Here's the complete question:
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
Let's first determine the
least possible integer.
We'll use the answer choices to help us along...
A) Could the smallest value on the card be 3?
Well, the next larger integer is 4, and 3 x 4 = 12, which is OUTSIDE the given range of 15 to 200
So, we can ELIMINATE A and B
C) Could the smallest value on the card be 4?
The next larger integer is 5, and 4 x 5 = 20, which is WITHIN the given range
So, 4 must be the LEAST possible value on the card
ELIMINATE E
Now, let's determine the
greatest possible integer.
The 2 remaining answer choices tell us that the greatest possible integer is EITHER 13 OR 14
Let's test 14 first (WHY? Since we're looking for the GREATEST value, it makes sense to check the biggest value first)
The next larger integer is 15, and 14 x 15 = 210, which is OUTSIDE the given range of 15 to 200
So, we can ELIMINATE D
IMPORTANT: We're not going to waste valuable time testing to see whether 13 works, since we've already eliminated A, B, D and E
Answer: C
Cheers,
Brent
Last edited by Brent@GMATPrepNow on Tue Aug 28, 2018 6:07 am, edited 1 time in total.
Brent Hanneson - Creator of GMATPrepNow.com
