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22 Jun 2020, 01:50
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
64% (01:56) correct
36%
(02:00)
wrong
based on 285
sessions
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At a certain college, students can major in science, math, history, or linguistics. If there are 1/3 as many science majors as there are history majors, and 2/3 as many math majors as there are history majors, how many of the 2000 students major in linguistics?
1. There are as many linguistics majors as there are math majors.
2. There are 250 more math majors than there are science majors.
1. There are as many linguistics majors as there are math majors.
2. There are 250 more math majors than there are science majors.
Dear IanStewart Bunuel GMATGuruNY VeritasKarishma MathRevolution,
Do we need to assume that each student can major in ONLY one field -- that there are no overlap whatsoever between each field?
Do we also need to assume that every student must have major -- that there are no students having no major at all?
Do we need to assume that each student can major in ONLY one field -- that there are no overlap whatsoever between each field?
Do we also need to assume that every student must have major -- that there are no students having no major at all?
07 Jul 2021, 06:07
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Nikhil30
Yes, these kinds of sentences are confusing. If we say "there are three times as many apples as bananas", that means "the number of apples is three times the number of bananas". It's confusing, because at first it sounds like we're multiplying the apples by 3, but we're not. This sentence means A = 3B (where A is the number of apples, B the number of bananas).
The same is true when you have a fraction in a sentence like this. If we say "there are 1/3 as many science majors as history majors", it might appear we should multiply science majors by 1/3, but that's not what this sentence means. It means "the number of science majors is 1/3 the number of history majors", and so it means, algebraically, S = (1/3)*H, or S = H/3.
These kinds of sentences show up all the time in GMAT math, so it's very important to know what they mean. If you find them confusing (which is normal!) I'd suggest you take a minute or two each day just to practice translating two or three sentences like this into algebra. It shouldn't take long before you're translating sentences like this correctly every time.
General Discussion
22 Jun 2020, 02:24
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varotkorn
Yes, you need to assume both of those things, at least if the answer is D.
The stem tells us the ratio of Science to Math to History majors is 1 to 2 to 3. If, from Statement 1, the number of Linguistics majors equals the number of Math majors, the ratio of S to M to L to H is 1 to 2 to 2 to 3, and thus 2/8 of all students are Linguistics majors, so (2/8)(2000) = 500 students major in Linguistics.
If the ratio of Science to Math majors is 1 to 2, we have twice as many Math majors as Science majors. So if there are 250 more Math majors than Science majors, the number of Science majors is 250 and the number of Math majors is 500. Using the 1 to 2 to 3 ratio, we have 750 History majors, and the remaining 500 people must major in Linguistics.
