algebra II qn8

Question

what is y?

1) cube(y)+2y = y +2*sqr(y)
2) sqr(y) = y

Taking statement 1, dividing both sides by y, we get sqr(y) - 2y +1 = 0 => (y-1)^2 = 0=> y-1 = 0 and hence y =1

Taking statement 2, dividing both sides by y, we straight away get y =1, but the OA is given as niether statement is sufficients...could some one please explain

DavidArchuleta · Answer

Hey, never divide both sides for any thing that you are not sure whether or not it could be Zero. In both statements, y=1 or 0

ISBtarget · Answer

thanks for the info

Even otherwise, take statement 1

take y out of left and right handside y ( y^2+2) = y ( 2y+1)

cancel out y on both sides , we get y^2 -2y+1 which is (y-1)^2 = 0 , which is y =1.

could you please explain

scoregmat · Answer

Here it goes..
2) You Cannot divided both sides by y and say y>1 so,
y2 = y
y2-y = 0
y(y-1) = 0
Solution is either y= 0 or y=1

Similarly for condition 1) 
y3 + 2y = y +2(y2)
y3 -2y2 + y = 0 ... taking y as common equation becomes...
y(y2-2y+1) = 0
y = 0 or 
(Y-1)2 = 0

Solution is either y = 0 or y = 1

Both the condition together are not able to provide single value of Y....
Hope this clears your confusion now...

algebra II qn8

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards