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# In the XY-plane, the line with equation ax + by + c = 0, where abc ≠ 0

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In the XY-plane, the line with equation ax + by + c = 0, where abc ≠ 0 [#permalink]
Hello dave13,

You have solved it almost perfectly in statement 1. ( though you missed a minus sign). However, solving to find b is not required, just knowing that a unique value can be found is sufficient as it is a DS
ALWAYS remember this to save time.

For statement 2. -c/b = 5/2

So all we know is the ratio of c and b -> we cannot predict the exact value of b based on this. As b could be 2 or 4 or 8 ... any number based on what c is as long as the ratio is the same ( -5/2)

Hope you got why the answer should be (A) and statement (2) is not sufficient.

Best,

dave13 wrote:
have a good day!

thanks Gladiator59 for nice explanation i understand i dont need to solve DS questions like PS, but i am still learning, so I need to see logical solutions in DS as well at this learning stage
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Re: In the XY-plane, the line with equation ax + by + c = 0, where abc ≠ 0 [#permalink]
dave13 wrote:

Statement One: a = 2, and slope −3

the slope = $$-\frac{a}{b}$$ = -3

$$-a = -3b$$

$$-3b= -2$$

$$b = -\frac{2}{3}$$ Sufficient

Statement Two: c = 5/2

y intercept is $$-\frac{c}{b}$$

But we dont know anything of B. it is indeed insufficient

IMO: A

p.s.
Gladiator59 thank you ! Edited my solution. can you please check if all is correct. i got confused reagrding minus sign i missed in ST ONE.

Again in the last step of statement calculation, you have missed removing the minus sign. So b = 2/3.

Makes sense to solve DS like PS to get more practice - but don't make a habit of it.
Regards,