Find all School-related info fast with the new School-Specific MBA Forum

It is currently 24 Oct 2014, 17:49

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If the square root of the product of three distinct positive

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 30 Oct 2005
Posts: 19
Followers: 0

Kudos [?]: 0 [0], given: 0

If the square root of the product of three distinct positive [#permalink] New post 09 Nov 2005, 18:42
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 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
Manager
Manager
avatar
Joined: 14 Apr 2003
Posts: 85
Followers: 1

Kudos [?]: 1 [0], given: 0

Re: DS: exponents [#permalink] New post 09 Nov 2005, 18:57
marth750 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


a b c = c^2
a b = c

1. C = 12 a*b = 12. == suff.
2. a+ b + c = 20
a+b+ab=20 == suff by using values.
Manager
Manager
avatar
Joined: 01 Nov 2005
Posts: 127
Followers: 1

Kudos [?]: 16 [0], given: 0

 [#permalink] New post 09 Nov 2005, 20:37
sqrt(abc) = c
ab = c

1) abc = c^2 = 12^ = 144, ab = 144/12 = 12 => suff.

2) (a+b+c) = 20, a+b+ab = 20, ab = 20-a-b, => insuff?

i think A
Senior Manager
Senior Manager
avatar
Joined: 07 Jul 2005
Posts: 405
Followers: 3

Kudos [?]: 13 [0], given: 0

 [#permalink] New post 09 Nov 2005, 20:44
From the question stem we have

sqrt(xyz) = x, where x is the largest number. Solving we have

yz = x, where we are trying to solve for yz

(1) Sufficient. This implies yz = x =12

(2) Insufficient.

(x+y+z) = 20 and we can't do anything with this


I pick A.
Senior Manager
Senior Manager
User avatar
Joined: 14 Apr 2005
Posts: 422
Location: India, Chennai
Followers: 1

Kudos [?]: 3 [0], given: 0

Re: DS: exponents [#permalink] New post 09 Nov 2005, 22:53
Let x,y,z be 3 disting numbers. Let z be the max.
From qn sqrt(xyz) = z

From stmt1. z = 12 -> sqrt(xyz) = 12
=> xyz=144 => xy = 12. So sufficient.

From stmt2 we get x+y+z = 20, and substituting the value of z from qn stem will also not help.

Hence A.
Manager
Manager
avatar
Joined: 01 Nov 2005
Posts: 127
Followers: 1

Kudos [?]: 16 [0], given: 0

 [#permalink] New post 09 Nov 2005, 23:19
can we have the OA for this one please?
Intern
Intern
avatar
Joined: 30 Oct 2005
Posts: 19
Followers: 0

Kudos [?]: 0 [0], given: 0

 [#permalink] New post 15 Nov 2005, 03:41
The OA is D.

Though, I don't see how this could be. I think the correct answer is A.

sorry for delay.
SVP
SVP
User avatar
Joined: 24 Sep 2005
Posts: 1898
Followers: 10

Kudos [?]: 110 [0], given: 0

Re: DS: exponents [#permalink] New post 15 Nov 2005, 05:07
marth750 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


uhm, let's consider (2)
a+b+c= 20/3*3 =20
we have sqrt(abc)= c ---> abc=c^2 ---> ab=c
--> a+b+ab= 20 ---> a(b+1)+ b+ 1= 20+1 --->
(a+1)(b+1)=21 . Since a and b are positive integer, we can obtain 4 cases:
Case 1: a+1=1 and b+1=21 ---> impossible coz a can be 0 since a is a positive integer
Case 2: a+1=21 and b+1=1 , similar to case 1
Case 3: a+1=3, b+1=7 ---> a=2 and b=6 --->ab=12
Case 4: a+1=7, b+1=3 ----> a=6, b=2 -----> ab=12
Thus from statement (2), we obtain ab=12 ----> suff
(1) is also suff as others proved.

