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R and M are positive even numbers. Is root (R*M) a positive

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Senior Manager
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R and M are positive even numbers. Is root (R*M) a positive [#permalink] New post 06 Sep 2006, 01:35
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A
B
C
D
E

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R and M are positive even numbers. Is root (R*M) a positive integer?

1) (root R + root M) is positive even integer.

2) Root R is a positive even integer.

I think the answer should be E...Your views !!!
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Re: DS - R&M [#permalink] New post 06 Sep 2006, 02:04
sumitsarkar82 wrote:
R and M are positive even numbers. Is root (R*M) a positive integer?

1) (root R + root M) is positive even integer.

2) Root R is a positive even integer.

I think the answer should be E...Your views !!!


I pick A

1) says r^1/2 + m^1/2 = 2k for some k

=> r + m + 2(rm)^1/2 = 4k^2
=> 2(rm)^1/2 = 4k^2 -r -m

now RHS should be even as 4k is even, r is even and m is even

=> (rm)^1/2 should be a positive integer.
so sufficient.

2) does not say anthing about m so insufficient.
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Re: DS - R&M [#permalink] New post 06 Sep 2006, 02:09
iced_tea wrote:
I pick A

1) says r^1/2 + m^1/2 = 2k for some k

=> r + m + 2(rm)^1/2 = 4k^2
=> 2(rm)^1/2 = 4k^2 -r -m

now RHS should be even as 4k is even, r is even and m is even

=> (rm)^1/2 should be a positive integer.
so sufficient.



What if

a) R = 16, M =4
root R could be 4, root M could be -2

b) R = 16, M =4
root R could be 4, root M could be 2

Satisfies (root R + root M) is positive even integer. But root (R*M) could be +v2 or -ve
Re: DS - R&M   [#permalink] 06 Sep 2006, 02:09
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R and M are positive even numbers. Is root (R*M) a positive

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