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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

4

2

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: 16 Apr 2018, 12:00

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2

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

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.

Hence, 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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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

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'.

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)

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.

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.