Data Sufficiency

In a triangle ACB, if
a) angle ACB is a right angle
b) CE intersects AB
c) and CB = 5

what is the length of side AB?

(1) CE is perpendicular to AB

(2) AE = EB

OA is C But I am getting A

Could anyone please explain?

Thanks!

Juggernaut_86 wrote:In a triangle ACB, if
a) angle ACB is a right angle
b) CE intersects AB
c) and CB = 5

what is the length of side AB?

(1) CE is perpendicular to AB

(2) AE = EB

OA is C But I am getting A

Could anyone please explain?

Thanks!

It's Answer is C!

Only by using two statements, you'll be able to calculate the Side AB for the triangle.

Statement 1 tells us that CE bisects the Hypotenuse, therefore BE=AE, we have two congruent triangles
As BC=5, we can use the 45:45:90 rule and find out the length of AB, which is, 5*sqrt(2). Sufficient

Statement 2 tells us the same thing. If BE=AE, that means CE is perpendicular to AB. Sufficient

This is incorrect.

First, note that there is nothing that tells us that E is on the line segment AB. We just know that CE intersects AB. This doesn't actually affect the answer though.

(1) CE is perpendicular to AB

Even if E is on AB, this does NOT mean that AE = BE. This just means what it says, which is that CE and AB intersect at a right angle. If you draw a 5-12-13 right triangle, and draw a line CE that is perpendicular to the hypotenuse, you will see that this does not split AB into equal parts. Statement 1 is insufficient.

(2) AE = EB

Without known anything about CE, this fact alone tells us nothing about AB. It just tells us that E happens to be its midpoint.

Only when we combine the statements can we conclude that ACB is a 45-45-90 triangle, which allows us to find AB.

Yes, Answer: C

gmatboost wrote:This is incorrect.

First, note that there is nothing that tells us that E is on the line segment AB. We just know that CE intersects AB. This doesn't actually affect the answer though.

(1) CE is perpendicular to AB

Even if E is on AB, this does NOT mean that AE = BE. This just means what it says, which is that CE and AB intersect at a right angle. If you draw a 5-12-13 right triangle, and draw a line CE that is perpendicular to the hypotenuse, you will see that this does not split AB into equal parts. Statement 1 is insufficient.

(2) AE = EB

Without known anything about CE, this fact alone tells us nothing about AB. It just tells us that E happens to be its midpoint.

Only when we combine the statements can we conclude that ACB is a 45-45-90 triangle, which allows us to find AB.

Only when we combine the statements can we conclude that ACB is a 45-45-90 triangle, which allows us to find AB.
HOW CAN WE SAY that ACB IS 45-90-45 triangle ?? bcos we don know if EC=EB

please help

Assuming E is the midpoint of AB, consider triangles AEC and BEC:

AE = EB
Both triangles share side CE
Angles AEC and BEC are both right angles
That means that the hypotenuses of the triangles are equal: AC = CB

That is enough for us to know that ACB is 45-45-90

We could go a step further to answer your specific question:
Since ACB = 90
and angle ACE = angle BCE it must be the case that angle ACE = angle BCE = 45

This makes triangle ACE and BCE both 45-45-90 triangles.

1947 wrote:
HOW CAN WE SAY that ACB IS 45-90-45 triangle ?? bcos we don know if EC=EB

please help

Hi- you can see the attached doc to clear your doubt.

Hi sakett,

You are correct in proving that but bcos of limited time available we need to understand that

since CE is common side and AEC=CEB=90 there can be no other way but AC=CB

Thanks again !!

1947 wrote:Hi sakett,

You are correct in proving that but bcos of limited time available we need to understand that

since CE is common side and AEC=CEB=90 there can be no other way but AC=CB

Thanks again !!

Well I was pressing the quote button and pressed Thank

Anyways, Dude I know this from my school days-- .. I was trying to clear your doubt because you asked the question in your previous post..