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2 bulbs selected from 10 bulbs

by nh8404052006 » Sat Dec 13, 2008 5:16 am
A box contains 10 light bulbs, fewer than half of which are defective. Two bulbs are to be drawn simultaneously from the box. If n of the bulbs in box are defective, what is thevalue of n?

(1) The probability that the two bulbs to be drawn will be defective is 1/15.
(2) The probability that one of the bulbs to be drawn will be defective and the other will not be defective is 7/15.

Please explain
OA: D
S02Q06
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Re: 2 bulbs selected from 10 bulbs

by parallel_chase » Sat Dec 13, 2008 5:50 am
10 bulbs, n defective bulbs. n < 5. n=?

Statement I

n/10 * (n-1)/9 = 1/15

n^2 - n = 90/15

n^2 - n - 6 = 0

(n - 3)(n+2) = 0

n= 3 or -2

bulbs cannot be negative, and n<5, therefore 3.

Sufficient.

Statement II

(10-n)/10 * n/9 + (10-n)/9 * n/10 = 7/15

10n - n^2 = 21

n^2 - 10n + 21 = 0

(n-3)(n-7) = 0

n = 3 or 7

since we know n< 5, only 3 can be the answer.

Sufficient.

Hence D.


Hope this helps.
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by vittalgmat » Sat Dec 13, 2008 11:36 pm
I followed the same steps as parallel_chase and got D.
However I found one take away.

in Stmt 1: we will get the quadratic equation
n^2 -n -6 = 0

As we all know, for DS we dont need to solve this but here in particular,
we need to know whether both the roots are of same sign or of different sign.

To identify this , consider the generalized equation
ax^2 +bx +c = 0. If this equation can be represented in the form
(y + z)^2 = y^2 +2yz +z^2, then the equation will have identical roots (both with same signs and magnitude)

So, here looking at the equation we know that 6 is not a perfect square.
So we can conclude that root have opposite sign and the -ve root is not required coz we cannot have -ve defective bulbs.

By doing this little observation, we avoided factorizing n^2 -n -6 into
(n -3)(n+2) ...

we can conclude the stmt is sufficient.

Similar observation can be applied to stmt 2 and can shave off a few seconds which could be utilized on a tough problem.


HT helps
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Re: 2 bulbs selected from 10 bulbs

by revoltangel » Tue Dec 30, 2008 5:43 pm
Hi parallel,

could you please explain this part?
parallel_chase wrote:
Statement II

(10-n)/10 * n/9 + (10-n)/9 * n/10 = 7/15


Thanks :D
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by cramya » Tue Dec 30, 2008 6:05 pm
could you please explain this part?
Let x be the defective bulbs
Let y be the non defective bulbs

Given : x+y =10
y= 10-x (1)

Q: To find x

Stmt I

The probability that the two bulbs to be drawn will be defective is 1/15

Probability of drawing a defective bulb in the first draw = x/10

Probability of drawing a defective bulb in the second draw = x-1/9

Probability of both = x/10*(x-1)/9 = 1/15

We can solve for x


SUFF

Stmt II
The probability that one of the bulbs to be drawn will be defective and the other will not be defective is 7/15


Probability of drawing a defective bulb in the first draw = x/10
Probability of drawing a non defective bulb in the second draw
= y/9
= (10-x)/9 using (1)


Probability of drawing a non defective bulb in the first draw
= y/10
= (10-x)/10 using (1)

Probability of drawing a defective bulb in the second draw = x/9

Probability of both:

x/10 * 10-x/9 + (10-x)/10*x/9 = 7/15

Can solve for x

SUFF

Choose D)

Like PC said in the real exam if u can get to the equation choose D) and dont solve for x. Just arriving at a conclusion that its sufficient is all we need.

Hope this helps and hoping PC wouldn't mind my explanation...
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Re: 2 bulbs selected from 10 bulbs

by logitech » Tue Dec 30, 2008 6:30 pm

ONCE AGAIN, THIS IS A GMAT QUESTION

Defective numbers: n
non defective: 10-n

1) n/10 x (n-1)/9 = whatever SUF
2) n/10 x (10-n)/9 = whatever SUF

choose D
LGTCH
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by cramya » Tue Dec 30, 2008 6:39 pm
ONCE AGAIN, THIS IS A GMAT QUESTION

Really wow I thought I was in the wrong forum. Thanks Logitech :-)


Yes its a GMAT question and we do understand that but for someone trying to figure this out (to get a feel for whats given and how to translate it to determine sufficiency)

1) n/10 x (n-1)/9 = whatever SUF
2) n/10 x (10-n)/9 = whatever SUF

is like trying to find a needle in a haystack

Q: So what do we do??

EXPLAIN AND WHATS THE DIFFERENCE IF ITS A GMAT QUESTION OR GRE QUESTION OR SAT QUESTION OR XYZAB CD QUESTION- THEY ALL REQUIRE GOOD EXPLANATIONS AND AS LONG AS THERE ARE TAKEAWAYS FROM THESE THAT CAN BE APPLIED TO GMAT QUESTIONS


Jus kidding welcome back Logitech....


