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In a certain deck of cards

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by rajeet123 » Tue Jun 11, 2019 8:49 am
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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
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by rajeet123 » Tue Jun 11, 2019 8:49 am
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.
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by GMATGuruNY » Tue Jun 11, 2019 8:56 am
rajeet123 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
We can PLUG IN THE ANSWERS, which represent the least and greatest integers on the cards.

D: least = 4, greatest = 14
(14)(next larger integer) = 14*15 = 210.
Too big, since each possible product must be less than 200.
Implication:
The greatest integer must be LESS THAN 14.
Eliminate A, B, D and E.

The correct answer is C.
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by Scott@TargetTestPrep » Fri Jun 14, 2019 8:26 am
rajeet123 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

Since the smallest product is at least 15, and since 3 x 4 = 12, we can eliminate answers A and B.

We also see that 4 must be the minimum integer on any of the cards since 4 x 5 = 20, which is the smallest product above 15. We can, therefore, eliminate answer choice E, and we are left to choose between answers C and D.

Let’s check the maximum value from answer choice C.

13 x 14 = 182

13 could be the maximum value. Let’s test answer choice D.

14 x 15 = 210

Since 210 is greater than 200, D is not correct.

Answer: C

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