Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 06 Jul 2015, 22:50

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# In a certain class, 1/3 of the students are honors students,

Author Message
TAGS:
CEO
Joined: 15 Aug 2003
Posts: 3467
Followers: 61

Kudos [?]: 719 [0], given: 781

In a certain class, 1/3 of the students are honors students, [#permalink]  05 Dec 2003, 02:51
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
In a certain class, 1/3 of the students are honors students, and 1/4 of the students play varsity sports. If 12 students play varsity sports and are honors students, what is the least possible number of students in the class?

20
22
36
48
144

Last edited by Praetorian on 05 Dec 2003, 05:06, edited 1 time in total.
SVP
Joined: 03 Feb 2003
Posts: 1607
Followers: 7

Kudos [?]: 87 [0], given: 0

Please, clarify the wording. Hardly can people understand it.
Manager
Joined: 22 Nov 2003
Posts: 54
Location: New Orleans
Followers: 1

Kudos [?]: 0 [0], given: 0

Students [#permalink]  05 Dec 2003, 18:17
My logic:

The question stem doesn't specify that only 12 students play varsity sports or are honor students; it just says that 12 are both.

If we want the least possible number of total students we have to assume the smaller of the percentages to be only what is specified.

We assume there are only 12 students who play varsity sports and thus these students account for 25% of the entire class. And of course if there are 12 students who play varsity sports, there are a total of 16 students who are honor students (12 just happen to also play varsity sports).

The least number of students is 48.

Is this correct?
Manager
Joined: 26 Aug 2003
Posts: 233
Location: United States
Followers: 1

Kudos [?]: 2 [0], given: 0

I say 48 students.

I reckon with csperber on the logical approach.

Here's a theoretical approach:
For now let's assume all students must be involved in at least one of the categories.

x = total students

(x/3 - 12) + (x/4 - 12) = x
4x - 144 + 3x - 144 = x
6x = 288
x = 48
Director
Joined: 13 Nov 2003
Posts: 971
Location: Florida
Followers: 1

Kudos [?]: 35 [0], given: 0

wonder_gmat wrote:
I say 48 students.

I reckon with csperber on the logical approach.

Here's a theoretical approach:
For now let's assume all students must be involved in at least one of the categories.

x = total students

(x/3 - 12) + (x/4 - 12) = x
4x - 144 + 3x - 144 = x
6x = 288
x = 48

why have you excluded 12 (both) from the individual numbers?
it should be like:
x/3 + (x/4 - 12) = x ..... this would give -ve value

try drawing this on the venn diagram.
CEO
Joined: 15 Aug 2003
Posts: 3467
Followers: 61

Kudos [?]: 719 [0], given: 781

wonder_gmat wrote:
I say 48 students.

I reckon with csperber on the logical approach.

Here's a theoretical approach:
For now let's assume all students must be involved in at least one of the categories.

x = total students

(x/3 - 12) + (x/4 - 12) = x
4x - 144 + 3x - 144 = x
6x = 288
x = 48

i had trouble understanding why you subtracted 12 from both x/3 and

x/4.

thanks
praetorian
Senior Manager
Joined: 12 Oct 2003
Posts: 251
Location: USA
Followers: 1

Kudos [?]: 5 [0], given: 0

48

we know from the problem stem that the number of students playing varsity sports and the number of students who are honor students taken together has (should it be have or has here ?? explain ... ) to be greater than or equal to the number of students from each category taken alone.

Also, 1/3 of students represents a greater number than 1/4 of students.

So, x/3 + x/4 - 12 >= x/3
x/4 - 12 >= 0
x/4 >= 12
x >= 48

what say?
SVP
Joined: 30 Oct 2003
Posts: 1794
Location: NewJersey USA
Followers: 5

Kudos [?]: 43 [0], given: 0

calculation done by wonder_gmat is wrong.
-------------------------------------------------
x/3 - 12) + (x/4 - 12) = x
4x - 144 + 3x - 144 = x
-------------------------------------------------
Actually it is 4x - 144 + 3x - 144 = 12x
You will get -ve result here.

The explaination given by pitts20042006 makes more sense.
Intern
Joined: 27 Nov 2003
Posts: 34
Location: Moscow
Followers: 0

Kudos [?]: 1 [0], given: 0

The fact that x>=48, does not mean the minimum of X is indeed 48.

It's better to go the other way: we need at least 12 students form both categories to satisfy the condition.
However, sport students is smaller group, meaning we have to take this group as reference. So, we need at least 12 sport students, and all of them are honors students. => We need at least 48 students (48/4=12). Consequently, we have 48/3=16 honors students.
Intern
Joined: 29 Aug 2003
Posts: 49
Location: Detroit, MI
Followers: 0

Kudos [?]: 2 [0], given: 0

Re: PS : Students [#permalink]  15 Dec 2003, 10:33
praetorian123 wrote:
In a certain class, 1/3 of the students are honors students, and 1/4 of the students play varsity sports. If 12 students play varsity sports and are honors students, what is the least possible number of students in the class?

20
22
36
48
144

My approach was like this. First of all, the answer should be divisible by both 3 and 4. So, A and B are out, leaving us with C, D and E

Starting with 36,
Honors students = 12
Students that play sports = 9

The problem mentions that 12 students do both. If so, -3 students should be playing sports alone, which is not feasible, while no students are honor students alone, which is okay.

Looking at 48,
Honors students = 16
Students that play sports = 12

In this case, there could be no students that play varsity sports alone and is still valid and

So, I went with 48.

Also, pitts ....

if we consider x/3 + x/4 - 12 >= x/4 then we get the answer as x >= 36
Senior Manager
Joined: 12 Oct 2003
Posts: 251
Location: USA
Followers: 1

Kudos [?]: 5 [0], given: 0

amarsesh wrote
Quote:
Also, pitts ....
if we consider x/3 + x/4 - 12 >= x/4 then we get the answer as x >= 36

But that is why I had written:
Quote:
Also, 1/3 of students represents a greater number than 1/4 of students.

so we consider x/3 and not x/4
Similar topics Replies Last post
Similar
Topics:
4 3/5 of a certain class left on a field trip. 1/3 of the students who s 3 06 Oct 2014, 08:53
In a class of 30 students, there are 17 girls and 13 boys. 8 24 Oct 2008, 13:16
In a class of 30 students, there are 17 girls and 13 boys. 2 28 Jun 2008, 00:06
In a certain class, 1/3 of the students are honors students, 1 15 Jun 2008, 14:34
A certain junior class has 1000 students and a certain 3 19 Feb 2006, 12:58
Display posts from previous: Sort by