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:

If the square root of the product of three distinct positive [#permalink]
19 Nov 2009, 12:45

2

This post received KUDOS

Expert's post

2

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

85% (hard)

Question Stats:

48% (02:35) correct
52% (01:18) wrong based on 227 sessions

If the square root of the product of three distinct positive integers is equal to the largest of the three numbers, what is the product of the two smaller numbers?

(1) The largest number of the three distinct numbers is 12. (2) The average (arithmetic mean) of the three numbers is 20/3.

Re: Three distinct positive integers [#permalink]
19 Nov 2009, 15:16

1

This post received KUDOS

Bunuel wrote:

If the square root of the product of three distinct positive integers is equal to the largest of the three numbers, what is the product of the two smaller numbers?

(1) The largest number of the three distinct numbers is 12. (2) The average (arithmetic mean) of the three numbers is 20/3.

0<x<y<z

sqrt (xyz) = z xy = z

1: z = 12. Suff..

2: x + y + z = 20 x + y + xy = 20 The smallest integer cannot be 1.

After trail and error, x = 2, y = 6 and z =12. Suff..

Re: Three distinct positive integers [#permalink]
19 Nov 2009, 15:20

6

This post received KUDOS

Bunuel wrote:

If the square root of the product of three distinct positive integers is equal to the largest of the three numbers, what is the product of the two smaller numbers?

(1) The largest number of the three distinct numbers is 12. (2) The average (arithmetic mean) of the three numbers is 20/3.

Bunuel, is this a problem you created, or is it from an existing source? It's a cleverly designed question. One can use trial and error to show that Statement 2 is also sufficient, but it's not required, as shown below:

Let our numbers be a, b, c, where 0 < a < b < c. Then if sqrt(abc) = c, it must be that ab = c, so to find ab (and thus answer the question) we only need to find the largest of our three numbers, and Statement 1 is sufficient.

For Statement 2, if the mean is 20/3, then the sum of our three numbers is 20, so we know: a + b + ab = 20, and a + b + ab is certainly even. If a and b were both odd, or if one were odd and the other even, then a + b + ab would be odd, which is not the case. So a and b must both be even. Thus a and b are two different positive even numbers which give a product less than 20. If a were greater than 2, then a would be at least 4 and b would be at least 6 (since b > a), which gives too large a product. So a must be 2, and using the equation above, substituting a=2, we have 2 + b + 2b = 20, or 3b = 18, and b = 6.

So Statement 2 not only lets us find the value of ab, it actually lets us find both a and b individually, and is sufficient, and the answer is D. _________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Re: Three distinct positive integers [#permalink]
19 Nov 2009, 15:36

9

This post received KUDOS

Expert's post

2

This post was BOOKMARKED

IanStewart wrote:

Bunuel wrote:

If the square root of the product of three distinct positive integers is equal to the largest of the three numbers, what is the product of the two smaller numbers?

(1) The largest number of the three distinct numbers is 12. (2) The average (arithmetic mean) of the three numbers is 20/3.

Bunuel, is this a problem you created, or is it from an existing source? It's a cleverly designed question. One can use trial and error to show that Statement 2 is also sufficient, but it's not required, as shown below:

Let our numbers be a, b, c, where 0 < a < b < c. Then if sqrt(abc) = c, it must be that ab = c, so to find ab (and thus answer the question) we only need to find the largest of our three numbers, and Statement 1 is sufficient.

For Statement 2, if the mean is 20/3, then the sum of our three numbers is 20, so we know: a + b + ab = 20, and a + b + ab is certainly even. If a and b were both odd, or if one were odd and the other even, then a + b + ab would be odd, which is not the case. So a and b must both be even. Thus a and b are two different positive even numbers which give a product less than 20. If a were greater than 2, then a would be at least 4 and b would be at least 6 (since b > a), which gives too large a product. So a must be 2, and using the equation above, substituting a=2, we have 2 + b + 2b = 20, or 3b = 18, and b = 6.

So Statement 2 not only lets us find the value of ab, it actually lets us find both a and b individually, and is sufficient, and the answer is D.

I took this question from some blog. And the OA given was A. But I disagreed. I think the answer should be D.

The way I solved it was slightly different from yours:

0<a<b<c, \sqrt{abc}=c --> ab=c

(1) Clearly sufficient.

(2) a+b+c=20 --> a+b+ab=20 --> (a+1)(b+1)=21

a, b, and c are integers, so:

a+1=1 and b+1=21, doesn't work, as a becomes 0 and we know that integers are more than 0.

Re: Three distinct positive integers [#permalink]
19 Nov 2009, 15:44

Bunuel wrote:

IanStewart wrote:

I took this question from some blog. And the OA given was A. But I disagreed. I think the answer should be D.

Well, it's not a very clever question if the OA given is A Nice solution by the way. _________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Re: If the square root of the product of three distinct positive [#permalink]
30 Oct 2012, 04:36

1

This post received KUDOS

Expert's post

sanjoo wrote:

statment 1: take largest num as Z

x>y>z..square root xyz=square root z

if z=12..

that means xyz must b 144?? xy must b is equal to 12..12*12=144..square root of 144 is equal to 12..

Statement 2..

Bunuel wrote:

The way I solved it was slightly different from yours:

0<a<b<c, \sqrt{abc}=c --> ab=c

(1) Clearly sufficient.

(2)a+b+c=20 --> a+b+ab=20 --> (a+1)(b+1)=21

a, b, and c are integers, so:

a+1=1 and b+1=21, doesn't work, as a becomes 0 and we know that integers are more than 0.

OR a+1=3 and b+1=7. a=2 and b=6 --> ab=12

Hence sufficient.

Answer: D.

bunuel i didnt get statment 2. bold part..

You mean this part: a+b+c=20 --> a+b+ab=20 --> (a+1)(b+1)=21?

We know that ab=c. Now, substitute c to get: a+b+ab=20. Add 1 to each part: a+b+ab+1=21. Finally, a+b+ab+1 can be written as (a+1)(b+1), thus we have that (a+1)(b+1)=21.

Re: If the square root of the product of three distinct positive [#permalink]
30 Aug 2014, 17:04

1

This post received KUDOS

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. _________________

I submitted my Cambridge MBA application in on time. But do have to say I took a laziez faire approach to the whole submission thing. Even went to the...

For my Cambridge essay I have to write down by short and long term career objectives as a part of the personal statement. Easy enough I said, done it...