Source: Official Guide Revised GRE 1st Ed. Part 6; Set 1; #2

22

In the figure above, squares PQRV and VRST

In the figure above, squares PQRV and VRST have sides of length 6. Quantity A The area of the shaded region Quantity B 36 Quantity A is greater., Quantity B is greater., The two quantities are equal., The relationship cannot be determined from the information given.

2 Explanations

3

Saverio Ungania

Why are you assuming that the rectangle is splitted in half? There is no evidence about it, the question just says "In the figure above, squares PQRV and VRST have sides of lenght 6". But we have no idea whether the line splits in half the rectangle. It could pass through a point near the center, but not necesseraily in the center, since the questions doesn't say anything to us. Do we have to assume this? And why?

May 18, 2015 • Comment

Jonathan , Magoosh Tutor

Hi Saverio,
We know for certain. We have two squares with side of length 6 that share a common side, which is the line that splits the rectangle (RV). Since these are squares, all the sides have length 6. Since QR, RS, PV and VT all must have length 6, we know that the rectangle is split in half.

Jun 10, 2015 • Reply

Cecilia C Hernandez

How we can assume that PS splits the rectangle into two equal triangles, PQS and PTS?

Jul 18, 2015 • Reply

Jonathan , Magoosh Tutor

Hi Cecilia. Please see my response to Saverio above: We have two squares with side of length 6 that share a common side, which is the line that splits the rectangle (RV). Since these are squares, all the sides have length 6. Since QR, RS, PV and VT all must have length 6, we know that the rectangle is split in half. The resulting triangles are both right triangles with smaller sides of 6 and 12, so they must be equal.

Jul 27, 2015 • Reply

2

Gravatar Chris Lele, Magoosh Tutor

Oct 6, 2012 • Comment

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