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# Rules 1. Time yourself 2. Work your solution on a seperate

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CEO
Joined: 15 Aug 2003
Posts: 3469
Followers: 61

Kudos [?]: 702 [0], given: 781

Rules 1. Time yourself 2. Work your solution on a seperate [#permalink]  10 Mar 2004, 19:23
Rules

1. Time yourself
2. Work your solution on a seperate sheet of paper

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 is 12.
(2) The average (arithmetic mean) of the three numbers is 20/3
Director
Joined: 03 Jul 2003
Posts: 655
Followers: 2

Kudos [?]: 22 [0], given: 0

Ans: D

Time more than 4 mins
Manager
Joined: 11 Oct 2003
Posts: 102
Location: USA
Followers: 1

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

A.. [#permalink]  10 Mar 2004, 20:58
I think it it is A..2 min
Manager
Joined: 28 Jan 2004
Posts: 203
Location: India
Followers: 2

Kudos [?]: 14 [0], given: 4

I will go for A (only statement 1 can be used to answer).
Time taken 30 seconds.

Sol. Three integers be X,Y,Z and largest be Z.
sqrt(XYZ) = Z ,replace Z by 12
sqrt(XY*12) = 12
or sqrt(XY) = sqrt(12)
or XY = 12
Director
Joined: 13 Nov 2003
Posts: 793
Location: BULGARIA
Followers: 1

Kudos [?]: 27 [0], given: 0

Agree with mantha and mdfrahim, think that the answer is A)
Time: 2,5 min.
SVP
Joined: 30 Oct 2003
Posts: 1797
Location: NewJersey USA
Followers: 5

Kudos [?]: 41 [0], given: 0

a) sqrt( a * b * 12 ) = 12
so a * b = 12
Sufficient
b) a+b+c = 20
Only number that satisfies this and a * b = c is c = 12
Sufficient
< 2 minutes
CEO
Joined: 15 Aug 2003
Posts: 3469
Followers: 61

Kudos [?]: 702 [0], given: 781

Re: [#18] 2 Min. Challenge : Product [#permalink]  11 Mar 2004, 05:30
praetorian123 wrote:
Rules

1. Time yourself
2. Work your solution on a seperate sheet of paper

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

D is correct

good work anand
Senior Manager
Joined: 23 Sep 2003
Posts: 294
Location: US
Followers: 1

Kudos [?]: 2 [0], given: 0

I agree with Anandnk and Kpadma.

The only distinct positive integers that satisfy the requirement that their sum = 20, and that the largest integer = the product of the other 2 integers are 6, 2 and 12.

If you try other combinations, you'll find that they don't sum to 20. Example: a=3; b=4 ; ab = c = 12 but 3 + 4 + 12 <> 20. Same with 8, 2 and 16.
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