In a certain group of 50 people, how many are doctors who have a law

Question

In a certain group of 50 people, how many are doctors who have a law degree?

(1) In the group, 36 people are doctors. 
(2) In the group, 18 people have a law degree.

KarishmaB · Accepted Answer

The question is very simple but it has a small pitfall - some test takers will certainly answer (C) and move on. When we read "Doctors who have a law degree", we immediately think of the intersection of the two sets - doctors and lawyers.

So what might come to mind is Total = n(D) + n(L) - n(D and L)

Here is the catch: we don't have the total i.e. the union of the two sets. 50 people is just a certain group. It is not necessary that each one of them is certainly a doctor or a lawyer or both. 
In effect, we do not have the number of "neither".

Hence, answer here will be (E).

BrentGMATPrepNow · Answer

Target question :    How many are doctors who have a law degree?

Given : There are 50 people

When I scan the two statements, I see that we have the ingredients for applying the  Double Matrix method 
This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions). 
Here, we have a population of 50 people, and the two characteristics are: 
- Doctor or NOT a doctor
- Has law degree or doesn't have law degree

So, we can set up our double matrix as follows: 
 https://i.imgur.com/psOrxYn.png 
NOTE: I have placed a star in the box that represents doctors who have a law degree, since this is what the  target question  is asking us about

Statement 1 : In the group, 36 people are doctors.   
If the group has 50 people, and 36 are doctors, we can conclude that there are 14 non-doctors in the group. 
Let's add this information to our matrix:
 https://i.imgur.com/2sJVijk.png

As you can see, there's no way to determine the value that must go in the starred box. 
As such, statement 1 is NOT SUFFICIENT

Statement 2 : In the group, 18 people have a law degree  
If 18 of the 50 people have a law degree, than the remaining 32 people do NOT have a law degree. 
Let's add this information to our matrix:
 https://i.imgur.com/29yVNXb.png

As you can see, there's no way to determine the value that must go in the starred box. 
As such, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
When we combine the two statements, we get the following: 
 https://i.imgur.com/3DMTM3M.png

There are several ways to complete this matrix. Here are two cases:

case a:  
 https://i.imgur.com/ElWzpYF.png 
In this case,  there are 10 doctors with law degrees .

case a:  
 https://i.imgur.com/AdCQ2Wv.png 
In this case,  there are 5 doctors with law degrees . 
Since we cannot answer the  target question  with certainty, the combined statements are NOT SUFFICIENT

Answer: E

RELATED VIDEO
 https://www.youtube.com/watch?v=jK-tiBrrf04

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=Uq9GFMGBAAE

sashiim20 · Answer

Total number of people in the group  = 50

(1) In the group, 36 people are doctors.

Number of doctors  = 36

Number of not doctors  = 50 - 36 = 14

We cannot find Doctors with law degree. Hence I is Not Sufficient.

(2) In the group, 18 people have a law degree.

Number of people with law degrees  = 18

Number of people without law degrees  = 50 - 18 = 32

We cannot find Doctors with law degree. Hence II is Not Sufficient.

Combining (1) and (2);

Total = 50

Number of doctors = 36

Number of people with law degree = 18.

We cannot find Doctors with law degree. Answer (E)...

roadrunner · Answer

Total=50

1)
No. of Doctors = 36
No. of Not Doctors = 14
No information regarding lawyers ==> Stmt 1 is insufficient

2. 
No. of Lawyers = 18
No. of Not Lawyers = 32
No information regarding doctors ==> Stmt 2 is insufficient

1 & 2) Still cannot deduce no. of doctors who are lawyers

Answer is E

ydmuley · Answer

In a certain group of 50 people, how many are doctors who have a law degree?

Total No. Of People = 50

(1) In the group, 36 people are doctors.

This tells us that there are 36 Doctors, however this does not give us any information on whether they have a law degree or no

Total = 50
Doc = 36
Non-Doc = 14

Hence,  (1) =====> is NOT SUFFICIENT

(2) In the group, 18 people have a law degree.

This tells us that there are 18 people who are having law degree, however, it does not provide us any information on whether they are doctors or non-doctors

Total = 50
Law Degree = 18
Non-Law Degree = 32

Hence,  (2) =====> is NOT SUFFICIENT

Combining (1) and (2) we get:

Total = 50
Doc = 36
Non-Doc = 14

Total = 50
Law Degree = 18
Non-Law Degree = 32

Even after combining we are not aware of how many doctors are having a law degree as they are two exclusive sets with no connection provided.

We can have doctors falling under "Law Degree" or "Non-Law Degree" or BOTH as we are not aware of this distribution we will not be able to answer this question.

Hence, Answer is E

amanvermagmat · Answer

Of course neither statement alone is sufficient. 
when we combine, we get that out of 50, 36 are doctors and 18 have a law degree.

But we don't know how many have neither degree. without that info we cant say how many have both degrees.
Say 'x' people have both degrees, then: 36-x are only doctors, 18-x are only lawyers. People having at least one degree = 36-x + x + 18-x = 54 - x, and those having neither degree are: 50 - (54-x) = x-4.

