Test 2 problem 35 online

[mww7786]

f the box pictured to the right is a cube, then the difference in length between line segment BC and line segment AB is approximately what fraction of the distance from A to C? (picture a cube to the right)

10%
20%
30%
40%
50%

[dbernst]

mww7786,

two questions:

1. What is the specific source of this problem (what "online test" was this problem drawn from? for legal reason, we must know before we can answer)

2. How are the letters on the cube arranged?

Thanks!
-dan

[StaceyKoprince]

As Dan said, please remember to cite the author. This is another one of ours, from our CAT, so I'm moving it to that folder.

Alternatively, just post questions from our CAT in the appropriate folder (MGMAT CAT Math or MGMAT CAT Verbal) and then you won't have to cite it separately.

You can either describe the diagram or post a screenshot.

[mww7786]

Hey Dan and Stacy and Kim,

The MGMAT resource has been critical to my preparation. I recommend it highly on all the forums I participate in as very very important to solid GMAT prep. Congratulations on gathering together such a useful resource.

Also, I must apologize for not following the protocol earlier. I will certainly get in line.

I really wish we could organize down here in Florida. I know that we're not yet in your foundation, and therefore the PR and Kaplan guys are down here leading us all astray. I really think that Florida, Texas, Georgia would be marketable if you could get the resources together. Andrew is a genius.

Thanks again,
Mark West
850-445-5387

[StaceyKoprince]

I believe we're getting Texas going as I type! Our physical expansion is generally going to be slow, though, as we are highly constrained by our teaching model. Simply put, there aren't very many people who meet our test-taking and teaching requirements - and we're not willing to compromise on our teachers, so that's always going to limit the speed of our growth.

That's why we do hold our virtual live courses, though. I've had people in my classes from all over the world, not just the US. I know it sounds like it couldn't be as good as a real classroom - frankly, I thought that, too, when I first joined the company! But once I actually started observing classes and then teaching via the web conferencing platform myself, I realized that it is really an elegant solution. Roughly half of my students tell me, by the end of the course, that they actually prefer it now to a regular classroom! And the rest usually say it's about the same as learning in a regular class. (We ask them about this on the end-of-course survey.)

So there is another classroom solution if you live someplace where we don't yet have an office! :)

[DennaMueller]

I am also having trouble with this question, which was also mentioned here: http://www.manhattangmat.com/forums/viewtopic.php?f=32&t=2886&p=9883&hilit=If+the+box+pictured#p9883:

If the box pictured to the right is a cube, then the difference in length between line segment BC and line segment AB is approximately what fraction of the distance from A to C?
10%
20%
30%
40%
50%



The correct answer according to the green checks and red x's is C:30%, which matches my answer of 33%. The answer explanation says the correct answer is 80% and the letter is B.

This is the answer explanation:

Let x be the length of an edge of the cube. We can find the length of BC by first finding the length of CD. CD must be x since it is the hypotenuse of a 45-45-90 triangle with legs of length x.

Using the Pythagorean theorem, BC can be calculated:

AB = CD = x, so BC = x.
Thus, we need to determine what fraction x is of x. The approximate values are 1.4x and 1.7x. our answer is 1.4x/1.7x, which is 82%, or closest to 80%.

The correct answer is B.

This is what I did and why I think the answer is C:30%.

AC=5 (I made up a number)
BC= 5*1.7(cubed root of 3)
AB= 5*1.4(squared root of 2)

BC-AB=8.5-1.5
BC-AB=1.5

Then I answered the question "the difference in length between line segment BC and line segment AB is approximately what fraction of the distance from A to C" by dividing 5 (AC) by 1.5 (BC-AB).

[StaceyKoprince]

Hmm. It looks like the problem was changed but the solution wasn't updated to match. I'll let our curriculum director know ASAP.

So, let's see. I like your approach, but I'd like to tweak it a little bit. Note that I don't multiply out the 1.4 and 1.7 unless I have to. I never do math unless it's required, and that's particularly true when I'm rounding, because I want to hold off on introducing error as long as I can. :)

If AC =5, then:
AB = 5*RT2 (or 5*1.4)
BC = 5*RT3 (or 5*1.7)

Difference between AB and BC = BC - AB = 5*RT3 - 5*RT2
pull a 5 out front: 5(RT3-RT2) = 5(1.7-1.4) = 5(0.3) Okay, I finally introduce the error here by using 1.7 and 1.4 for my roots, but note that I'm not compounding that error by multiplying each by 5 in an approximate way!

Distance from A to C = AC = 5

Difference / distance = 5(0.3)/5 = 0.3 or 30%. You've got it!

[JohnniewalesA987]

Based on this Box Length question. I thought a cube is constructed from a square and the rule is that when given the diagonal of a square, use the 45-45-90 ratio (Manhattan Prep Gmat, Geometry 6th edition pg 65), but in these solution, I see the 30-60-90 ratio being used. Please what is the correct rule. also the explanation of the solution is doesnt seem coherent with the diagram drawn. (sorry I dont know how to import the diagram.)


[/size]

Hmm. It looks like the problem was changed but the solution wasn't updated to match. I'll let our curriculum director know ASAP.

So, let's see. I like your approach, but I'd like to tweak it a little bit. Note that I don't multiply out the 1.4 and 1.7 unless I have to. I never do math unless it's required, and that's particularly true when I'm rounding, because I want to hold off on introducing error as long as I can.

If AC =5, then:
AB = 5*RT2 (or 5*1.4)
BC = 5*RT3 (or 5*1.7)

Difference between AB and BC = BC - AB = 5*RT3 - 5*RT2
pull a 5 out front: 5(RT3-RT2) = 5(1.7-1.4) = 5(0.3) Okay, I finally introduce the error here by using 1.7 and 1.4 for my roots, but note that I'm not compounding that error by multiplying each by 5 in an approximate way!

Distance from A to C = AC = 5

Difference / distance = 5(0.3)/5 = 0.3 or 30%. You've got it!

[RonPurewal]

the √3 here comes from the pythagorean theorem.
a^2 + b^2 = c^2
with a = 1 and b = √2
... you'll get c = √3. work it out.

the point, of course, is that the number √3 doesn't ONLY appear in the 30º-60º-90º situation.
that's one situation in which it occurs, but there are certainly others.

[RonPurewal]

...and, to have any more discussion of this problem, we really, really, REALLY need a picture posted here.

any further posts without the diagram will be deleted.
thank you.