Word Problem

This topic has expert replies
Senior | Next Rank: 100 Posts
Posts: 31
Joined: Fri Apr 10, 2015 4:04 am

Word Problem

by tapanmittal » Fri Jun 19, 2015 1:52 am
In a statewide poll, Y people were asked two questions, the only
answers to which were "yes" or "no." If 3
4 of them answered "no"
to question 1, and 2
3 of those answered "yes" to question 2,
which of the following expressions represents the number of
people interviewed who did not answer "no" to both questions?

(A) Y/12
(B) Y/4
(C) Y/2
(D) 3Y/4
(E) 11Y/12
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 am
Location: Montreal
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

by Ian Stewart » Fri Jun 19, 2015 2:01 am
I assume those are meant to be fractions, so 3/4 answer no to the first question, and 2/3 of those answer yes to the second question.

Then (3/4)Y people answer no to the first question. If 2/3 of these answer yes to the second question, the rest, or 1/3, must answer no. So (1/3)(3/4)Y = (1/4)Y answer no to both questions. The rest of the people, or Y - (1/4)Y = (3/4)Y, must have answered yes to at least one question.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Fri Jun 19, 2015 2:36 am
A clearer wording might be as follows:
In a statewide poll, Y people were asked two questions, the only answers to which were "yes" or "no." If 3/4 of the people answered "no" to question 1, and of those, 2/3 answered "yes" to question 2, which of the following expressions represents the number of people interviewed who did not answer "no" to both questions?

(A) Y/12
(B) Y/4
(C) Y/2
(D) 3Y/4
(E) 11Y/12
Let the total number of people = 12.

3/4 of them answered "no" to question 1.
Thus, the number who answered "no" to question 1 = (3/4)(12) = 9.

Of those, 2/3 answered "yes" to question 2.
Thus, of the 9 people who answered "no" to question 1, 1/3 also answered "no" to question 2:
(1/3)(9) = 3.

Which of the following expressions represents the number of people interviewed who did not answer "no" to both questions?
Since only 3 people answered "no" to both questions, the number of people who did NOT answer "no" to both questions = 12-3 = 9. This is our target.

Now plug Y=12 into the answer choices to see which yields our target of 9.
Only D works:
3Y/4 = (3*12)/4 = 9.

The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Senior | Next Rank: 100 Posts
Posts: 31
Joined: Fri Apr 10, 2015 4:04 am

by tapanmittal » Fri Jun 19, 2015 3:38 am
Thanks GMATGuruNY..I was missing on the keywords highlighted in red by you :)

GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Tue Jun 23, 2015 6:24 pm
I'm thinking Y - (No to Both), which is

Y - (3/4)*(1/3)*Y, or

Y - (1/4)Y, or (3/4)Y