Line p lies on a coordinate plane. What is the area of the region boun

Question

Line p lies on a coordinate plane. What is the area of the region bounded by the x-axis, the y-axis and line p?

(1) The slope of line p is −5/3.

(2) The y-intercept of line p is 10.

Kudos for a correct  solution .

santorasantu · Accepted Answer

Let the equation of the line be y=mx+c. Area of triangle = 1/2*x-intercept*y-intercept

from 1- m = -5/3, no info on the intercept, x intercept = 3c/5, y-intercept = c- can be anything NSF
from 2- y intercept = 10, so line passes through (0,10). X - intercept is not known -NSF

combined, c= 10 = y-intercept, x-intercept = 3c/5 = 6
area = 1/2*10*6 = 30.
 Answer : c?

chetan2u · Answer

ans C.. both statements reqd
 first gives the slope and second gives with help of statement 1 value of x and y

eddyki · Answer

since its y=mx+c for the line, we need m and c.

(1) -> gives us m
(2) -> gives us c.

we got all information to determine the area.

Its  C

DesiGmat · Answer

Here we go...

We need atleast two points to locate a line in the coordinate plane.

let line p : y = mx + c

St1: The slope of line p is −5/3.
 m = -5/3
 y = -5/3x + c -------> 3y = c - 5x ---(1)

Clearly not sufficient

St2: The y-intercept of line p is 10.
 one point is (0,10)
 No idea about the second point.

Not sufficient

Combining: 
Substitute (0,10) in (1)

3*10 = c ----> C = 30

eq of line -----> 3y = 30 - 5x

Two points are ----
(0,10) and (6,0)
We can calculate the area.
Check the figure attached

option C is correct

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

The correct response is (C). The region described will form a right triangle. To find the area of a right triangle we must have the base and the height. The “height” is the y-intercept, which is given to us in the second statement.

The “base” in this case will be the length of the x-intercept. If we know the equation for line p, we could plug in y = 0 to find the x-intercept. The only way to get the equation of a line is to know the slope, which is given to us by the first statement. Combined, the statements are sufficient.

y = mx + b y = -5/3x + 10

The height is 10.

0 = -5/3x + 10 -10 = -5/3x -30 = -5x 6 = x

The base is 6. The area of the triangle = ½ * 10 * 6 = 30.

rhine29388 · Answer

from statement 1 we get only slope of the intersecting line insufficient
from statement 2 we get only y - intercept of the line insufficient
combining both statements
we need both slope of the line and its y - intercept to actually get the equation of line.
base = 6 and height = 10
area = 1/2 * base * height = 1/2 * 6 * 10 = 30 sq units
so correct answer C

Line p lies on a coordinate plane. What is the area of the region boun

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GMAT Data Sufficiency (DS) Questions

Line p lies on a coordinate plane. What is the area of the region boun

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