How many of the students in a certain class are taking both a history

Question

How many of the students in a certain class are taking both a history and a science course?

1) Of all the students in the class, 50 are taking a history course
2) Of all the students in the class, 70 are taking a science course

mikemcgarry · Accepted Answer

Dear shapla , I'm happy to respond. :-)

Given the prompt, before we get to the statements, think about everything we don't know. We don't know how many students are taking history, or are taking science, or are in the class as a whole. It's probably apparent that neither statement by itself is sufficient to answer the prompt question. Let's consider them together. Suppose we know that (1) 50 students are taking history (2) 70 students are taking science and we want to know about the overlap, the folks taking both. We still don't know the class size. Consider these two scenarios: SCENARIO #1 : Class size = 70 In this scenario, everyone is taking science, so the 50 who are taking history are necessarily taking it in addition to science. In this scenario, those 50 would be the overlap, the number of students taking both. SCENARIO #2 : Class size = 1000 An extraordinarily large class size, perhaps typical of a university. Here, if we picked 50 people at random and assigned them to history, then picked 70 people at random and assigned them to science, we would be likely to get few overlaps, if any. It would be easy for one set of 50 to take history, and other set of 70 to take science, leaving 880 students unenrolled in either. So, there may be no overlap, or there may be some handful of students enrolled in both. We have no way of determining. One scenario led us to one answer. Another scenario left the prompt question unanswered. We would only have sufficient information if every imaginable scenario produced the same answer to the prompt question. Given the information we have, even with both students, we have absolutely no hope of answering the prompt question. Even with both statements combined, the information is insufficient . Answer = (E) My friend, if GMAT DS is relatively new to you, you might find this blog article helpful: https://magoosh.com/gmat/2013/gmat-data- ... ency-tips/ Please let me know if you have any questions about what I have written here. Best of luck, my friend! Mike :-)

shapla · Answer

Thanks Mike!!The explanation was really lucid. Though the DS part in GMAT is not novice to me, but i always find it hard compared to the other section. 
Thanks for sharing the article blog which seems really helpful.

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

How many of the students in a certain class are taking both a history and a science course?

1) Of all the students in the class, 50 are taking a history course
2) Of all the students in the class, 70 are taking a science course

This question is frequently given on GMAT Math questions, which is "2by2" like a table below.

Attachment:

GCDS shapla How many of the students in a certain class are (20160115).jpg [ 23.95 KiB | Viewed 26844 times ]

On the table, there are 4 variables(a,b,c,d), which should match with the number of equations. So you need 4 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer. When 1) & 2), they become a+c=50, a+b=40. However, you cannot get value of a in a unique way, which is not sufficient. Therefore, the answer is E.

 For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

anairamitch1804 · Answer

Total = history + Science - Both + Neither.

The class can have 4 sets of Students.

1. Take only history:
2. Take only Science:
3. Take both.
4. Take neither of the two.

1, WE have been given 50 but we haven't been told how many of them also do Science. Insuff
2. WE have been given 70 but we haven't been told how many of them also do history. Insuff.

St 1 + St 2 :-
We still don't know about total class size and we don't know value of Neither. 
Hence E.

GMATBusters · Answer

Visualization is the key

WhatsApp Image 2018-07-30 at 01.10.02.jpeg

Singh997 · Answer

The trick to solving DS Questions is that - You don't actually have to solve the question being asked.

Of course that is subject to difficulty level and topic. Typically in Quant DS, there are times you have to solve roughly to figure out whether the data provided in the Question is sufficient.

Here, in this case -

a - we know the number of students taking history
b - we know the number of students taking science

The Question asked is - how many students are taking  both ?

Is the data provided in statement a and b  sufficient  to answer this Question? Can we use the statements to find the common number of students? Because we know  individually  the number of students taking history and science. No information has been provided for us to infer how many have opted for both.

Therefore, the answer is no.

Hence Option E is the correct answer.

bumpbot · Answer

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How many of the students in a certain class are taking both a history

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