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# If the square root of the product of three distinct positive

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If the square root of the product of three distinct positive [#permalink]  27 May 2008, 23:42
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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

A) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.

B) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.

C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.

D) Either statement BY ITSELF is sufficient to answer the question.

E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

(D) If you call the three numbers x, y and z, and let x be the biggest, then the question tells you that x = square root of the product of x, y and z. If you square both sides of this equation you get:
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Re: DS [#permalink]  28 May 2008, 00:47
kapilnegi 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 is 12.

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

A) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.

B) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.

C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.

D) Either statement BY ITSELF is sufficient to answer the question.

E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

If (1) only, the product of the 2 smaller numbers must be 12, so we will have 2 answers for the 2 smaller numbers: (6 and 2) and (4 and 3) => (1) only is insufficient => eleminate A and D
If (2) only, we assume the 3 numbers are x, y and z (x is the largest one)
we will have: x = yz and x + y + z = 20 or yz + y + z = 20 (y, z are distintive positve integers)
we assume y is the bigger one then y(z+1) + z = 20
=> y is smaller than or equal to 9
Try all positve integers smaller than or equal to 9, then we can have 6 for y, 2 for z and 12 for x is the only set of numbers which meet the requirements.
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Re: DS [#permalink]  28 May 2008, 02:18
I'll go with D. The question is to find the product of two numbers. (6,2) and (4,3) will have the same product 12. 1 is also suff.

nvhungtct wrote:
kapilnegi 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 is 12.

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

A) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.

B) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.

C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.

D) Either statement BY ITSELF is sufficient to answer the question.

E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

If (1) only, the product of the 2 smaller numbers must be 12, so we will have 2 answers for the 2 smaller numbers: (6 and 2) and (4 and 3) => (1) only is insufficient => eleminate A and D
If (2) only, we assume the 3 numbers are x, y and z (x is the largest one)
we will have: x = yz and x + y + z = 20 or yz + y + z = 20 (y, z are distintive positve integers)
we assume y is the bigger one then y(z+1) + z = 20
=> y is smaller than or equal to 9
Try all positve integers smaller than or equal to 9, then we can have 6 for y, 2 for z and 12 for x is the only set of numbers which meet the requirements.
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Re: DS [#permalink]  28 May 2008, 04:01
how can you find the product just knowing the average ?

i say A
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Re: DS [#permalink]  28 May 2008, 05:23
There is no straight methof of doing that, however in this question there is only one set of values which can satisfy x+y+z = 20, and xy=z. Remember x,y,z are distinct positive integers.

pmenon wrote:
how can you find the product just knowing the average ?

i say A
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Re: DS [#permalink]  28 May 2008, 07:16
kapilnegi 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 is 12.

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

A) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.

B) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.

C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.

D) Either statement BY ITSELF is sufficient to answer the question.

E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

(D) If you call the three numbers x, y and z, and let x be the biggest, then the question tells you that x = square root of the product of x, y and z. If you square both sides of this equation you get:

S1 Suff: Def. B/c the product of x and y is 12 anyway you work it. 6,2 or 3,4.

S2 Suff: sqrt(xyz)=z x+y+z=20

Test it. 1,2, 18. Nope

1,3,17 Nope

etc...

1,4,16

1,5,15 Nope

etc... But this is way too long. A very quick method is...

We should realize that x*y must equal z. B/c essentially to get sqrt(xyz)=z.

we MUST have sqrt(z^2)=z.

Thus x*y=z. The only way this would work is if we have 6,2. (B/c X+Y+Z=20). 3,4 is not an option b/c 3*4 dsnt equal 13.

D
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Re: DS [#permalink]  28 May 2008, 23:38
durgesh79 wrote:
I'll go with D. The question is to find the product of two numbers. (6,2) and (4,3) will have the same product 12. 1 is also suff.

Sorry, I missed the question.
(1) is also suff. So the right answer must be D.
Thanhks durgesh79
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Re: DS [#permalink]  29 May 2008, 21:32
The question asks for the product of smaller two nos which (1) gives as 12 .. It is not asking u wht combination gives u 12. so statement (1) is sufficient as well)
Kapil, wht is the OA?

nvhungtct wrote:
kapilnegi 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 is 12.

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

A) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.

B) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.

C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.

D) Either statement BY ITSELF is sufficient to answer the question.

E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

If (1) only, the product of the 2 smaller numbers must be 12, so we will have 2 answers for the 2 smaller numbers: (6 and 2) and (4 and 3) => (1) only is insufficient => eleminate A and D
If (2) only, we assume the 3 numbers are x, y and z (x is the largest one)
we will have: x = yz and x + y + z = 20 or yz + y + z = 20 (y, z are distintive positve integers)
we assume y is the bigger one then y(z+1) + z = 20
=> y is smaller than or equal to 9
Try all positve integers smaller than or equal to 9, then we can have 6 for y, 2 for z and 12 for x is the only set of numbers which meet the requirements.
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Re: DS [#permalink]  30 May 2008, 02:50
[quote="kapilnegi"]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

A) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.

B) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.

C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.

D) Either statement BY ITSELF is sufficient to answer the question.

E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

(D) If you call the three numbers x, y and z, and let x be the biggest, then the question tells you that x = square root of the product of x, y and z. If you square both sides of this equation you get:[/quot

A for me.

(1) If the largest number is 12 then

12 squared is = 144 so 12 x (yz) = 144

so 12yz= 144 divide both sides by 12 and you get 12.

therefore the product of the two smaller numbers is 12. This is sufficient

(2) Mean = 20/3 therefore x + Y + Z = 20. This is not sufficient
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Re: DS [#permalink]  30 May 2008, 07:40
kapilnegi 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 is 12.

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

A) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.

B) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.

C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.

D) Either statement BY ITSELF is sufficient to answer the question.

E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

(D) If you call the three numbers x, y and z, and let x be the biggest, then the question tells you that x = square root of the product of x, y and z. If you square both sides of this equation you get:

I´d say D:

(1) The largest number is 12
So, we know that the product of the smallest numbers is 12

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

By this, we know that the smallest numbers are 2 and 6 (2+6+12 = 20)
Re: DS   [#permalink] 30 May 2008, 07:40
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