If perpendicular lines m and n intersect at (0,b) in the

Question

If perpendicular lines m and n intersect at (0,b) in the standard (x,y) plane, what is the value of b?

(1) The slope of the line m is -1/2

(2) The point (-1,0) is on the line n

BrentGMATPrepNow · Accepted Answer

Given : Perpendicular lines m and n intersect at (0,b)

Target question :    What is the value of b?

Statement 1 : The slope of the line m is -1/2  
Since line n is PERPENDICULAR to line m, we know that line n has slope 2
However, we can raise and lower the two lines so that the value of b is different. 
To see what I mean, here are two possible cases: 
 https://i.imgur.com/GUcDkmD.png 
 https://i.imgur.com/VP086TI.png 
As you can see, with each case, we get a different  value of b . 
Since we cannot answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : The point (-1,0) is on the line n 
So, we know that the lines are perpendicular AND line n goes through the point (-1, 0)
However, since we don't know the SLOPES of the two lines, the value of b can change. 
To see what I mean, here are two possible cases: 
 https://i.imgur.com/GSaA3Yl.png 
 https://i.imgur.com/RTnZ5zv.png 
As you can see, with each case, we get a different  value of b.  
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
Statement 1 tells us that line m has slope -1/2 and line n has slope 2
Statement 2 tells us that line n passes through (-1,0)
These two pieces of information, LOCK line n into just ONE POSSIBLE line
In fact, this also means the y-intercept (0, b) is also LOCKED in. 
We get: 
 https://i.imgur.com/YMdWqvM.png 
This also means that line m is also LOCKED in.
 https://i.imgur.com/rGweWLD.png

Since both lines are now locked in, there is only one possible value of b. 
Are we going to bother to actually find the value of b? 
No, that would be a waste of valuable time. We need only recognize that there is ONLY ONE possible pair of lines that satisfy the two statements, which means we COULD find the value of b 
Since we COULD answer the  target question  with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

mau5 · Answer

From F.S 1 , all we know is that the slope of the line n is 2. Clearly Insufficient.

From F.S 2, we know a point on the line n, but don't know the slope.Insufficient.

Taking both together, we know that slope of line  n = \frac{(b-0)}{(0-(-1)}  = b. And given that the slope is 2. Thus, b=2. Sufficient.

C.

pradeepss · Answer

To find b we need equation of line.
1. gives us equation of line m but we do not know x intercept so not sufficient.
2. we cannot find the equation of line n so not sufficient.

1&2 we know slope of m we can get slope of n (inverse negative) and can find equation of line n. which can give us b.

Answer: C

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If perpendicular lines m and n intersect at (0,b) in the standard (x,y) plane, what is the value of b?

(1) The slope of the line m is -1/2

(2) The point (-1,0) is on the line n
 
In the original condition, for the line, there are 2 variables(the slope and the standard y plane). Since there are 2 lines, there should be 4 variables. Also, the two lines perpendicularly meet and multiplication of the slope is -1, which makes 1 equation. In order to match with the number of euqations, you need 3 more equations. For 1) 1 equations, for 2) 1 equation, which is likely to make E the answer. In 1) & 2), the slope if line m is -1/2 and the slope of line n should be 2. So, b=2 is derived from (b-0/0-(-1))=2, which is unique and sufficient. Therefore, the answer is C.

 For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

Ferrarif1286 · Answer

1) slope of m is -1/2; however, there are infinite number of lines that can have slope of -1/2 and cross the y-axis at x=0. NS

2) (-1,0) is on line n. However, you don't know what is the slope of n; n can slope upwards or downwards to satisfy (0,b) since b can be negative or positive number.

1+2) slope of m is -1/2. Since m and n are perpendicular, that means n has slope of 2. Given n has the point (-1,0) with a slope of 2, you can find out where it crosses the y-axis. C

Kritisood · Answer

Let equation of the two lines be

line n: y=nx+a ---1
line m: y=mx+c ---2

given they intersect at (0,b). Hence, (0,b) satisfies equation of both lines;
putting (0,b) in equation 1 we get b=a ; hence to find b we need to find value of a

statement one  tells us m =-1/2 and therefore n = 2 as they are perpendicular to each other -- insufficient as it doesnt give us value of b

statement two  tells us the point (-1,0) is on the line n 
putting (-1,0) in eq 1 we get n=a
but we dont know the value of n

combining both  we know n=2 and n=a=b therefore b =2

Priya2912 · Answer

statement 1:
slope of m=-1/2 so slope of n=2 
this does not help to find out about the value of b.
so insufficient

statement 2:
we cannot find value of b alone with this as well.

combining both statements:
we know slope of n=2 from statement1 and (-1,0) lie on line n 
so equation of line n is
(y-y1)=n(x-x1)
y-0=2(x+1)
y=2x+2

we know (0,b) is also on line n, replacing the values in the equation we get
b=2(0) + 2
b=2
hence sufficient

Answer is C

Abulikabuli · Answer

Find value of b.
1) We don’t know sign of b.
but still line equation of m can be written as y= -(1/2)x + b
and euation of n is y=2x + b …(logic slope of perpendiculars form a product of -1)
Plug in (0,b) in each case you get b=b. So Insuf.

2) I can find slope of n as b. (rise over run) My equation for n will be y=bx + b
Plug in -1,0 you get 0=0 Insuf.

Combine,
y=2x+b … plug in (-1,0)… you get b=2
C both are suff.

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