn't really get the idea that the card numbers were consecutive.

Agreed. I couldn't think of anything other the next consecutive integer and hence used that. Wasn't completely sure but the answer options made sense with this assumption.

Quote:

The part that was confusing to me was the wording, "If each possible product is between 15 and 200..." I took that to mean it had to be 15 at the lowest and 200 at the highest. Since there aren't any perimeters that fit those integers, it burnt up my time and left me frustrated. Learned and moved forward though.

Between could mean either - including the extremes or excluding the extremes. It is usually specified when you do need to know it. 15 cannot be represented as a product of two consecutive integers and hence you know that the extremes are not included. Hence giving this information here was no essential.

Another Method: Look for the square root - 15 square root will be 3.something but 3*4 = 12 (which does not lie in 15 to 200). So 4 must be the smallest integer. 200 square root will be 14.something because 14^2 = 196. 14*15 will be more than 200 so the largest number must be 13.

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