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 500,000 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:

Two pieces of fruit are selected out of a group of 8 pieces [#permalink]

Show Tags

09 Nov 2012, 01:34

3

This post received KUDOS

3

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

39% (02:42) correct
61% (02:26) wrong based on 205 sessions

HideShow timer Statistics

Two pieces of fruit are selected out of a group of 8 pieces of fruit consisting only of apples and bananas. What is the probability of selecting exactly 2 bananas?

(1) The probability of selecting exactly 2 apples is greater than 1/2. (2) The probability of selecting 1 apple and 1 banana in either order is greater than 1/3.

Re: Two pieces of fruit are selected out of a group of 8 pieces [#permalink]

Show Tags

09 Nov 2012, 03:27

2

This post received KUDOS

Pansi wrote:

Two pieces of fruit are selected out of a group of 8 pieces of fruit consisting only of apples and bananas. What is the probability of selecting exactly 2 bananas?

(1) The probability of selecting exactly 2 apples is greater than ½.

(2) The probability of selecting 1 apple and 1 banana in either order is greater than 1/3

Total No. of ways of selecting = 8C2 = 28

1)No. of apples = 7, No. of bananas = 1, Probability : \(\frac{7C2}{8C2} = \frac{21}{28}\) No. of apples = 6, No. of bananas = 2, Probability : \(\frac{6C2}{8C2} = \frac{15}{28}\) No. of apples = 5, No. of bananas = 3, Probability : \(\frac{5C2}{8C2} = \frac{10}{28}\)

So, No. of apples can be 6 or 7. Insufficient

2)No. of apples = 7, No. of bananas = 1, Probability : \(\frac{7C1*1C1}{8C2} = \frac{7}{28}\) No. of apples = 6, No. of bananas = 2, Probability : \(\frac{6C1*2C1}{8C2} = \frac{12}{28}\) No. of apples = 5, No. of bananas = 3, Probability : \(\frac{5C1*3C1}{8C2} = \frac{15}{28}\)

So, No. of apples can be 5 or 6. ( More values other than 7 are also possible, but two values are enough to make the statement insufficient.)Insufficient

1 & 2 together. No. Of apples = 6, No. of bananas = 2. Enough info to find what is required. Sufficient.

Although, I'm not very strong at combinatronics and hence I'm not 100% sure of my method. Also since the question states that there ARE bananas, I'm assuming that no. of apples cannot be 8.

Kudos Please... If my post helped.
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Two pieces of fruit are selected out of a group of 8 pieces of fruit consisting only of apples and bananas. What is the probability of selecting exactly 2 bananas?

Say there are \(x\) bananas and \(y\) (\(y=8-x\)) apples. The question is \(P(bb)=\frac{x}{8}*\frac{x-1}{7}=?\). Basically we need to find how many bananas are there.

(1) The probability of selecting exactly 2 apples is greater than 1/2 --> \(\frac{y}{8}*\frac{y-1}{7}>\frac{1}{2}\) --> \(y(y-1)>28\) --> \(y\) can be 6, 7, or 8, thus \(x\) can be 2, 1, or 0. not sufficient.

(2) The probability of selecting 1 apple and 1 banana in either order is greater than 1/3. \(2*\frac{x}{8}*\frac{8-x}{7}>\frac{1}{3}\) --> \(x(8-x)>\frac{28}{3}=9\frac{1}{3}\), thus \(x\) can be 2, 3, 4, 5, or 6. Not sufficient.

Re: Two pieces of fruit are selected out of a group of 8 pieces [#permalink]

Show Tags

09 Nov 2012, 03:54

Bunuel wrote:

Two pieces of fruit are selected out of a group of 8 pieces of fruit consisting only of apples and bananas. What is the probability of selecting exactly 2 bananas?

Say there are \(x\) bananas and \(y\) (\(y=8-x\)) apples. The question is \(P(bb)=\frac{x}{8}*\frac{x-1}{7}=?\). Basically we need to find how many bananas are there.

(1) The probability of selecting exactly 2 apples is greater than 1/2 --> \(\frac{y}{8}*\frac{y-1}{7}>\frac{1}{2}\) --> \(y(y-1)>28\) --> \(y\) can be 6, 7, or 8, thus \(x\) can be 2, 1, or 0. not sufficient.

(2) The probability of selecting 1 apple and 1 banana in either order is greater than 1/3. \(2*\frac{x}{8}*\frac{8-x}{7}>\frac{1}{3}\) --> \(x(8-x)>\frac{28}{3}=9\frac{1}{3}\), thus \(x\) can be 2, 3, 4, 5, or 6. Not sufficient.

(1)+(2) From above x can only be 2. Sufficient.

Answer: C.

Hope it's clear.

Just concerned. When the question statement says that there are bananas AND apples, do we need to consider situations in which there are only apples or only bananas??? I'm asking this not for just this question but for the GMAT on the whole.
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Re: Two pieces of fruit are selected out of a group of 8 pieces [#permalink]

Show Tags

09 Nov 2012, 04:04

MacFauz wrote:

Bunuel wrote:

Two pieces of fruit are selected out of a group of 8 pieces of fruit consisting only of apples and bananas. What is the probability of selecting exactly 2 bananas?

