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if t is not equal to 0, is r > 0? i) rt = 12 ii) r + t =

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if t is not equal to 0, is r > 0? i) rt = 12 ii) r + t = [#permalink] New post 28 Mar 2006, 19:40
if t is not equal to 0, is r > 0?

i) rt = 12
ii) r + t = 7

Please explain
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 [#permalink] New post 28 Mar 2006, 20:56
Answer is C

Statement 1: if R=-6 and T=-2 than RT=12. Similarly, if R=6 and T=2, than RT=12. R could be pos. or neg. => Insufficient

Statement: If R=2 and T=5, R+T=7. Alternatively, if R=-10 and S=17, R+T=12. Again, R can be neg. or pos. => Insufficient

Taken together: The only way for R*T to equal 12 and for R+T=7, is for both variables to be >0.
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Re: Data sufficiency [#permalink] New post 28 Mar 2006, 21:11
jodeci wrote:
if t is not equal to 0, is r > 0?

i) rt = 12
ii) r + t = 7

Please explain


It's obvious that 1) and 2) alone can't provide sufficient information to conclude whether r> 0

combine the two:

r and t are indeed the roots of the equation:
x^2 - 7x + 12= 0
x^2 - 7x+12 = 0 --> (x-3) (x-4) = 0 ---> x= 3 or 4

It doesn't matter which value is of r ...since both values > 0 --> r>0

C it is.
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 [#permalink] New post 29 Mar 2006, 06:05
1) rt = 12
Could be 1/4(48) = rt and r > 0

Could also be (-1)(-12) = rt and r < 0.

Insufficient.

2) r + t = 7

Can be (r,t) = (4,3) (3,4) (5,2) (2,5), (6,1) (1,6) (-1,8). Insufficient.

Using 1) and 2).

r+t = 7
r + 12/r = 7

Can solve for r.

Sufficient.

Ans C
  [#permalink] 29 Mar 2006, 06:05
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if t is not equal to 0, is r > 0? i) rt = 12 ii) r + t =

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