k2 wrote:I took the GMAT prep exam and got 700 but I did get stumped by some easy questions and from looking at the answers still cant figure out how they got there so any help would be appreciated:
what is the greatest prime factor of 4^17- 2^28?
a)2
b)3
c)5
d)7
e)11
Five pieces of wood have an average (arithmetic mean) of length of 124 cm and a median length of 140 cm. what is the max possible length, in com, of the shortest piece of wood?
a) 90
b) 100
c) 110
d) 130
e) 140
1) 4^17 - 2^28 = (2^2)^17 -2^28
=2^34 - 2^28
=2^28.2^6 - 2^28
=2^28(2^6-1)
=2^28(63)
Greatest prime factor of 2^28 is 2, and of 63 is 7.
So D
2) Can be done by substituting answer choices. Start with C
110+ _ + 140 + _ + _ = 124.5 = 620
3 pieces must add up to 620 - 250 = 370
2nd piece can be between 110 and 140 (both inclusive).
If 2nd piece is 110, then one of the other two pieces will be less than 140. So 1st piece must be less 110
Choose B
100 + _ + 140 + _ + _ = 620
or 3 pieces add up to 380. If 2nd piece is 100, the other two pieces can be 140.
So option B.
Am I correct? This was very tricky and Im still not very confident with my answer
