2 gmat prep 2 questions

[JDesai01]

1. (sqroot(9 + sqroot(80)) + sqroot(9 - sqroot(80)))^2 = ?

2. What is the greatest prime factor of 4^17 - 2^28?

Thank you

[JDesai01]

Figured out the first one..

[JDesai01]

And now got the 2nd one.. sorry for the bother. Thanks

[mkingsly]

Hi,

Can you post the answer pls?
I am getting 20 for the question1 and (2^28).(3^2).7 for question2.

Thanks,
Kingsly.

[JDesai01]

1. 20
2. 7

[karthikeyan.sivanantham]

guys,
Can you please post the solution, will be much appreciated.

Thanks,
karthik

[VP_RedSoxFan]

Here's my unsolicited help on number 2 since I think it is such a classic GMAT problem. Since no one asked for help, feel free to tell me to shut up .

4^17 - 2^28 = (2^2)^17 - 2^28 = 2^34 - 2^28 from here, factor out a 2^28 leaving you with:

2^28 * (2^6 - 1)

Since we know the 2^28 portion just really represents 28 factors of 2, we know that those are not the highest prime factors of this product. If we solve for 2^6 - 1, we get 63 whose prime factors are 3, 3, 7.

7 is therefore the greatest prime factor of this number (the other prime factors are 3, 3, and 28 2's).

[LSUKnowIt]

2^28 * (2^6 - 1)

I understand where the 2^6 comes from but can someone please explain to me where the -1 comes from????

Thanks

[uncbeers]

If you search there are really good explanations of this question but I will try to help you.

4^17 = (2^2)^17 = 2^34

2^34 - 2^28 = Factor from here!

2^28 * (2^6 - 1) (If you were to multiply this out it goes right back to the form above)

Does this help?

[LSUKnowIt]

I appriciate the help but i still dont get it.

34-28 is 6 so I think that's where the 6 comes from but that -1 is throwing me off still. It's just not clicking for me for some reason

[LSUKnowIt]

I appriciate the help but i still dont get it.

34-28 is 6 so I think that's where the 6 comes from but that -1 is throwing me off still. It's just not clicking for me for some reason

[nyparis1]

Could someone pls advise on the first Q?
1. (sqroot(9 + sqroot(80)) + sqroot(9 - sqroot(80)))^2 = ?

Thanks

[uncbeers]

LSU I sent you a PM with a few more examples and steps in it.

nyparis- there are some really good examples of that problem being solved in other threads. The answer can get quite long if all steps are written out so my advce is to do a search for '(sqroot(9 + sqroot(80))' or something similar.

EDIT: Here is one of those threads: https://www.beatthegmat.com/sq-roots-t12808.html

[LifetimesofSC]

I too am lost at the -1.

I would like some examples regarding that step.

Thanks