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How many students in a room are currently taking either geography

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How many students in a room are currently taking either geography  [#permalink]

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New post 03 Jan 2019, 06:51
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79% (00:45) correct 21% (00:23) wrong based on 38 sessions

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How many students in a room are currently taking either geography or history, but not both?

(1) The number of students in the room who are taking at least one of the subjects history and geography is 127.
(2) The number of students in the room who are taking both geography and history is 46.

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Re: How many students in a room are currently taking either geography  [#permalink]

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New post 03 Jan 2019, 07:08
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itisSheldon wrote:
How many students in a room are currently taking either geography or history, but not both?

(1) The number of students in the room who are taking at least one of the subjects history and geography is 127.
(2) The number of students in the room who are taking both geography and history is 46.


The formula I use is
Total = Group A + Group B - Both Group + Neither Group

We want to know Group A + Group B

A: The number of students in the room who are taking at least one of the subjects history and geography is 127:

So Total = 127 AND Neither = 0. But we dont know Both Group : NOT SUFFICIENT

B: The number of students in the room who are taking both geography and history is 46.

So Both Group = 46. But Total and Neither Group is unknown. : NOT SUFFICIENT

BOTH A and B TOGETHER. WE Know the values.: SUFFICIENT
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Re: How many students in a room are currently taking either geography  [#permalink]

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New post 03 Jan 2019, 21:51
itisSheldon wrote:
How many students in a room are currently taking either geography or history, but not both?

(1) The number of students in the room who are taking at least one of the subjects history and geography is 127.
(2) The number of students in the room who are taking both geography and history is 46.


Let H be the number of students taking History

Let G be the number of students taking Geography

Let x be the number of students taking both History and Geography

H-x = History alone

G-x = Geography alone

So, Either Geography or History but not both = H-x +G-x = H + G - 2x = ?

St 1 : H + G - x =127

Not Sufficient

St 2 :

x = 46

Not Sufficient

St 1 and St 2 Combined

H + G- 2x = (H + G - x) - x

= 127 - 46 = 81

Sufficient

Choice C
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Re: How many students in a room are currently taking either geography  [#permalink]

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New post 03 Jan 2019, 22:51
Hi,

It’s a pretty-straight forward sets question.

You can use venn-diagrams to solve the sets questions.

Question: How many students chose exactly one of the subject (i.e., history or geography) ?

Statement I is insufficient:

The number of students in the room who are taking at least one of the subjects history and geography is 127.

Given, no. of students who took atleast one of the subjects is equal to 127.

But we want students who chosen exactly one subject.

From the below diagram,

We can see that, if we know the number of students who chosed both, we can find the answer.

Statement II is insufficient:

The number of students in the room who are taking both geography and history is 46.

Now we can clearly see that, statement II individually not sufficient.

But combining both I and II, we will get the answer.

That is, 127 – 46 = 81.

So the answer is C.

Hope this helps.

Regards,
Junaid.
Byjus GMAT Quant Expert
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Re: How many students in a room are currently taking either geography  [#permalink]

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New post 10 Jan 2019, 05:46
fitzpratik wrote:
itisSheldon wrote:
How many students in a room are currently taking either geography or history, but not both?

(1) The number of students in the room who are taking at least one of the subjects history and geography is 127.
(2) The number of students in the room who are taking both geography and history is 46.


The formula I use is
Total = Group A + Group B - Both Group + Neither Group

We want to know Group A + Group B

A: The number of students in the room who are taking at least one of the subjects history and geography is 127:

So Total = 127 AND Neither = 0. But we dont know Both Group : NOT SUFFICIENT

B: The number of students in the room who are taking both geography and history is 46.

So Both Group = 46. But Total and Neither Group is unknown. : NOT SUFFICIENT

BOTH A and B TOGETHER. WE Know the values.: SUFFICIENT


Hi fitzpratik ,

So if the stem is not referring about Neither subgroup we just assume that it is 0 or u realized it from somewhere else?
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Re: How many students in a room are currently taking either geography  [#permalink]

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New post 10 Jan 2019, 06:05
1
UNSTOPPABLE12 wrote:
fitzpratik wrote:
itisSheldon wrote:
How many students in a room are currently taking either geography or history, but not both?

(1) The number of students in the room who are taking at least one of the subjects history and geography is 127.
(2) The number of students in the room who are taking both geography and history is 46.


The formula I use is
Total = Group A + Group B - Both Group + Neither Group

We want to know Group A + Group B

A: The number of students in the room who are taking at least one of the subjects history and geography is 127:

So Total = 127 AND Neither = 0. But we dont know Both Group : NOT SUFFICIENT

B: The number of students in the room who are taking both geography and history is 46.

So Both Group = 46. But Total and Neither Group is unknown. : NOT SUFFICIENT

BOTH A and B TOGETHER. WE Know the values.: SUFFICIENT


Hi fitzpratik ,

So if the stem is not referring about Neither subgroup we just assume that it is 0 or u realized it from somewhere else?


The question stem usually mentions that students are taking EITHER geography or history, we cannot assume they are giving any other exam.

If the question stem would have been :

Students are taking either geography or history, among other subjects, ....then our assumption of Neither = 0 might not be true.
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How many students in a room are currently taking either geography  [#permalink]

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New post 10 Jan 2019, 06:53
itisSheldon wrote:
How many students in a room are currently taking either geography or history, but not both?

(1) The number of students in the room who are taking at least one of the subjects history and geography is 127.
(2) The number of students in the room who are taking both geography and history is 46.



To make this problem work, we have to assume that all students are taking at least one class, otherwise we have too many unknown. Venn Diagrams are great, as they can allow us to use the NVNE sufficiency strategy for DS, however for two overlapping set problems, I prefer to use a 2x2 table.

(1) We can construct the following table the first table. The cells labelled X and Y represent the total students taking only history or only geography. With (1) we still don't know how many are in both geography and history so NS

(2) We can construct the second table. We don't know the total number of students, so (2) is clearly NS

(1) and (2) We can construct the third table. Since we know have the total and the number of students taking both classes, we can determine the remaining 2 cells in the center of the table, X+Y, which is exactly what we are looking for. Sufficient. The answer is C
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