GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 22 Sep 2018, 06:11

Close

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
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.

Close

Request Expert Reply

Confirm Cancel

Mike's pencil box contains 30 pens. 15 of the pens are red, and all of

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Retired Moderator
avatar
Joined: 29 Apr 2015
Posts: 853
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
GMAT ToolKit User Premium Member
Mike's pencil box contains 30 pens. 15 of the pens are red, and all of  [#permalink]

Show Tags

New post Updated on: 24 May 2015, 06:52
2
6
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

75% (01:20) correct 25% (01:09) wrong based on 203 sessions

HideShow timer Statistics

Mike's pencil box contains 30 pens. 15 of the pens are red, and all of the others are either blue or black. If Mike were to choose a random pen from the pencil box, what is the probability that it would be blue?

(1) The probability that the pen will be red minus the probability that the pen will be black equals 0.3
(2) The probability that the pen will be red or blue is 0.8

Could anyone help me calculating the probabilities of picking a blue pencil? DS is clear for me, but the true calculation of the numbers...

According to Stat.(1), The probability that the pen will be red minus the probability that the pen will be black equals 0.3. This would allow us to calculate the probability of the pen being black. (since P(red)-P(black)=0.3.).

If you know the probability of black and red, you know the probability of blue:

P(red)+P(black)+P(blue) = 1

Therefore this statement is sufficient. Stat.(1)->S->AD.

According to Stat.(2), The probability that the pen will be red or blue is 0.8. Since the probability of a single event with two possible outcomes with an OR relation equals to the sum of their probabilities, this means that:

P(red)+P(blue)= 0.8

By plugging in P(red) in the equation above, it is possible to calculate P(blue). Therefore, this statement is sufficient. Stat.(2)->S->D.

_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.


Originally posted by reto on 24 May 2015, 05:47.
Last edited by Bunuel on 24 May 2015, 06:52, edited 1 time in total.
Edited the question.
e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 2007
Re: Mike's pencil box contains 30 pens. 15 of the pens are red, and all of  [#permalink]

Show Tags

New post 24 May 2015, 06:26
3
Hi reto,

We are given in the question the number of red pens and the total number of pens. Hence we can find the probability of a red pen being picked up.

Total number of pens = 30
Total number of red pens = 15

P(Red Pen) = \(\frac{15}{30} = \frac{1}{2} = 0.5\)

Probability of a black or a blue pen being picked up is directly dependent on the number of black and blue pens respectively.

Statement-I
St-I tells us that P(Red) - P(Black) = 0.3
0.5 - P(Black) = 0.3 i.e. P(Black) = 0.2. We can interpret this as the number of black pens being 20% of the total pens.

So Number of black pens = 20% of 30 = 6. From here we can say that total number of blue pens = 30 - 15 - 6 = 9

Statement-II
St-II tells us that P(Red or Blue) = 0.8 i.e. P(Red) + P(Blue) - P(Red and Blue) = 0.8.

Since a pen can't be red and blue at the same time, therefore P(Red and Blue) = 0.
P(Red) + P(Blue) = 0.8

0.5 + P(Blue) = 0.8 i.e. P(Blue) = 0.3.We can interpret this as the number of blue pens being 30% of the total pens.

So Number of blue pens = 30% of 30 = 9. From here we can say that total number of black pens = 30 - 15 - 9 = 6.

Hope this helps :)

Regards
Harsh
_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

GMAT Tutor
avatar
S
Joined: 24 Jun 2008
Posts: 1344
Re: Mike's pencil box contains 30 pens. 15 of the pens are red, and all of  [#permalink]

Show Tags

New post 24 May 2015, 09:25
reto wrote:
Mike's pencil box contains 30 pens. 15 of the pens are red, and all of the others are either blue or black. If Mike were to choose a random pen from the pencil box, what is the probability that it would be blue?

(1) The probability that the pen will be red minus the probability that the pen will be black equals 0.3
(2) The probability that the pen will be red or blue is 0.8

Could anyone help me calculating the probabilities of picking a blue pencil? DS is clear for me, but the true calculation of the numbers...


When you pick just one thing from a group, probabilities are just proportions. So here, the probability of picking a red pen is 15/30 = 1/2, or in other words, 1/2 the pens are red, or 50% of the pens are red. So it's not really a probability question at all; it's just a ratio question.

We have a box where 50% of our pens are red, and the rest are blue and black. Statement 2 is slightly easier - it tells us that 80% are either red or blue, so if 50% are red, then 30% are blue. Similarly, Statement 1 tells us that 20% of the pens are black, so 30% will be blue.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2835
Re: Mike's pencil box contains 30 pens. 15 of the pens are red, and all of  [#permalink]

Show Tags

New post 27 Jun 2018, 18:14
reto wrote:
Mike's pencil box contains 30 pens. 15 of the pens are red, and all of the others are either blue or black. If Mike were to choose a random pen from the pencil box, what is the probability that it would be blue?

(1) The probability that the pen will be red minus the probability that the pen will be black equals 0.3
(2) The probability that the pen will be red or blue is 0.8


We see that the P(red) = 15/30 = 0.5 and thus P(blue or black) = P(blue) + P(black) = 0.5. We need to determine P(blue). So if we know P(black), then we can determine P(blue) since P(blue) = 0.5 - P(black).

Statement One Alone:

The probability that the pen will be red minus the probability that the pen will be black equals 0.3.

So we have:

P(red) - P(black) = 0.3

0.5 - P(black) = 0.3

P(black) = 0.2

Thus, P(blue) = 0.5 - 0.2 = 0.3. Statement one alone is sufficient.

Statement Two Alone:

The probability that the pen will be red or blue is 0.8.

So we have:

P(red) + P(blue) = 0.8

0.5 + P(blue) = 0.8

P(blue) = 0.3

Statement two alone is also sufficient.

Answer: D
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: Mike's pencil box contains 30 pens. 15 of the pens are red, and all of &nbs [#permalink] 27 Jun 2018, 18:14
Display posts from previous: Sort by

Mike's pencil box contains 30 pens. 15 of the pens are red, and all of

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.