Some basic questions.

[savyasachi_s]

#1 deleted by ron
#1 was a question from gmatfocus, which is a banned source. you can't post gmatfocus questions; please read the rules before you post.

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Q2. If the sequence x1, x2, x3, ..., xn, ... is such that x1 = 3 and xn+1 = 2xn - 1 for n ≥ 1, then x20 - x19 =


A. 2^19
B. 2^20
C. 2^21
D. (2^20) - 1
E. (2^21) - 1

Here I got the right answer, but it took me way more that 2 minutes to get to the answer. Is there a better approach to solving this problem?
The way I solved it is below. It might look simple, but it took me a long time to observe the pattern of 2s being multiplied.

x20 - x19 = 2*(x19 -x18) = 2*2 (x18 -x17).... = 2^(n-2) * 2 = 2^19

Q3.Of the 500 business people surveyed, 78 percent said that they use their laptop computers at home, 65 percent said that they use them in hotels, and 52 percent said that they use them both at home and in hotels. How many of the business people surveyed said that they do not use their laptop computers either at home or in hotels?
A. 45
B. 55
C. 65
D. 95
E. 130

Ans: Here my answer doesn't match with the options given. So I was wondering what is wrong with my approach.
Given Home users = 78. Hotel users = 65 and common users = 52.
So people who use it only at home = 78 - 52 = 26.
People using only at hotel = 65 - 52 = 7.
People using at both places = 52.
So total = 52 + 26 + 7 = 85.
So people not using = 15% of 500 = 75. But that is not an option. Am I doing something wrong here?

[RonPurewal]

again, please read the rules for this folder.

you MUST provide SOURCES for the problems that you post in this folder. otherwise, we can't answer them (so that we don't run the risk of copyright or fair-use violations), and we will have to delete them in short order if you don't supply the source soon.

if the problems are from banned sources, we will, of course, remove them.

sources please?
thanks.

[pratik.munjal]

Ron, this is an official question, and continues to trouble many test takers. Can you please explain how to solve it?

[kritika.singhal1]

Savyasachi,

Didn't you notice, 65-52 =13 and not 7 as you mentioned.

[jnelson0612]

Ron, this is an official question, and continues to trouble many test takers. Can you please explain how to solve it?

pratik, we are not allowed to discuss official questions here, by request of the GMAC.