Until we know the value of (x-4) we cant find 'x'. So insufficient.  Answer is E

ashygoyal · Answer

To add to it, If we use the formula : Total - neither = D + L - (D&L)
We have Total,
We have D, We have L, 
But we cant find (D&L) until we have 'neither'.

Please correct me if I am wrong.

Regards,
ashygoyal

ashygoyal · Answer

Hi Karishma,

I think the correct approach would be to use 
Total   - neither   = n(D) + n(L) - n(D and L), instead of
Total = n(D) + n(L) - n(D and L)

KarishmaB · Answer

Please note: "... what might come to mind is Total = n(D) + n(L) - n(D and L)"
"Here is the catch:... we do not have the number of neither"

The point is we use Total as the union of two sets very often and hence might forget "neither".

akshayk · Answer

Total = 50
Docs who have law degrees = ?

1) 36 are docs
14 are not docs. Law degrees= ?
Insufficient.

2) 18 have law degree.
32 have no law degree.
# of docs = ?
Insufficient.

1+2)
# of doctors = 36
# of law degree = 18
Either 18 doctors have law degrees, or 14 non-docs have law degrees, and 4 doctors have law degrees.
Other variations are also possible.
Insufficient.

E is the answer.

ashygoyal · Answer

Please note: "... what might come to mind is Total = n(D) + n(L) - n(D and L)"
"Here is the catch:... we do not have the number of neither"

The point is we use Total as the union of two sets very often and hence might forget "neither". 
Sorry, I think my last reply lacked detail !
My point was, 
When you combine both statements..
U will observe, u have the following info:
N(total)
N(doctors)
N(law degree holders)

At this point if you use: 
N(total) = n(docs) + n(law) - n(both)

Then u r surely gonna fall in the 'C Trap' because u will think, u have got 3 values from question and u can easily find 4th one.

But, if you had the correct formula in mind, i.e.
N(total)- neither= n(doc) +n(law) - n(both)

You will realise that, u still have two values missing. Without the 'neither' u cant find n(both).
Hence, info.is incomplete and answer is E.

So my point was, always have the formula (which involves 'neither') in your mind !

Hope I was able to put forward my part of understanding. Please correct me if my thought process is wrong.

Regards,
ashygoyal

Thanks and Regards, 
ashygoyal

harikrish · Answer

In a certain group of 50 people, how many are doctors who have a law degree?

(1) In the group, 36 people are doctors. 
(2) In the group, 18 people have a law degree.

Solution:

Statement 1:Insufficient . No info about law degree.

Statement 2: Insufficient. No info about doctors.

Combine. We don't know the common in both. People involved in both law degree and doctor.

Therefore the answer is Option E.

ScottTargetTestPrep · Answer

We have a group of 50 people and need to determine how many of those people are doctors with a law degree.

We can use the following formula:

total = # of doctors + # of lawyers - # both + # neither

50 = # of doctors + # of lawyers - # both + # neither

Statement One Alone:

In the group, 36 people are doctors.

So, we have:

50 = 36 + # of lawyers - # both + # neither

24 = # of lawyers - # both + # neither

We cannot determine the number of people who are both. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

In the group, 18 people have a law degree.

So, we have:

50 = # of doctors + 18 - # both + # neither

32 = # of doctors - # both + # neither

We cannot determine the number of people who are both. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using statements one and two, we have:

50 = 36 + 18 - # both + # neither

-4 = - # both + # neither

# both = 4 + # neither

We still cannot determine the number of “both” since we don’t know the number of “neither.”

Answer: E

vishnusheth · Answer

Going to keep it small and simple. 
 T - N = A + B -  Both  
T = Total; N = Neither; A = Doctor's Degree; B = Law Degree; We need to find out The Number of people who have both the degrees (i.e..,Both)
 Total  = 50  (given) 
 Statement 1:  A = 36
=> 50-N = 36+B-  x   ----------Not sufficient. 
 Statement 2:  B = 18
=> 50-N = A+18-  x   ----------Not Sufficient. 
Together, 50-N = 36+18-  x  
Since we still don't know the value of N, we cannot determine   x  
 Hence, E

Kudos?

tunguyen31 · Answer

I got this question wrong, so to clarify if the subject says : " a group of 50 doctor who have law degree", then we can apply Total = n(D) + n(L) - n(D and L) correct?

MHIKER · Answer

Total = Dorctors + Lawyers - Both + Neither

50= Dorctors + Lawyers - Both + Neither

(1) Only the number of Doctors is given. Insufficient.

(2) Only the number of Lawyers is given. Insufficient.

Considering both;

50=36+15-Both+ Neither ; We don't have information about either. Insufficient.

The answer is  E .

GMATinsight · Answer

Answer: Option E Video solution by GMATinsight https://www.youtube.com/watch?v=73RwhV6eHtI

GMATinsight · Answer

Answer: Option E

Video solution by  GMATinsight

https://www.youtube.com/watch?v=5wkFJCNOfrM

In a certain group of 50 people, how many are doctors who have a law

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