SAT Question of the Week #1 Solutions:

by Oren Lahav

Here’s the solutions to SAT Sample Question of the Week #1!

This question was sent via the SAT Prep group newsletter, which also contains weekly tips and SAT Prep suggestions. To subscribe, join this community.

Hello everyone! If you’ve missed the last couple of newsletters or just didn’t open them, we’re sending out a weekly super-challenging SAT question of the week each Monday, with the solution posted on Thursday. These questions are a level above the tough SAT ones, and they don’t come with choice options either. This means that if you can solve these, you’re pretty much ready to do well on your SATs! This week we had a math question, but get ready for a hard reading problem next week.

This week’s question was…

I’ve got a cool rectangle called ABCD, like the one in the picture above. Point E is the midpoint of side BC. The (green) area of quadrilateral ABED is given by the formula 6A ^ 2-5A-6=0 . What’s the area of rectangle ABCD?

And here’s your answer:

First of all, let’s solve out quadratic equation to find the area of ABED:
6A ^ 2-5A-6=0
6A ^ 2-9A+4A-6=0
3A(2A-3)+2(2A-3)=0
(3A+2)(2A-3)=0

Thus A is either 3A+2=0 , i.e. $A=\frac{ -2}{3}$ , or 2A -3=0 and $A=\frac{3}{2}$ . Clearly, A represents area so it can’t be negative, and so our only answer is $A=\frac{3}{2}$ .

Now, take a look at the picture. If you draw an imaginary line perpendicular to BC through point E, you’ll find that the picture is split into two equal rectangles (we know they’re equal because we’re given that BE=EC), one of which is halved by the line ED. It’s easy to see how $A_{ABED}=\frac{3A_{ABCD}}{4}$ . But we already know the area of ABED, so:
$\frac{3}{2}=\frac{3A_{ABCD}}{4}$
$A_{ABCD}=\frac{3* 4}{2 * 3}=2$

And so the answer is that the area of ABCD is 2 squared units.

Got the answer? Great!

Didn’t get the right answer? It’s ok, at least now you know what to do!

Wait up for next week’s question of the week coming up Monday, and a newsletter each Thursday.

Ask The Experts

All time most popular tags

4 Comments

Vote

Current Rating: 0; Rate Up; Rate Down

Link

Krista – Mon, 02 Jun 2008 19:58:04 -0000

Great job guys! Another shoutout goes to souradeep for getting the correct answer the day the question was posted! Check out Question #2 to get the English side of your SAT brain motoring!

Flag as Inappropriate

Reply to This

Vote

Current Rating: 0; Rate Up; Rate Down

Link

Oren Lahav – Mon, 02 Jun 2008 13:57:40 -0000

Thanks koolsohini and diptesh, you are absolutely right about my mistake. The lesson has now been corrected to reflect the correct answer.
This shows you how important watching the little plus and minus signs can be!

Flag as Inappropriate

Reply to This

Vote

Current Rating: 1; Rate Up; Rate Down

Link

diptesh – Sat, 31 May 2008 11:59:18 -0000

the fourth step in the quad. eq. solving is wrong. If it would have been done correctly, the answer should have been 2, which, i think, is the right answer!

Flag as Inappropriate

Reply to This