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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

In a tin can, there is a certain number of pencils, 40 [#permalink]
15 Nov 2012, 08:39

1

This post received KUDOS

2

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

70% (03:48) correct
30% (02:22) wrong based on 119 sessions

In a tin can, there is a certain number of pencils, 40 percent without erasers, and 35 percent without points. If of the pencils 1/6 have no erasers and no points, what fractional part of the pencils have both points and erasers?

A) 11/12 B) 7/12 C) 5/12 D) 1/3 E) 1/4

There is a seemingly simple problem but I have got struck at a subtle point. Could someone post a solution so that I can compare it with the official explanation. Thanks

Re: Groups, Percents, Fractions [#permalink]
15 Nov 2012, 08:59

1

This post received KUDOS

mhadi wrote:

There is a seemingly simple problem but I have got struck at a subtle point. Could someone post a solution so that I can compare it with the official explanation. Thanks

In a tin can, there is a certain number of pencils, 40 percent without erasers, and 35 percent without points. If of the pencils 1/6 have no erasers and no points, what fractional part of the pencils have both points and erasers?

A) 11/12 B) 7/12 C) 5/12 D) 1/3 E) 1/4

Form a double matrix like shown, using some smart number (any multiple of 6 with enough 0s) eg 600.

from this, fraction that we want is = 250/600 = 5/12

Re: In a tin can, there is a certain number of pencils, 40 [#permalink]
15 Nov 2012, 13:17

1

This post received KUDOS

n(aUb)=n(a)+n(b)-n(anb) so total without erasers and points will be 0.75-1/6 which will be 7/12. So pencils with both erasers and points will be 1-7/12 which should be 5/12 C

Re: In a tin can, there is a certain number of pencils, 40 [#permalink]
15 Nov 2012, 13:39

Amateur wrote:

n(aUb)=n(a)+n(b)-n(anb) so total without erasers and points will be 0.75-1/6 which will be 7/12. So pencils with both erasers and points will be 1-7/12 which should be 5/12 C

Re: In a tin can, there is a certain number of pencils, 40 [#permalink]
15 Nov 2012, 14:57

2

This post received KUDOS

g3kr wrote:

Amateur wrote:

n(aUb)=n(a)+n(b)-n(anb) so total without erasers and points will be 0.75-1/6 which will be 7/12. So pencils with both erasers and points will be 1-7/12 which should be 5/12 C

Can you explain more clearly

Venn diagrams..... Consider two samples a, b which overlap..... we have the formula I wrote above.... so if you consider no erasers to be sample space a, and no points to be sample space b.... when they say 0.4 had no erasers, it means they also contain a few which donot have points too.... likewise when they say 0.35 had no points they contain pencils which didnot have erasers too.... so pencils without erasers and points are represented in both the cases above... so if you add no erasers and no points samples, think about it, you are adding pencils without erasers and points twice.... So subtract quantity (1/6) from what you got by adding 0.35+0.4=0.75. So on the whole pencils with no erasers only +pencils with no points only +pencils with no both erasers and points = 0.75-1/6=7/12.... so 7/12 are pencils which are defective on the whole.... but you want good pencils... anything apart from defective pencils are good right... Remember set theory, sum of all samples=1... So good pencils will be 1-7/12 which is 5/12

Re: In a tin can, there is a certain number of pencils, 40 [#permalink]
19 Jun 2014, 09:55

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

: Social ventures, both non-profits and for-profits, seek to better the world in such industries as education, microfinance, workforce development, public health and community development, among others. Organizations that...

Essay B for Stanford GSB will essentially ask you to explain why you’re doing what you’re doing. Namely, the essay wants to know, A) why you’re seeking...

Over the last week my Facebook wall has been flooded with most positive, almost euphoric emotions: “End of a fantastic school year”, “What a life-changing year it’s been”, “My...