explanation please

Thanks a lot Ian

I saw this this DS question and i have been trying to figure it out.If you can please help with a little explanation i will be grateful

Are lines p (with slope m) and q (with slope n) perpendicular to each other?

1. m + 2 = n
2. m + n = 0

I don't know the answer to this question. I feel both the statements are required to answer the question (when combined the values of m & n are -1 & 1 respectively, which satisfies the perpendicular slope concept). Any contentions?

thanks

I think it should be x = 4

x = 1 is not possible, because square root x > 0, so x - 2 > 0, so x > 2

Are lines p (with slope m) and q (with slope n) perpendicular to each other?

1. m + 2 = n
2. m + n = 0

I don't know the answer to this question. I feel both the statements are required to answer the question (when combined the values of m & n are -1 & 1 respectively, which satisfies the perpendicular slope concept). Any contentions?

Well I am not an Expert like Ian but yes I do have a solution for this statement

Since its given that m and n are slopes and not the line
so m+2=n does not really gives a solution


However,
m+n=0
this gives m=-n
so slopes, m and n are equal and of opposite sign
Thus the condition of Perpendicularity is m*n=-1

But over here it's not given whether the value of m or n is 1

Untill its not given,then both answers are insuff(E)

Else B

Hope this helps

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gmat740 wrote: However,
m+n=0
this gives m=-n
so slopes, m and n are equal and of opposite sign
Thus the condition of Perpendicularity is m*n=-1

This question has been recently discussed here: https://www.beatthegmat.com/slope-t33092.html, but I wanted to address a small math error.

If m + n = 0

then:

m = -n

as you stated, BUT to get -1 on the right side we must DIVIDE both sides by n, leaving us with:

m/n = -1,

which is NOT the condition of perpendicularity (which is why statement (2) is insufficient by itself).

Thanks a lot Stuart, I got it.I mised out a point over here.

Quote:
Are lines p (with slope m) and q (with slope n) perpendicular to each other?

1. m + 2 = n
2. m + n = 0

I don't know the answer to this question. I feel both the statements are required to answer the question (when combined the values of m & n are -1 & 1 respectively, which satisfies the perpendicular slope concept). Any contentions?

Statement 1 by itself is not sufficient to make us check whether or not m n = -1.

Same with statement 2.

Combining the two enables us to have m + 2 = -m or m = -1 and hence n = 1 and so m n = -1 is found to be yes, true! So how about C?