First let us assume a value for X.
x = 3.So ,2x+1 = 7.Atmost the student can select 3 books from 7 books.
There are 3 cases

1 book selected = no.of ways = 7c1 = 7
2 books selected = no.of ways = 7c2 = 21
3 books selected = no.of ways = 7c3 = 35

total no.of ways = 63.So the value of x = 3.

1)
THE PEAKS OF A MOUNTAIN RANGE, acting like rocks in a streambed , produce ripples in the air flowing over them; the resulting flow pattern, with crests and troughs that remain stationary although the air that forms them is moving rapidly, is known as "standing waves".

Above sentence as written is correct. It contains THEM twice, first them refers to Peaks, I could understand that. but second them here refers 'Crests and troughs'.

My confusion is why second them doesnot refer - Peaks. I can understand that second them will not refer to "rocks" or "ripples" because they are not used as subjects in the sentence.

Or in general when there are several nouns behind a pronoun, how do we decide pronoun refers to which noun in the sentence?

2)
About AWA Section - WHICH ESSAY COMES first on gmat test - ISSUE or ARGUMENT.

Pls help ...

1. In the 1980's the rate of increase of the minority population of the United States was nearly twice as fast as the 1970's.
(A) twice as fast as
(B) twice as fast as it was in
(C) twice what it was in
(D) two times faster than that of
(E) two times greater than

2. Most recovering heroin addicts seek to be free of drug dependency and others' prejudicial treatment as well.

(A) of drug dependency and others' prejudicial treatment as well.
(B) both of drug dependency and also of prejudicial treatment.
(C) both of drug dependency and also from prejudicial treatment.
(D) both of drug dependency but also from prejudicial treatment.
(E) both of drug dependency and of prejudicial treatment as well.

Here is another one..

The peaks of a mountain range, acting like rocks in a streambed, produce ripples in the air flowing over them; the resulting flow pattern, with crests and troughs that remain stationary although the air that forms them is moving rapidly, are known as "standing waves."

(A) crests and troughs that remain stationary although the air that forms them is moving rapidly, are
(B) crests and troughs that remain stationary although they are formed by rapidly moving air, are
(C) crests and troughs that remain stationary although the air that forms them is moving rapidly, is
(D) stationary crests and troughs although the air that forms them is moving rapidly, are
(E) stationary crests and troughs although they are formed by rapidly moving air, is

Please explain!!

Help in another sitter...

If p and q are consecutive natural nos (in increasing order), then which of the following is true?
a. q^2

p
c. (q+1)^2 > p^2
d (p+2)^3 < q^3

If i am not wrong, natural nos are positive nos starting from 1. In that case option b and c, both seem to satisfy.

However the OA is option C.

Am i missing out on something.

2. In a leveraged buyout, investors borrow huge sums of money to buy companies, hoping to pay off the debt by using the company's earnings and to profit richly by the later resale of the companies or their divisions.

A. by using the company's earnings and to profit
B. by using the companies' earnings and by profiting
C. using the companies' earnings and profiting
D. with the company's earnings, profiting
E. with the companies' earnings and to profit

1. That the new managing editor rose from the publications soft news sections to a leadership position is more of a landmark in the industry than her being a woman.
A. her being a woman
B. being a woman is
C. her womanhood
D. that she was a woman
E. that she is a woman