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## GRE - Quantitative Reasoning - Inequalities

### If 0 < y < x, then which of the following is a possible value of (more)

If 0 < y < x, then which of the following is a possible value of

$\frac { 27x+ 23y }{ 3x+ 2y }$

I. 8.7
II. 9.2
III. 10.8

A) I only
B) II only
C) III only
D) I and II only
E) II and III only

$\frac { 27x\quad +\quad 23y }{ 3x\quad +\quad 2y } \\ \\ \frac { 27x\quad +\quad 18x\quad +\quad 5x }{ 3x\quad +\quad 2y } \\ \\ \frac { 27x\quad +\quad 18x }{ 3x\quad +\quad 2y } +\quad \frac { 5x }{ 3x\quad +\quad 2y } \\ \\ 9\quad +\quad positive\quad number\\ \\ \\ \\$

the given expression is > 9

E is correct

### r, s, and t are three consecutive odd integers such that r < s < t. (more)

r, s, and t are three consecutive odd integers such that r < s < t.

Quantity A : r s 1
Quantity B : s t − 1

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Since r, s, t are consecutive odd integers and r<s<t

s = r + 2

and t = r + 4

r + s + 1 = r + r + 2 + 1 = 2r + 3

s + t - 1 = r + 2 + r + 4 - 1 = 2r + 5

Quantity B is greater

Option B is correct

### If x<0, which of the following represents a positive number? (more)

If x<0, which of the following represents a positive number?

A) x/|x|
B) |x|/x
C) x|x|
D) -x|x|
E) x|x|

Given x < 0

=> |x| > 0

A) x/|x| = negative / positive = negative

B) |x| / x = positive / negative = negative

C) x|x| = negative * positive = negative

D) -x|x| = - negative* positive = -negative = positive ........... Correct

Option D is correct