Probability: Tough Nut

[tabsang]

In a class, each of the students were asked to pick an integer between 1 and 20, both inclusive. What is the probability that at least two students have picked up the same integer?

(1) There were less than 30 students.
(2) There were 30 students.

OA: [spoiler](B)[/spoiler]

It's quite evident as to why [spoiler](B)[/spoiler] is the answer here.
My question though is that is there anyway that we can solve this question?
I agree that it's a DS question but I couldn't help but wonder if there was a mathematical solution for this.

Cheers,
Taz

[ritind]

Here's my take on the ques
Probability that atleast two students have picked up the same no = 1 - Probability of all the students picking different numbers
Since there are 30 students
Lets assumne that first 20 students picked up different numbers
21st student onwards, the no he'll pick would have been chosen by a previous student
So the Probability of all the students picking different numbers = 0
Therefore Probability that atleast two students have picked up the same no = 1 - 0 = 0

[puneetkhurana2000]

If there are more than 20 students, P(two students picking up the same integer) is 100%.

Statement 1) 1 <= Number of Students < 30, Not Sufficient!!!

Statement 2) Number of Students = 30, this is more than 20 so Sufficient!!!

Answer B.

[puneetkhurana2000]

This question does not seem to be an actual GMAT question, what is the source?

Thanks

Puneet

[tabsang]

This question does not seem to be an actual GMAT question, what is the source?

Thanks

Puneet

Agreed. The question is questionable. (1) and (2) contradict each other.
This question is from the study material of a local GMAT tutorial.

[e-GMAT]

In a class, each of the students were asked to pick an integer between 1 and 20, both inclusive. What is the probability that at least two students have picked up the same integer?

(1) There were less than 30 students.
(2) There were 30 students.

OA: [spoiler](B)[/spoiler]

It's quite evident as to why [spoiler](B)[/spoiler] is the answer here.
My question though is that is there anyway that we can solve this question?
I agree that it's a DS question but I couldn't help but wonder if there was a mathematical solution for this.

Cheers,
Taz

Nice, but easy question.

Of course statement 1 is not sufficient.
=> a. If # of students < 20; probability < 1;
=> b. If # of students > 20; probability = 1;

Statement II:-
Since, # = 30. This is case (b). So probability = 1. By latest 21st student on wards, repetition will occur for sure.

-Shalabh Jain