Tough GMAT Questions

[Mark D]

I received these questions on a practice exam from mba.com. Haven’t been able to work through the math to get to the answers they listed. Please review and share the secret sauce. Thanks.


1. What is the greatest prime factor of 4^17 - 2^28 ? [Answer: 7]

2. (1/5)^m * (1/4)^18 = 1/(2(10)^35) . Solve for "m". [Answer: 35]

[rhoeta]

=4^14 ((4^3)-1)= 4^14 (63)=4^14 (7*3*3), hence 7

Just break the 10 into 2*5

=10^35/5^n =(4^18)/2*(2^35)
2^35*5^35/5^n =2^36/2^36
5^35/5^n =1
5^35 =5^n
n=35

[Guest]

am having trouble understanding this explanation, would some clarify?

thx

=4^14 ((4^3)-1)= 4^14 (63)=4^14 (7*3*3), hence 7

Just break the 10 into 2*5

=10^35/5^n =(4^18)/2*(2^35)
2^35*5^35/5^n =2^36/2^36
5^35/5^n =1
5^35 =5^n
n=35

[Sudhan]

1)
We need to simplify the factors here:-

4^17-2^28= 4^17-(2^2)*14 (becuase 28= 14*2)
= 4^17- 4^14
= 4^14(4^3-1)
= 4^14(64-1)
= 4^14(63)
Factors of 63= 3*3*7

Here the Greatest factor will be 7

2)

(1/5)^m* (1/4)^18= 1/2(10)^35
solve for m here:-

1/5^m * 1/4^18= 1/2 (5*2)^35 (since 10=5*2)
= 1/2(2^35)*(5^35)
= 1/( 2^36) * 5^35 (2^1=2)
equate the powers of 5 here

5^m = 5^35
when the base is equal , we can equate the powers

hence m=35
Here we are not concerned about 2 ^36 becauase its out of scope in this problem

Hope this helps

[StaceyKoprince]

By "practice exam from mba.com" I assume you mean GMATPrep? Please clarify.

Also, if you would like a response from an instructor, please post the full text of the problem, including all answer choices. Thanks!