In a certain deck of cards, each card has a positive...

swerve wrote: ↑

Fri Dec 22, 2017 1:53 pm

In a certain deck of card has a positive integer written on it. In a multiplication game, a child draws a card and multiples 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 card could be?

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

The OA is C.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

Let's start by determining the value of the SMALLEST possible number on the cards.

The answer choices tell us that the smallest number is 3, 4, or 5.

Given: In a multiplication game, a child draws a card and multiplies the integer on the card by the next larger integer.
If the smallest number is 3, then the next larger integer is 4.
The product 3 x 4 = 12, however the question tells us that all possible products are between 15 and 200
So, the smallest number cannot be 3.

Let's see if 4 can be the smallest possible number
If the smallest number is 4, then the next larger integer is 5, and the product 4 x 5 = 20, which IS between 15 and 200
Since the smallest possible number is 4, the correct answer is either C or D.

Let's test answer choice D, which tells us the LARGEST possible number is 14.
If the largest number is 14, then the next larger integer is 15, and the product 14 x 15 = 210, which is NOT between 15 and 200
So, we can eliminate answer choice D, which means the correct answer must be C

Cheers,
Brent