gmatprep question pack 1

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sam117: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Thu Feb 09, 2012 9:04 am

gmatprep question pack 1

by sam117 » Tue May 08, 2012 6:42 am

Is there a way to solve this in 2 mn? The official solution is very long.

A total of 800 students were asked whether they found two subjects, M and R, interesting. Each answer was either "yes" or "no" or "unsure", and the numbers of students who gave these answers are listed in the table above. If 200 students answered"yes" only for subject M, how many of the students did not answer "yes" for either subject?

A. 100
B. 200
C. 300
D. 400
E. 500

OA:
B

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Source: Beat The GMAT — Problem Solving | Tue May 08, 2012 6:42 am

niketdoshi123: Master | Next Rank: 500 Posts; Posts: 210; Joined: Thu Mar 08, 2012 11:24 pm; Thanked: 62 times; Followed by:3 members

by niketdoshi123 » Tue May 08, 2012 9:08 am

Total students = 800
Students answered "YES" only for subject M = 200
So the remaining students, who answered "YES" for subject M, also answered "YES" for subject R.=> 500-200 = 300
Students who answered "YES" only for subject R=400-300 = 100
Students who did not answer "yes" for either subject = 800-(200+300+100) = 200
Hence answer is B

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rockfeld: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Mon Oct 03, 2011 12:25 pm

by rockfeld » Sat Aug 18, 2012 1:54 pm

reply to niketdoshi123's solution. Why do you suppose that "the remaining students, who answered "YES" for subject M, also answered "YES" for subject R" ? the second choice of that 300 students could be any of: YES, NO, UNSURE. Am I missing smth?

) got it. the remain 300 stud. answered "yes to R" because if only one of them would answer "NO to R" or "Unsure to R", then this stud. would raise the initial # of students (200), that responded "Only Yes to M".

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George7: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Sat Oct 20, 2012 8:48 am

by George7 » Tue Oct 23, 2012 9:44 am

Can any expert help please? Thank you.

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George7: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Sat Oct 20, 2012 8:48 am

by George7 » Fri Nov 09, 2012 10:52 am

rockfeld wrote:reply to niketdoshi123's solution. Why do you suppose that "the remaining students, who answered "YES" for subject M, also answered "YES" for subject R" ? the second choice of that 300 students could be any of: YES, NO, UNSURE. Am I missing smth?

) got it. the remain 300 stud. answered "yes to R" because if only one of them would answer "NO to R" or "Unsure to R", then this stud. would raise the initial # of students (200), that responded "Only Yes to M".

Because it is written that "200 students answered YES only for subject M", this means that the remaining 300 students answered YES for M and for at least another subject, which can only be R. If it were not the case then the remaining 300 students would have answered YES only for subject M, this contradicts what the problem says.

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GMATGuruNY: 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 Nov 09, 2012 11:30 am

----------------YES---------NO----UNSURE
Subject M----500--------200-----100
Subject R----400--------100-----300

A total of 800 students were asked whether they found two subjects, M and R, interesting. Each answer was either "yes" or "no" or "unsure", and the numbers of students who gave these answers are listed in the table above. If 200 students answered "yes" only for subject M, how many of the students did not answer "yes" for either subject?

A. 100
B. 200
C. 300
D. 400
E. 500

Use a Venn diagram to represent all of the YES voters:

The TOTAL who voted YES for M = 500.
The number who voted YES for ONLY M = 200.
Thus, the number who voted YES for BOTH M AND R = 300.

Since the TOTAL number who voted YES for R=400, and 300 of these people voted YES for BOTH M AND R, the number who voted YES for ONLY R = 400-300 = 100.

Adding the values in the Venn diagram, we get:
Total number of YES voters = 200+300+100 = 600.

Since the total number of voters = 800, and the total number of YES voters = 600, the number who did NOT vote YES = 800-600 = 200.

The correct answer is B.

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pank27: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Sat Dec 21, 2013 5:03 am

by pank27 » Fri Aug 01, 2014 10:10 pm

Thanks for every one for nice explanation
--

I solved it this way.

Given: 200 students answered YES only for sub M. also from given table, total number of students, who answered YES to sub M = 500.
this implies, 500-200=300 students who answered YES to both sub M & sub R. => {MnR}

now i am applying sets formula of {M U R} = {M} + {R} - {MnR} = 500 + 400 - 300 = 600.
And ans to our que = Total - {M U R} = 800 - 600 = 200, are number of studs who didnt ans YES for either sub.

hope this helps too.

Thanks.

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Matt@VeritasPrep: 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 » Sat Aug 02, 2014 11:20 am

Another way of thinking about this:

500 people said "yes" to M. 200 said "yes" ONLY to M, so the other 300 must have said "yes" to both.

400 people said "yes" to R. From the above, we know that 300 of them said "yes" to both. That means 100 said "yes" only to R.

This gives us:
300 "yes" to both
200 "yes" only to M
100 "yes" only to R

For a total of 600 people who said "yes" to at least one. That means EVERYONE ELSE, or the other 200 people, said "no" to both.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Sat Aug 02, 2014 3:57 pm

----------------YES---------NO----UNSURE
Subject M----500--------200-----100
Subject R----400--------100-----300

A total of 800 students were asked whether they found two subjects, M and R, interesting. Each answer was either "yes" or "no" or "unsure", and the numbers of students who gave these answers are listed in the table above. If 200 students answered "yes" only for subject M, how many of the students did not answer "yes" for either subject?

A. 100
B. 200
C. 300
D. 400
E. 500

Another approach is to use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of students, and the two characteristics are:
- Said "yes" to liking subject M or didn't say "yes" to liking subject M
- Said "yes" to liking subject R or didn't say "yes" to liking subject R

IMPORTANT: Notice that I just lumped the "unsure" respondents in with those who answered "no." It's okay to do this since the question is only interested in those who did not answer "yes"
So, we can CONDENSE our table to get:
Subject M: 500 answered "yes," and 300 did NOT answer "yes"
Subject R: 400 answered "yes," and 400 did NOT answer "yes"

We can now set up our diagram as follows: