At University X, there are 146 students who are taking economics and 9

Question

At University X, there are 146 students who are taking economics and 97 students whoare taking history.

In the table below, pick two numbers that are consistent with the information that is given. In the first column, select the row that shows the number of students at University X who are taking at least one of economics and history, and in the second column, select the row that shows the number of students at University X who are taking both economics and history.

rocky620 · Accepted Answer

Let,
The Students who took Economics = E = 146
The Students who took History = H = 97
The Students who took Both = B
The Students who took Neither = N
Total Students = T

T = E+H-B+N
T = 243-B+N
T-N = 243-B....... EQ-1

We are required to find the number of students who took atleast 1 subject =  T-N , ans students who took both the subjects =  B

Substituting values for B in  EQ-1

When,
 B =78,  T-N =165
  B=83, T-N=160......CORRECT ANSWER  
 B =104,  T-N =139
 B =154,  T-N =89
 B =160,  T-N =83
 B =164,  T-N =79

LHE · Answer

Hi, it should be 160 for "Taking at least one of economics and history" and 83 for "Taking both economics and history".

Since the max no of students for history is 97 students, the number of students taking both economics and history should be lesser than 97 students.

Do let me know if this is right, thanks!

Sajjad1994 · Answer

OA of this question has been updated, It is:

Taking at least one of economics and history: 160
Taking both economics and history: 83

Thank you

Kunal.lost · Answer

Hi Bunuel KarishmaB , Could you please help with the approach to this question? Thanks in advance

KarishmaB · Answer

This is essentially a max-min sets question. Number of students taking both can vary from 0 to 97. There may be 'no overlap' to 'the history set may be inside the economics set.' So only two possible values are there: 78 If 78 students take both, then number of students who take at least one = 146 + 97 - 78 = 165 This value is not available in the answers. 83 If 83 students take both, then number of students who take at least one = 146 + 97 - 83 = 160 This value is available in the answers. Hence Select 160 and 83 Video for max min in Sets: https://youtu.be/oLKbIyb1ZrI

napolean92728 · Answer

We are given E = 146 and H = 97,

so  E ∪ H = E + H - E ∩ H  ,

on calculation,  E ∪ H + E ∩ H = 243 ,

only 160 and 83 satisfy this

Pr4n · Answer

For someone who is more comfortable with arthmetics than logic just looking at the question,

We know,

P or Q = P + Q - (P and Q)

We have P= 146 , Q =97

We can rewrite the above equation as,

(P or Q) + (P and Q) = P + Q = 146 + 97 = 243

Now, 243 is an odd number which means is a sum of either (even + odd) or (odd + even) numbers.
Now we know that P and Q will definitely be lower than 97, hence we try to find this relationship by subsituting the values given in the table.

For first Value (P or Q) is = 165 which is not there in the answers, hence the only odd option left and also it is less than 97 is option 2 for (P and Q)

Notice even if you were not able to use this logic "P and Q will definitely be lower than 97", there is only one odd value and that was definitely going to be the part of our solution.

So, knowing integer properties and the fact that P and Q is always <= P or Q, would have sufficed. We only needed to subsitute 83 to find P or Q.

At University X, there are 146 students who are taking economics and 9

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Taking at least one of economics and history	Taking both economics and history	Possible answers
		78
		83
		104
		154
		160
		164

GMAT Two-part Analysis (TPA) Questions

At University X, there are 146 students who are taking economics and 9

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

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My Rewards