Problem Solving

In the figure above, if PQRS is a square and QT = TR, which of the following statements is NOT true?
(A) PT = TS
(B) x = y
(C) u = v
(D) r = y
(E) The area of ΔPQT is equal to the area of ΔSRT.





Answer is D

IMO D.

How did you come up with that answer? Whats the methodology?

First, I don't see it is a square.
Second, I don't know if T is at the middle of QR

So I am not sure with A,B,C,E
But I am sure r=y is wrong because r=v. Read the review of OG and list it, it is a really basic rule.

Tell me if I am wrong with that and if you know this kind of logic is common in the gmat.

IMO D

I think the answer is D as well.

r = v because they are interior angles created when two parallel lines are cut by another line. pepeprepa is right about that, it is a standard geometry rule you'll need on exam day.

Therefore, for r = y, then y = v. If the whole thing is a square y = v when they are both 45 degrees which would only happen when the line that cuts them comes exactly from the other corner (this would create 2 45-45-90 triangles).

Since the cutting line comes from somewhere else, T, then y specifically does not equal v therefore making r never equal to y.

Ans = [D] Hope that helps.

The Answer is D.
Because
The triangles PQT and SRT are congruent (because of ASA condition)
So all other options are true except D.

It clearly says that QT=TR.
So, TR=1/2 QR.
For, r=v
TR should be equal to RS.
But as it is a square, RS = TR = 1/2 QR.

So, r cannot be equal to v.

method is to identify triangle(PQT) and (TRS) as congruent (QT=RS, angQ=angR=90', QT=TR therefore SAS rule applies) this will automatically give us answer D.

for r to be equal to y
TR has to be equal to RS

which is not the case
TR is RS/2