So, D is correct answer!
Director
Director
avatar
Joined: 27 Jun 2005
Posts: 517
Location: MS
Followers: 2

Kudos [?]: 16 [0], given: 0

Re: DS: exponents [#permalink] New post 15 Nov 2005, 09:43
the reason why I thought that the B is not sufficient is
it gives you two equations

a+b+c=20
bc =a

and 3 Variables

I have read somewhere that you need same number of equations as the number of variables to get the values of all the variables...!!!

I guess that's not always true as you just proved it ....or am I missing something.




laxieqv wrote:
marth750 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


uhm, let's consider (2)
a+b+c= 20/3*3 =20
we have sqrt(abc)= c ---> abc=c^2 ---> ab=c
--> a+b+ab= 20 ---> a(b+1)+ b+ 1= 20+1 --->
(a+1)(b+1)=21 . Since a and b are positive integer, we can obtain 4 cases:
Case 1: a+1=1 and b+1=21 ---> impossible coz a can be 0 since a is a positive integer
Case 2: a+1=21 and b+1=1 , similar to case 1
Case 3: a+1=3, b+1=7 ---> a=2 and b=6 --->ab=12
Case 4: a+1=7, b+1=3 ----> a=6, b=2 -----> ab=12
Thus from statement (2), we obtain ab=12 ----> suff
(1) is also suff as others proved.

So, D is correct answer!
Manager
Manager
avatar
Joined: 11 Jul 2005
Posts: 86
Location: New York
Followers: 1

Kudos [?]: 0 [0], given: 0

Re: DS: exponents [#permalink] New post 15 Nov 2005, 14:49
cool_jonny009 wrote:
the reason why I thought that the B is not sufficient is
it gives you two equations

a+b+c=20
bc =a

and 3 Variables

I have read somewhere that you need same number of equations as the number of variables to get the values of all the variables...!!!

I guess that's not always true as you just proved it ....or am I missing something.



No, You are correct. It is not posible to find the individual values with absolute certanity. But the questions asks for the product of two variables. In such cases, the statement has to be analyzed very carefully. You can find the product but not the individual values.
Director
Director
avatar
Joined: 27 Jun 2005
Posts: 517
Location: MS
Followers: 2

Kudos [?]: 16 [0], given: 0

 [#permalink] New post 15 Nov 2005, 16:47
thanx amy_v for the clarification....i got it
SVP
SVP
User avatar
Joined: 03 Jan 2005
Posts: 2251
Followers: 12

Kudos [?]: 204 [0], given: 0

Re: DS: exponents [#permalink] New post 15 Nov 2005, 19:04
cool_jonny009 wrote:
I have read somewhere that you need same number of equations as the number of variables to get the values of all the variables...!!!

I guess that's not always true as you just proved it ....or am I missing something.



You are right if you want to solve for three variables you need three equations. In other words, two equations would not be sufficient to determine our answer, in this question. However, notice that there is one more restriction in the question stem, that both a and b are positive integers.

We know that ab=c
and a+b+c=20
we can derive a=(20-b)/(1+b)
Here clearly there are infinite pairs of a and b that would satisfy this equation. However we can only find two pairs of a and b that are positive integers (2,6) or (6,2) which give us a definite product of ab=12.
_________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

Re: DS: exponents   [#permalink] 15 Nov 2005, 19:04
    Similar topics Author Replies Last post
Similar
Topics:
If the square root of the product of three distinct positive yezz 9 02 Sep 2006, 09:17
If the square root of the product of three distinct positive sudhagar 7 10 Nov 2005, 23:53
If the square root of the product of three distinct positive TS 10 08 Jun 2005, 17:48
If the square root of the product of three distinct positive TS 1 26 May 2005, 18:20
If the square root of the product of three distinct positive Dookie 5 15 Nov 2004, 12:24
Display posts from previous: Sort by

If the square root of the product of three distinct positive

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.