Regards,
Cramya
Last edited by cramya on Wed Dec 31, 2008 12:08 am, edited 2 times in total.
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by cramya » Tue Dec 30, 2008 6:51 pm
Again a forum is not to showcase what u know in a way only u can understand but to pass on that knowledge/info in a way everyone can understand. We all benefit from it.. WIN WIN situation

I am sure there will be takers for this thought..


Regards,
CR
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by revoltangel » Wed Dec 31, 2008 2:03 pm
haha thanks cramya. you really helped clarify the problem for me.
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by logitech » Wed Dec 31, 2008 2:14 pm
Cramya stay in the SCOPE of GMAT. You know what I mean. Otherwise the rest is BLA BLA BLA BLA...

why do we take GMAT ? to get in Business School

Is GMAT different than many CATS ? YES

Do we need classical math here ? JUST ONLY TO UNDERSTAND IT

What do we need to work on ? GMAT solutions.

This is 75 minutes show. And GMAT does not care LESS about what you KNOW.

It is all about EXECUTION!

I will repeat this again: EXECUTION.

So this is why I wrote this is a GMAT QUESTION.

If you are good at math, you are fine. IF NOT, you have to change your paradigm. WORK ON GMAT solutions. We won't be math teachers in HIGH SCHOOLS.

And this is a two way street. We are not only here to GIVE.

People who knows me in this forum are aware that I am here to HELP people and LEARN from people.

I am not a sweet talker but I say what you NEED to hear, not what you WANT to hear.

Guys if you want to ace the QUANT in GMAT. Grasp the fundamentals and be creative.

Alrighty it is NEW YEAR'S EVE! And I wish everybody happiness and success along with health in 2009.

Best,
LGTCH
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by cramya » Wed Dec 31, 2008 2:15 pm
haha thanks cramya. you really helped clarify the problem for me.
No problem ;anytime!

RevoltAngel,
Look at this post too.
https://www.beatthegmat.com/probability- ... 10706.html

Stuart has provided an excellent explanation on when to add probabilities (ALTERNATE EVENTS OCCURRING) versus when to multiply (MULTIPLE EVENTS OCCURRING).

Regards,
Cramya
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by cramya » Wed Dec 31, 2008 2:23 pm
Logitech,
Like I said before if we are doing this problem at home(any of us) we can move on by convincing ourselves what the answer is in 2 lines or better write it on the same line as it may look more elegant; I dont know whatever.

The reason why any of us provide detailed explanations is for others who may see the detailed explanation as a benefit(the main reason why most of us visit a forum atleast IMO eg:it helped clarify for RevoltAngel, right..). We may need to revisit this post sometime and the detailed explanation provided may help us too. The explanation is to help others and ourselves not to spend so much time on the real exam. If u understand the concept by reading the detailed explanation then you wont, correct?

For example : A GMAT DEBRIEF could just read

TOOK GMAT. SCORED 770 THANKS NO QUESTIONS BYE...

Why do people spend time explaining what they did, how they did it etc...? We want this explnation right. The same applies to a problem. This way we dont have double standards when it comes to explanations.


I am not a sweet talker but I say what you NEED to hear, not what you WANT to hear
Thats great!

There is a distinction between sugar coating things and being polite or courteous and it is very easy to confuse the 2. No one likes sugar coaters and at the same time no one likes unpoliteness either. I am sure u will agree.

Anyways it is ok to have a difference of opinion as I understand both of us are different individuals. If we did have the same opnion in everything then that would freak me out :P

Happy new year to you too!


-- CR


Ok I leave this post not the forum :-) contented as I have some takeaways from this post by providing a solution and learning what I need to from other user posts.


The rest(comments) is extra baggage which I will leave with this post and not carry along in to the new year :-)

Sorry guys for the long post-> I am tired after typing all these lines anyways, Happy New Year All and wish all of u great success in your GMAT exams and life in general....

Regards,
Cramya
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2 bulbs selected from 10 bulbs

by ifairo » Thu Jan 01, 2009 9:31 pm
I think, the answer is A, and not D. Please correct me if I am wrong.

By I) =>

n * (n-1) / 90 = 1 / 15, so n = 3 or -2. We can see the actual value is not negative so n must be 3.

By II) =>

n * (10 -n) / 90 = 7 / 15. This time, n could be 3 or 7. Please check. So, we can't decide n, right?

Based on these two calculations, I think the answer is A, and not D.

Regards.
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by cramya » Thu Jan 01, 2009 10:10 pm
This post is not leaving me :-)

This time, n could be 3 or 7. Please check. So, we can't decide n, right?
A box contains 10 light bulbs, fewer than half of which are defective

Ifairo,
U r correct in your calculations but since the question reads fewer than half are defective we can eliminate 7 and therefore the only value possible is 3

Hope this helps!
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2 bulbs selected from 10 bulbs

by ifairo » Sat Jan 03, 2009 12:37 am
Yes, you are correct. Thanks.
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