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Help with 2 PS Questions

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by ellochewy » Wed Sep 28, 2011 10:35 pm
I had difficulty solving these two PS problems that I found on GMATPrep.
The first one, I know has to have a short cut, I just don't know what it is.
For the second one, I have no idea what it's asking.
The correct answer is the choice that has a box around it.

Can you help explain the second one is asking in addition to how to solve it?

Thanks very much!
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by Anurag@Gurome » Wed Sep 28, 2011 10:44 pm
4^17 = (2^2)^17 = 2^34
2^28 cannot be factorized further.
So, 2^34 - 2^28 = 2^28(2^6 - 1) = 2^28(64 - 1) = 2^28 * 63
= 2^28 * 3^2 * 7

So, he greatest prime factor is 7.

The correct answer is D.
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by shankar.ashwin » Wed Sep 28, 2011 10:44 pm
I first question asks you lastest prime factor of 4^17 - 2^28

4^17 = 2^34

Now, 2^34-2^28 = 2^28(2^6-1)

= 2^28(64-1)
= 2^28(9*7)

From this you can say 7 is the greatest prime factor.
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by shankar.ashwin » Wed Sep 28, 2011 10:47 pm
For equal No. of cheese and fruit kinds, you can either have 1 of each variety or 2 of each (cheese and fruit)

1 of each : 2C1*6C1 = 12
2 of each : 2C2*6C2 = 15

Total : 27
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by Anurag@Gurome » Wed Sep 28, 2011 10:54 pm
A dessert platter should contain same number of types of cheese and fruits, so a desert can contain:

I. Two types of cheese 2 types of fruits implies 6C2 * 2C2 = 15 * 1 = 15

II. 1 type of cheese 1 type of fruits implies 6C1 * 2C1 = 6 * 2 = 12

I and II implies, 15 + 12 = 27

The correct answer is E.
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