Say there are \(x\) bananas and \(y\) (\(y=8-x\)) apples. The question is \(P(bb)=\frac{x}{8}*\frac{x-1}{7}=?\). Basically we need to find how many bananas are there.

(1) The probability of selecting exactly 2 apples is greater than 1/2 --> \(\frac{y}{8}*\frac{y-1}{7}>\frac{1}{2}\) --> \(y(y-1)>28\) --> \(y\) can be 6, 7, or 8, thus \(x\) can be 2, 1, or 0. not sufficient.

(2) The probability of selecting 1 apple and 1 banana in either order is greater than 1/3. \(2*\frac{x}{8}*\frac{8-x}{7}>\frac{1}{3}\) --> \(x(8-x)>\frac{28}{3}=9\frac{1}{3}\), thus \(x\) can be 2, 3, 4, 5, or 6. Not sufficient.

(1)+(2) From above x can only be 2. Sufficient.

Answer: C.

Hope it's clear.

Just concerned. When the question statement says that there are bananas AND apples, do we need to consider situations in which there are only apples or only bananas??? I'm asking this not for just this question but for the GMAT on the whole.

Choice (2) makes it clear that there is banana in the group of fruits, doesn't it? And yeah, it's always bad to assume ANYTHING on gmat, especially for Data Sufficiency and CR questions! So, when considering choice (1) by itself, no. of bananas=0 should also be one of the options.
_________________

Re: Two pieces of fruit are selected out of a group of 8 pieces [#permalink]

Show Tags

11 Nov 2012, 02:53

Bunuel wrote:

Two pieces of fruit are selected out of a group of 8 pieces of fruit consisting only of apples and bananas. What is the probability of selecting exactly 2 bananas?

Say there are \(x\) bananas and \(y\) (\(y=8-x\)) apples. The question is \(P(bb)=\frac{x}{8}*\frac{x-1}{7}=?\). Basically we need to find how many bananas are there.

(1) The probability of selecting exactly 2 apples is greater than 1/2 --> \(\frac{y}{8}*\frac{y-1}{7}>\frac{1}{2}\) --> \(y(y-1)>28\) --> \(y\) can be 6, 7, or 8, thus \(x\) can be 2, 1, or 0. not sufficient.

(2) The probability of selecting 1 apple and 1 banana in either order is greater than 1/3. \(2*\frac{x}{8}*\frac{8-x}{7}>\frac{1}{3}\) --> \(x(8-x)>\frac{28}{3}=9\frac{1}{3}\), thus \(x\) can be 2, 3, 4, 5, or 6. Not sufficient.

(1)+(2) From above x can only be 2. Sufficient.

Answer: C.

Hope it's clear.

I have solved this question with similar logic, but answered E because i understoon the 2nd statement as no matter what is the order the probability will be greater than 1/3, but in your solution i see that "in either order" means in both ways. Could you please clarify that?
_________________

If you found my post useful and/or interesting - you are welcome to give kudos!

Two pieces of fruit are selected out of a group of 8 pieces of fruit consisting only of apples and bananas. What is the probability of selecting exactly 2 bananas?

Say there are \(x\) bananas and \(y\) (\(y=8-x\)) apples. The question is \(P(bb)=\frac{x}{8}*\frac{x-1}{7}=?\). Basically we need to find how many bananas are there.

(1) The probability of selecting exactly 2 apples is greater than 1/2 --> \(\frac{y}{8}*\frac{y-1}{7}>\frac{1}{2}\) --> \(y(y-1)>28\) --> \(y\) can be 6, 7, or 8, thus \(x\) can be 2, 1, or 0. not sufficient.

(2) The probability of selecting 1 apple and 1 banana in either order is greater than 1/3. \(2*\frac{x}{8}*\frac{8-x}{7}>\frac{1}{3}\) --> \(x(8-x)>\frac{28}{3}=9\frac{1}{3}\), thus \(x\) can be 2, 3, 4, 5, or 6. Not sufficient.

(1)+(2) From above x can only be 2. Sufficient.

Answer: C.

Hope it's clear.

I have solved this question with similar logic, but answered E because i understoon the 2nd statement as no matter what is the order the probability will be greater than 1/3, but in your solution i see that "in either order" means in both ways. Could you please clarify that?

The probability of selecting 1 apple and 1 banana in either order equals to the probability of selecting an apple and then a banana (x/8*(8-x)/7) PLUS the probability of selecting a banana and then an apple ((x-8)/8*x/7) --> x/8*(8-x)/7+(8-x)/8*x/7=2*x/8*(8-x)/7.

Re: Two pieces of fruit are selected out of a group of 8 pieces [#permalink]

Show Tags

31 Jul 2014, 07:07

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.
_________________

Re: Two pieces of fruit are selected out of a group of 8 pieces [#permalink]

Show Tags

02 Sep 2015, 22:30

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.
_________________

There’s something in Pacific North West that you cannot find anywhere else. The atmosphere and scenic nature are next to none, with mountains on one side and ocean on...

This month I got selected by Stanford GSB to be included in “Best & Brightest, Class of 2017” by Poets & Quants. Besides feeling honored for being part of...

Joe Navarro is an ex FBI agent who was a founding member of the FBI’s Behavioural Analysis Program. He was a body language expert who he used his ability to successfully...