Set A = {2, 3, 4, 5}, and set B = {4, 5, 6, 7, 8}. If P = th

Brent@GMATPrepNow wrote:Set A = {2, 3, 4, 5}, and set B = {4, 5, 6, 7, 8}. If P = the product of one number chosen from set A and one number chosen from set B, how many DIFFERENT values of P are possible?

A) 14
B) 15
C) 16
D) 18
E) 20

Answer: C
Difficulty level: 600 - 650
Source: www.gmatprepnow.com

Let's list and count all possible outcomes.

Possible products when 2 is selected from set A: 8, 10, 12, 14, 16
Possible products when 3 is selected from set A: 12, 15, 18, 21, 24
Possible products when 4 is selected from set A: 16, 20, 24, 28, 32
Possible products when 5 is selected from set A: 20, 25, 30, 35, 40
When we IGNORE the duplicates in red, we get:
TOTAL outcomes = 16

Answer: C
IMPORTANT: I created the question to highlight the fact that, when it comes to counting questions, many students are reluctant to simply list and count the possible outcomes.

In this case, all 5 answer choices are relatively small, so we can be sure that it won't take long to list and count the outcomes.

That said, even when the answer choices are large, listing possible outcomes can often lead to useful insights regarding the correct answer.

Cheers,
Brent

Brent@GMATPrepNow wrote:

Brent@GMATPrepNow wrote:Set A = {2, 3, 4, 5}, and set B = {4, 5, 6, 7, 8}. If P = the product of one number chosen from set A and one number chosen from set B, how many DIFFERENT values of P are possible?

A) 14
B) 15
C) 16
D) 18
E) 20

Answer: C
Difficulty level: 600 - 650
Source: www.gmatprepnow.com

Let's list and count all possible outcomes.

Possible products when 2 is selected from set A: 8, 10, 12, 14, 16
Possible products when 3 is selected from set A: 12, 15, 18, 21, 24
Possible products when 4 is selected from set A: 16, 20, 24, 28, 32
Possible products when 5 is selected from set A: 20, 25, 30, 35, 40
When we IGNORE the duplicates in red, we get:
TOTAL outcomes = 16

Answer: C
IMPORTANT: I created the question to highlight the fact that, when it comes to counting questions, many students are reluctant to simply list and count the possible outcomes.

In this case, all 5 answer choices are relatively small, so we can be sure that it won't take long to list and count the outcomes.

That said, even when the answer choices are large, listing possible outcomes can often lead to useful insights regarding the correct answer.

Cheers,
Brent

Apt advice Brent. When it comes to counting questions, many students are reluctant to simply list and count the possible outcomes.

-Jay
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