In a nationwide poll, P people were asked 2 questions. If

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

In a nationwide poll, P people were asked 2 questions. If

by BTGmoderatorDC » Tue Jul 31, 2018 4:23 pm

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In a nationwide poll, P people were asked 2 questions. If 2/5 answered "yes" to question 1, and of those 1/3 also answered "yes" to question 2, which of the following represents the number of people polled who did not answer "yes" to both questions?

A. 2/15*P
B. 3/5*P
C. 3/4*P
D. 5/6*P
E. 13/15*P

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Source: Beat The GMAT — Problem Solving | Tue Jul 31, 2018 4:23 pm

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by [email protected] » Tue Jul 31, 2018 6:09 pm

Hi All,

We're told that in a nationwide poll, P people were asked 2 questions, 2/5 answered "yes" to question 1, and OF THOSE people, 1/3 also answered "yes" to question 2. We're asked which of the following represents the number of people polled who did NOT answer "yes" to BOTH questions. This question can be solved in a couple of different ways, including by TESTing VALUES.

From a strategic standpoint, we should look to choose a value for P that is a multiple of both 5 and 3 (since 2/5 and 1/3 are fractions that we'll have to deal with when we do our calculations). Let's TEST P = 15

IF... there are 15 people....
then (2/5)(15) = 6 answered 'yes' to question 1
and (1/3)(6) = 2 of those people answered 'yes' to question 2.
Of the 15 original people, only 2 answered 'yes' to BOTH questions and 15 - 2 = 13 did NOT answer 'yes' to BOTH questions.

Thus, we're looking for an answer that equals 13 when P=15. Only one of the answers matches...

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Aug 10, 2018 5:38 pm

BTGmoderatorDC wrote:In a nationwide poll, P people were asked 2 questions. If 2/5 answered "yes" to question 1, and of those 1/3 also answered "yes" to question 2, which of the following represents the number of people polled who did not answer "yes" to both questions?

A. 2/15*P
B. 3/5*P
C. 3/4*P
D. 5/6*P
E. 13/15*P

The number of people who answered yes to both questions is (2/5)P x 1/3 = (2/15)P, so (13/15)P did not answer yes to both questions.

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]