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Question from Sets

by vinni.k » Wed Jun 13, 2012 11:04 am
In a test having two questions, 80 percent of the class answered the first question correctly, 60 percent answered the second question correctly and 55 percent answered both the questions correctly. What percent of the class answered at the most one question correctly ?

(A) 5%
(B) 15%
(C) 25%
(D) 45%
(E) 55%

Answer is D

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by GMATGuruNY » Wed Jun 13, 2012 1:10 pm
vinni.k wrote:In a test having two questions, 80 percent of the class answered the first question correctly, 60 percent answered the second question correctly and 55 percent answered both the questions correctly. What percent of the class answered at the most one question correctly ?

(A) 5%
(B) 15%
(C) 25%
(D) 45%
(E) 55%

Answer is D

Thanks & Regards
Vinni
55% answered both questions correctly.
Thus, EVERYONE ELSE -- the remaining 45% -- answered AT MOST one question correctly: either the first question only, the second question only, or neither of the two questions.

The correct answer is D.
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by vinni.k » Thu Jun 14, 2012 8:02 am
GMATGuruNY wrote:
55% answered both questions correctly.
Thus, EVERYONE ELSE -- the remaining 45% -- answered AT MOST one question correctly: either the first question only, the second question only, or neither of the two questions.

The correct answer is D.
Hi Mitch,

Thanks for your reply.

I am doubtful on the language of this question. What do we mean by "AT MOST one question" correctly ?
My interpretation for this language was either one question correctly or second question correctly.
i.e one question correct and second question incorrect = 25
second question correct and one question incorrect = 5

Number of students who answered at most one question correctly = no. of stu who answered first question correctly + no. of stu who answered second question correctly.

After adding them. My answer was 30. But it was no where in the answer choices. I agree i am wrong in solving this one, but "AT MOST one" - doesn't it mean either one or second ? Because neither means not even a single question got correct.

Please help in understanding this part.

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Vinni
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by GMATGuruNY » Thu Jun 14, 2012 9:41 am
vinni.k wrote:
GMATGuruNY wrote:
55% answered both questions correctly.
Thus, EVERYONE ELSE -- the remaining 45% -- answered AT MOST one question correctly: either the first question only, the second question only, or neither of the two questions.

The correct answer is D.
Hi Mitch,

Thanks for your reply.

I am doubtful on the language of this question. What do we mean by "AT MOST one question" correctly ?
My interpretation for this language was either one question correctly or second question correctly.
i.e one question correct and second question incorrect = 25
second question correct and one question incorrect = 5

Number of students who answered at most one question correctly = no. of stu who answered first question correctly + no. of stu who answered second question correctly.

After adding them. My answer was 30. But it was no where in the answer choices. I agree i am wrong in solving this one, but "AT MOST one" - doesn't it mean either one or second ? Because neither means not even a single question got correct.

Please help in understanding this part.

Thanks & Regards
Vinni
At most one means NOT MORE THAN ONE.

The group that answered NOT MORE THAN ONE question correctly is composed of the following:
-- those who answered only the first question correctly
-- those who answered only the second question correctly
-- those who answered neither question correctly.

In other words, everyone BUT the students who answered BOTH questions correctly.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
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by vinni.k » Thu Jun 14, 2012 10:50 am
GMATGuruNY wrote: At most one means NOT MORE THAN ONE.

The group that answered NOT MORE THAN ONE question correctly is composed of the following:
-- those who answered only the first question correctly
-- those who answered only the second question correctly
-- those who answered neither question correctly.

In other words, everyone BUT the students who answered BOTH questions correctly.
Thank you so much Mitch. :) Got it.

Regards
Vinni
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by shekhar.kataria » Fri Jun 15, 2012 11:47 am
Hi Vinni.k

Can you please let us know the source of this question.

I doubt about the source because of the way Question is structured. IT gives us some values for Question A and B but never uses them, in the solution.

Mitch

Can this be a real GMAT type question?. DO you think the point i raised above is correct or not ?
Restlessness and discontent are the first necessities of progress.--Thomas A. Edison

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by GMATGuruNY » Sat Jun 16, 2012 2:53 am
shekhar.kataria wrote:Hi Vinni.k

Can you please let us know the source of this question.

I doubt about the source because of the way Question is structured. IT gives us some values for Question A and B but never uses them, in the solution.

Mitch

Can this be a real GMAT type question?. DO you think the point i raised above is correct or not ?
Every so often a GMAT question will include unnecessary information that seems designed to make a problem harder or more time-consuming than it needs to be.
OG12, page 4, Q4:
Among a group of 2,500 people, 35 percent invest in
municipal bonds, 18 percent invest in oil stocks, and
7 percent invest in both municipal bonds and oil
stocks. If 1 person is to be randomly selected from
the 2,500 people, what is the probability that the
person selected will be one who invests in municipal
bonds but NOT in oil stocks?
The total number of people here is irrelevant: the probability will be the same regardless of the total number. A test-taker who calculates 35%, 18% and 7% of 2500 will spend more time than one who simply works with the percentages directly. (I posted a solution here: https://www.beatthegmat.com/probability-t111572.html)

As for the problem at hand:
In a test having two questions, 80 percent of the class answered the first question correctly, 60 percent answered the second question correctly and 55 percent answered both the questions correctly. What percent of the class answered at the most one question correctly?
The first two percentages (80% and 60%) are not needed. The question writer might have included these percentages to make the problem more time-consuming: many test-takers will instinctively calculate the percentage who answered only the first question correctly and the percentage who answered only the second question correctly -- a waste of valuable time. As my solution above shows, these calculations are unnecessary.
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.

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I unlock the best way for YOU to solve problems.

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by vinni.k » Sun Jun 17, 2012 1:56 am
Hi Shekhar,

Mitch is right. There are some questions in GMAT that gives unnecessary information. In fact i solved this question by calculating unnecessary information that Mitch has already explained.

The source for this question is "IMS" practice questions.


Thanks & Regards
Vinni
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by shekhar.kataria » Sun Jun 17, 2012 4:51 am
Thanks mitch and vinni.k
Restlessness and discontent are the first necessities of progress.--Thomas A. Edison

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