Each of the 50 students participating in a workshop is either an under

Question

Each of the 50 students participating in a workshop is either an undergraduate or a graduate student. If P is the probability that a randomly selected participant will be a female graduate student, is P less than  \frac{1}{2} ?

1) Of the participants, 24 are female.

2) Of the participants, 18 are graduate students.

Kurtosis · Accepted Answer

Number of students = 50

Question asks whether number of female graduate students < 25.

St1: Female = 24 --> Even if all female are graduates, female graduate students < 25 --> Suffiicient

St2: Graduate students = 18 --> Even if all graduate students are female, female graduate students < 25 --> Sufficient

Answer: D

sevenplusplus · Answer

If P is the probability that a randomly selected participant will be a female graduate student, is P less than 1212?

I misread the statement as asking for P within "graduate student" subset only. That is, the probability < 1/2 of picking a female within graduate student. Did not realize that probability asked is for the entire set of 50 students...

Did anyone else ran into this silly error? Or could the problem be worded more carefully??

HarveyKlaus · Answer

Hi all,

I tried to answer this question in the matrix form as attached. The answer I got is correct however, Im not sure if thats the right approach as the information from both statements isn't matching. I interpreted "Each of the 50 students is either an undergraduate or a graduate student" as by putting 0 in the relevant columns as shown. Where am I wrong?

Thanks for your help!

MarkusKarl · Answer

Youve written that 0 males are undergrads and 0 females are graduates.

You should have put the total in the margin.

Posted from my mobile device

The 'is either a or b' means theres no overlapping.

Alok322 · Answer

Beautiful explanation  Vyshak !

maberra · Answer

How do we know it's not all the undergraduates that are female making F=32 hence p(f)=1/2? Why are we assuming from the info given on (2) that F=18 or less?

Krabhay · Answer

Statement 1: Out of 50 students, only 24 are female. 
This implies, that the probability that random student selected is a female is 0.48 i.e. less than 0.5
So, the probability that any selected candidate is a female graduate is surely less than 0.5. Hence, Sufficient.
Statement 2: Out of 50 students, only 18 are graduate. 
This implies that probability of total graduate is 0.36 i.e. less than 0.5
So, the probability that any selected candidate is a female graduate is surely less than 0.5. Hence, Sufficient.

meenakshimiyer · Answer

Statement 1: Out of 50 students, only 24 are female. 
This implies, that the probability that random student selected is a female is 0.48 i.e. less than 0.5
So, the probability that any selected candidate is a female graduate is surely less than 0.5. Hence, Sufficient.
Statement 2: Out of 50 students, only 18 are graduate. 
This implies that probability of total graduate is 0.36 i.e. less than 0.5
So, the probability that any selected candidate is a female graduate is surely less than 0.5. Hence, Sufficient.

Prasannathawait · Answer

Yes it's D
Because by both statements we will get that number of females will be less than 25.
Nice question and a classic GMAT trap.
It's an official Gmat prep question. Exam pack 6.

CEdward · Answer

P = female grads / females + males < 1/2?

St1 - 24 females
Suppose 
P = 24 / 50 < 1/2 YES
P = 12 / 50 < 1/2 YES

Sufficient.

St2 - 18 grad students
This means that irrespective of the number of female grad students, the total # of female grad students will always be less than 50%.
Sufficient.

D.

100mitra · Answer

Correct option D

We have : Students - 50 Nos 
to prove : Female Graduate less than 50%

1) Of the participants, 24 are female - (24/50) - 48%, if all female are graduate - condition fullfiled - Sufficient
2) Of the participants, 18 are graduate students - (18/50) - 36% -, if all graduate are female, condition fullfilled - Sufficient

Elimanates - A, B , C, and E
Winner - D

abhisheksr29 · Answer

Just a small trick:- Max number of female graduate students = number of female (if all female are graduates) or number of graduates (if all graduates are female)

S1- Max number of female graduate students = number of female (if all female are graduates) 
24/50 < 1/2
so a number smaller than 24 will definitely be less than 1/2. 
Sufficient

S1- Max number of female graduate students = number of graduates (if all graduates are female) 
18/50 < 1/2 
so a number smaller than 18 will definitely be less than 1/2. 
Sufficient

E

Sajjad1994 · Answer

No calculation is needed in this question at all, It is a totally logic based question and can be answered within 30 seconds.

phoenix0309 · Answer

why am i not able to see the options in this questions?

Bunuel · Answer

This is a data sufficiency question. Options for DS questions are always the same and usually omitted on the site.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Hope this helps.

Each of the 50 students participating in a workshop is either an under

Prep Toolkit

Top 5 GMAT Debrief Videos

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

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Each of the 50 students participating in a workshop is either an under

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

Perfect 805 Score Debrief by Julia

My Rewards