In the diagram below, what is the length of the line segment AC?

Question

(1) The coordinates of P and Q are (0, 6) and (2, 0), respectively.
(2) The length of the line segment AB is 2.

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2017-07-26_0944.png [ 7.01 KiB | Viewed 7880 times ]

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Official Answer

C

jedit · Answer

It should be  C

Before we solve this, consider that this diagram may not be drawn to scale as is the case with many GMAT questions.

Statement 1: Insufficient

It gives us nothing about the projections  PA  and  QC . It does however give us the slope of the line at  -3 .

Statement 2: Insufficient

This gives us no information about point the line  PQ .

Statement 1 + 2: Sufficient

Since we have a fixed slope and angles of the triangles, if we slide the line  AB  down where it meets P, this would not change the dimensions of the triangle as we have kept the length  AB  same.

Now, we can find the point of intersection of two lines  AC  and  BC  by setting  x = 2  (This may be hard to digest but note that we have slid the line  AB  down to the point  P  on Y axis. So draw a horizontal line at P that goes moves right to the tune of 2).

y = mx + c

y = -3*2 + 6  -- (we already know y intersect is 6).

y = 0

This means  C  point is actually the same as  Q . (moving 2 right makes y = 0, same coordinates as  Q ) Hence,

AC = PQ = \sqrt{2^2 + 6^2}

Shobhit7 · Answer

Ans C:
St. 1: Provides us with the slope of line AC = line PQ = -3, using Coordinates of P and Q.
And, Slope = Rise/Run = BC/AB = -3

St. 2: gives AB=2

Using St 1+2: BC=6 and Hence, we can calculate AC using Pythagoras.

TheMechanic · Answer

Using both the statement, we get the new figure as attached. It's easy to get the solution from it. Hence C. AC =  \sqrt{40}  or  2\sqrt{10}

anu8787 · Answer

I am getting C. POQ and ABC are similar. From st1 we get all the sides of POQ and from st2 we get one side of ABC, hence, we can find all other sides.

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Debashis Roy · Answer

Bunuel   VeritasKarishma   chetan2u 
Cant we say that the 2 small triangles(one in the 2nd quadrant and the other in the 4th quad) are similar to the traingle OPQ...since they have the same angles ....?

In the diagram below, what is the length of the line segment AC?

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GMAT Data Sufficiency (DS) Questions

In the diagram below, what is the length of the line segment AC?

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