Monday, September 2, 2013
Challenge problem of the week
Quantitative comparison:
In the figure, ABC is a right triangle, and PQRS is a square whose area is 396 unit square.
Quantity A Quantity B
The product of the length of AS and the length of RC 395
(A) Quantity A is greater.
(B) Quantity B is greater.
(C) The two quantities are equal.
(D) The relationship cannot be determined from the information given.
Logging you in...Comments by IntenseDebate
exploregre 15p · 603 weeks ago
This is very hard; you might not see this in the exam unless you are expecting to score 170 in quant section.
Lets assume,
angle A=x, angle C=y,
So in triangle ABC, x+y=90
so, angle A=90-y, angle C=90-x
Now in triangle APS, angle APS=90-x=angle C
similarly, Now in triangle CRQ, angle CQR=90-x=angle A
so triangle APS and triangle CRQ are similar.
so, AS/RQ=PS/RC
OR, AS*RC=PS*RQ
now, as pqrs is square, PS=RQ
so, AS*RC=PS*PS=PS^2=396 ( AREA OF SQUARE=396,GIVEN)
so Quantity A is greater!!!
Jodi Weiss · 439 weeks ago