Data Sufficiency

serendipiteez wrote:

In the diagram above, what is the value of y?

(1) x = 5

(2) a = b

Answer B

Can anyone point me to more examples of understanding this property of the triangle? I am struggling to understand how we can establish side y just by knowing that a and b is equal.

srcc25anu wrote:St1: X = 5
Y can be any length from 12 <= Y <= 20 (using triangle property that 3rd side must be less than sum of other 2 sides and greater than difference between other 2 sides)
Hence Insufficient

St2: a = b
Triangles CBD and ABC are similar as:
An. C is common
An CBA = An CAB
and since 2 angles in the traingles are equal, the third angle (An CDB and An CBA) must also be equal.

AC / BC = AB / BD = BC / CD or y / 16 = 9 / y
y^2 = 16 * 9 = 144
y = 12
Sufficient

Hence B

An CBA = An CAB

lunarpower wrote:hey, i wrote this problem!

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gmattesttaker2, i'm with you here -- i actually have pretty severe dyslexia, so i don't stand a chance of slogging through all those three-letter angles.

instead, you should do what srcc25anu did above, and draw a picture with the matching angles between the two triangles. (kudos to srcc25anu, by the way, for drawing an awesome picture -- and in full color, too!)

in that picture, we can see that ...
* y corresponds to 9 (since both are across from the brown angle marked "x")
* 16 corresponds to y (since both are across from the blue angle)
... and that's enough to set up the proportion.

macattack wrote:how do we establish the ration of the sides in similar triangles: ie why did we do AC/BC= etc.... thxxx

anuprajan5 wrote:

macattack wrote:how do we establish the ration of the sides in similar triangles: ie why did we do AC/BC= etc.... thxxx

Hey,

Well the rule is that if all angles are equal in 2 triangles, then they are similar trinagles and then the corresponding sides are in a ratio.

Regards
Anup