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At a graduation ceremony, some students earned bachelors in science de

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At a graduation ceremony, some students earned bachelors in science de  [#permalink]

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New post 21 Apr 2015, 06:10
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At a graduation ceremony, some students earned bachelors in science degrees, some earned bachelors in arts degrees, and some students double-majored and earned both degrees. If 200 students in total received bachelors degrees in the arts and sciences, how many students earned bachelors in science degrees?

(1) 120 students earned only a bachelors in arts.

(2) 40 students earned only a bachelors in science.


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Re: At a graduation ceremony, some students earned bachelors in science de  [#permalink]

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New post 21 Apr 2015, 06:47
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200 total students

(1) 120 students earned only a bachelors in arts.
120 with BA degrees
200-120 = 80 BS degrees
sufficient

(2) 40 students earned only a bachelors in science.
40 non BA students with BS degrees. We know there are 160 studentd who have BA degrees but we dont knoe the breakdown of students with BS degrees.
insufficient

Answer : A
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Re: At a graduation ceremony, some students earned bachelors in science de  [#permalink]

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New post 22 Apr 2015, 03:05
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Bunuel wrote:
At a graduation ceremony, some students earned bachelors in science degrees, some earned bachelors in arts degrees, and some students double-majored and earned both degrees. If 200 students in total received bachelors degrees in the arts and sciences, how many students earned bachelors in science degrees?

(1) 120 students earned only a bachelors in arts.

(2) 40 students earned only a bachelors in science.


Kudos for a correct solution.


Total student – 200

Statement A – 120 did only a bachelor in arts. This implies that the remaining (200-120=80) did a bachelor in sciences. This means the part of the overlapping set that covers Sciences and Both.

Sufficient

Statement B: With the information that 40 students graduated only in science, we have 2 unknowns – how many graduated both and how many graduated only science.

Insufficient.

Hence A is the correct answer

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aimtoteach

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Re: At a graduation ceremony, some students earned bachelors in science de  [#permalink]

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New post 22 Apr 2015, 03:08
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total no. of students given are 200.

Let the no. of students with bachelor's in only science be S, in only arts be A and in both be B.

a) Given that A = 120.
Now 200 = S + A + B
thus S + B = 200 - A = 200 -120 = 80.
Thus total students with bachelor's in science = 80. Sufficient

b) Given that S = 40.
Thus A + B = 160. And we cannot calculate A or B individually to calculate total no. of students with bachelor's in science. Insufficient.

Thus ans is A
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Re: At a graduation ceremony, some students earned bachelors in science de  [#permalink]

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New post 27 Apr 2015, 03:09
Bunuel wrote:
At a graduation ceremony, some students earned bachelors in science degrees, some earned bachelors in arts degrees, and some students double-majored and earned both degrees. If 200 students in total received bachelors degrees in the arts and sciences, how many students earned bachelors in science degrees?

(1) 120 students earned only a bachelors in arts.

(2) 40 students earned only a bachelors in science.


Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION:

A. In this Venn Diagram problem, it is important to recognize that there is no "neither" group - all 200 people earned at least one degree so you don't need to worry about anyone who did not earn one. Accordingly, your equations set up as either:

Arts + Sciences - Both = 200

or

Arts Only + Sciences Only + Both = 200

Statement 1 gives you the number of Arts Only as 120, meaning that you can use the second equation to see that:

120 + Sciences Only + Both = 200

Then you need to recognize that the question asks specifically for how many people received science degrees, total. In this way, if you received only a science degree OR if you received both an arts and a science degree, you count toward "Science Total", so you know that the remaining 80 people who did not receive only an arts degree must have received a science degree. Statement 1 is thus sufficient.

Statement 2 is not sufficient, as it only tells you about the "only science" group and not the "both" group, and both "science only" and "both science and arts" count toward the science total that you need.

The correct answer is A.
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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: At a graduation ceremony, some students earned bachelors in science de  [#permalink]

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