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

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In a certain group of 50 people, how many are doctors who have a law [#permalink]

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26 Jun 2017, 02:21
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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.

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Re: In a certain group of 50 people, how many are doctors who have a law [#permalink]

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26 Jun 2017, 21:53
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Bunuel wrote:
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.

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).
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In a certain group of 50 people, how many are doctors who have a law [#permalink]

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Updated on: 26 Jun 2017, 14:21
Bunuel wrote:
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.

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)...

Originally posted by sashiim20 on 26 Jun 2017, 02:45.
Last edited by sashiim20 on 26 Jun 2017, 14:21, edited 1 time in total.
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Re: In a certain group of 50 people, how many are doctors who have a law [#permalink]

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26 Jun 2017, 06:38
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

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In a certain group of 50 people, how many are doctors who have a law [#permalink]

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Updated on: 16 Apr 2018, 12:00
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Bunuel wrote:
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.

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:

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:

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:

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:

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

case a:

In this case, there are 10 doctors with law degrees.

case a:

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

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Originally posted by GMATPrepNow on 26 Jun 2017, 13:33.
Last edited by GMATPrepNow on 16 Apr 2018, 12:00, edited 1 time in total.
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Re: In a certain group of 50 people, how many are doctors who have a law [#permalink]

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26 Jun 2017, 14:01
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.

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Re: In a certain group of 50 people, how many are doctors who have a law [#permalink]

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03 Jul 2017, 00:53
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
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Re: In a certain group of 50 people, how many are doctors who have a law [#permalink]

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10 Jul 2017, 14:18
sashiim20 wrote:
Bunuel wrote:
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.

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)...

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
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Re: In a certain group of 50 people, how many are doctors who have a law [#permalink]

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10 Jul 2017, 14:21
VeritasPrepKarishma wrote:
Bunuel wrote:
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.

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).

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)
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Re: In a certain group of 50 people, how many are doctors who have a law [#permalink]

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12 Jul 2017, 03:20
ashygoyal wrote:
VeritasPrepKarishma wrote:
Bunuel wrote:
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.

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).

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)

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".
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Re: In a certain group of 50 people, how many are doctors who have a law [#permalink]

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12 Jul 2017, 03:27
Bunuel wrote:
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.

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.

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Re: In a certain group of 50 people, how many are doctors who have a law [#permalink]

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12 Jul 2017, 04:12
VeritasPrepKarishma wrote:
ashygoyal wrote:
VeritasPrepKarishma wrote:
[quote="Bunuel"]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.

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).

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)

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".[/quote]
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
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Re: In a certain group of 50 people, how many are doctors who have a law [#permalink]

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12 Jul 2017, 05:29
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.
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Re: In a certain group of 50 people, how many are doctors who have a law [#permalink]

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15 Nov 2017, 17:25
Bunuel wrote:
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.

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.”

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Re: In a certain group of 50 people, how many are doctors who have a law   [#permalink] 15 Nov 2017, 17:25
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