For all positive integers m

[mastevano]

Hello,

I am having trouble understanding this problem:






When I tried to solve the problem, I found each answer separately. In other words, I found box(9) = 27 and box(6)=3 and then multiplied the two to get 81.

What I don't understand is how one would know to multiply 9 and 6 first and find box(54)=27.

Thanks for your help!

[guest]

Mastevano,

I believe you are correct in your approach: box(9) = 27 and box(6)=3 and then multiplied the two to get 81.

But since the answers are in the box form, you must do the conversion again. You can either convert all the answers, or convert 81 backwards.

Let's try converting 81 backwards:
if box(m) = 3m
box (m) = 3m = 81
m = 27 (since 27 is odd, the answer is acceptable)
So box (27) should be our solution.

Also, try the other box:
if box(m) = 1/2m
box(m) = 1/2m = 81
m = 162 (162 is even so the answer is acceptable)
So the answer could also be box (162)

But only box (27) is in the answer choices, so that's the answer. I'm certain box (54) is also incorrect becaues box(54) does NOT equal box(9) x box(6) [try working it out - you'll get 27=81]

[mastevano]

It makes sense now!

[StaceyKoprince]

Thanks, guest, for answering the question! I love to see students helping each other out - if you can explain a problem to someone, then you really know you get it!

[lol!]

I was certain that the answer provided by GMAC was wrong!! LOL!

Thanks for the expln! It was rudimentary! :)

[StaceyKoprince]

You can be pretty much assured that nothing GMAC publishes is wrong. They test all questions on thousands of people before they use them - and then all of the these questions that get published were really used by tens of thousands of people on the real test. Only then do they pick out the best ones and publish them in OG or GMATPrep. So unless someone keys something in incorrectly in putting the software together or typesetting the book... there are no errors. (Well, on their part anyway.)

Don't worry - you're in good company. EVERYbody at some point is convinced that GMAC has the wrong answer on some problem. :)

[shaji]

You can be pretty much assured that nothing GMAC publishes is wrong. They test all questions on thousands of people before they use them - and then all of the these questions that get published were really used by tens of thousands of people on the real test. Only then do they pick out the best ones and publish them in OG or GMATPrep. So unless someone keys something in incorrectly in putting the software together or typesetting the book... there are no errors. (Well, on their part anyway.)

Don't worry - you're in good company. EVERYbody at some point is convinced that GMAC has the wrong answer on some problem. :)

Mathematics is the queen of all sciences and is pretty exact. Its no respector of persons/enities/organisations.

To err is human!!!Forgive Divine!!!

GMAC no doubt is a credible organsation.

[Guest]

Mastevano,

I believe you are correct in your approach: box(9) = 27 and box(6)=3 and then multiplied the two to get 81.

But since the answers are in the box form, you must do the conversion again. You can either convert all the answers, or convert 81 backwards.

Let's try converting 81 backwards:
if box(m) = 3m
box (m) = 3m = 81
m = 27 (since 27 is odd, the answer is acceptable)
So box (27) should be our solution.

Also, try the other box:
if box(m) = 1/2m
box(m) = 1/2m = 81
m = 162 (162 is even so the answer is acceptable)
So the answer could also be box (162)

But only box (27) is in the answer choices, so that's the answer. I'm certain box (54) is also incorrect becaues box(54) does NOT equal box(9) x box(6) [try working it out - you'll get 27=81]

Sorry for rehashing such a rudimentary concept, but I still dont get it. I did the same thing as Mast where I got 81, but I dont completely understand why you have to break down 81 again? I guess Im confused on why we break down 81 again, and when that is done we get 27, why dont we break that down again also?

Thanks for your help!

[rfernandez]

The answer choices are written in this weird "box" format. So box(81) is actually equal to 243. If you want to enter the answer 81, you need to select box(27) which is equivalent to 81.

Rey

[Guest]

i also made the same mistake and put 81...damm gmac is always trying to screw you.

[rfernandez]

They're certainly not going to give points away... It's a good takeaway to bear in mind, though, that the wrong answers are well-conceived. So double check to make sure.

Rey