VENN DIAGRAM QUESTION

[sudipto]

A school has a total enrollment of 90 students.there are 30 students taking physics, 25 taking english and 13 taking both. What percentage of students are taking either physics or english ?

A. 30%
B. 36%
C. 47%
D. 51%
E. 58%

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The official answer is C. It seems like they arrived at the answer by
interpreting "either english or physics" as "either english or physics or both" - is this interpretation correct, or should it be interpreted as " either english or physics but not both " ?

Thanks,
Sudipto

[cramya]

Can you please double chekc the number sin the problem? Also is this from the official guide?

[stop@800]

source please?

[sudipto]

Yup the numbers are correct.

The question is from a NOVA Prep CAT # 2

[cramya]

The only way we can get to the solution given in the book i.e. 47% is by doing this

30+25 - 13 = 42 so 42/90*100 = 46.6 ~= 47 %


This is my opinion:

Lets say Phy is group 1 and Englisg group 2

I am not sure if the solution above is correct. I am thinking when it says 30 are taking physics (does not say 30 are taking just physics which then becomes group 1 exclusive) then the 13 taking both is also included in this number and similarly if 25 are taking Eng then the 13 taking both are included in this number.

I would have done (30-13) + (25-13) = 29

So 29/90 * 100 = 32.2%.


Stop@800 what are your thoughts?

[gabriela13]

Hi,

Because it is a percent question, I usually use the formula P(a)+P(b)-P(ab).
So we have 30+25-13 (Physics, English, Both). We have 42 stdunetns that are Not enrolled in BOTH. (42/90)=.4667

[stop@800]

The only way we can get to the solution given in the book i.e. 47% is by doing this

30+25 - 13 = 42 so 42/90*100 = 46.6 ~= 47 %

If I go by the answer than your justification is absolutely correct.

I am not sure that either physics or english should include both or not.
I think it should as you also did.
because of the question wants us not to include both than it should have said either only physics or only english

However, to clarify our doubt, I will refer OG11 and will get back.

PS: I did not replied earlier as I wanted to refer OG first.

This is my opinion:

Lets say Phy is group 1 and Englisg group 2

I am not sure if the solution above is correct. I am thinking when it says 30 are taking physics (does not say 30 are taking just physics which then becomes group 1 exclusive) then the 13 taking both is also included in this number and similarly if 25 are taking Eng then the 13 taking both are included in this number.

I would have done (30-13) + (25-13) = 29

So 29/90 * 100 = 32.2%.


Stop@800 what are your thoughts?

[artistocrat]

If the answer is 47 then obviously they meant and/or. technically they are correct as 42 people did in fact take either english or physics. For the solution its irrelevant whether they took both.

[Ian Stewart]

This is a commonly acknowledged problem with the English word 'or'; sometimes we genuinely mean what computer scientists and logicians call an 'exclusive or' (in this question: physics *or* english, but *not* both), and sometimes we mean an 'inclusive or' (in this question: physics, or english, or both). Because the word can be ambiguous, a real GMAT question will always make clear which meaning is intended. The wording of test prep company questions is not always as precise as the real thing, as is clearly the case here.

In either case, cramya's solutions are perfect- knowing the correct answer, it's clear the question writer intended to ask 'what percent take either physics or english or both', and hence the answer is approximately 47%. Still, I take issue with the question in another respect: the correct answer is clearly not 47%, but is instead 46.666...%. If this were a real GMAT question, the question would make clear that the answers are approximations, and not exact values.

So the question, if it is accurately quoted, is not well written for two different reasons- the answers are only approximate, and the use of 'or' is ambiguous.