# Welcome to the LEAP Q&A Forum

## GRE - Quantitative Reasoning - Algebra

LEAP Administrator 4 months ago

### If x =1/y and y =1/(1-x), then y = (more)

If x =1/y and y =1/(1-x), then y =
(A) 2
(B) 1/2
(C) -1/2
(D) -1
(E) -2

Given,

x = 1/y

and y = 1/(1-x)

substituting x in second equation

y = 1 / (1 - 1/y)

y = y/(y - 1)

y2 - y = y

y2 - 2y = 0

y(y - 2) = 0

y = 0 or y = 2

since x = 1/y, y=0 is not possible

thus y = 2

LEAP Administrator 4 months ago

### The total cost of 8 bagels at a bakery is x dollars. At this cost per bagel, which of the following represents the total cost, in dollars, of y bagels? (more)

The total cost of 8 bagels at a bakery is x dollars. At this cost per bagel, which of the following represents the total cost, in dollars, of y bagels?

1. 8/xy

2. 8x/y

3. 8y/x

4. 8xy

5. xy/8

Cost of 8 bagels = x
Cost of 1 bagel = x/8

cost of y bagels = xy/8

LEAP Administrator 6 months ago

### (1-x)/(x-1) = 1/x Quantity A : x Quantity B : -1/2 (more)

(1-x)/(x-1) = 1/x

Quantity A : x
Quantity B : -1/2

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.

(1-x) / (x - 1) = 1/x

- (x - 1) / (x - 1) = 1/x

for x ≠ 1

-1 = 1/x

x = -1 < -1/2

Quantity B is greater

Option B is correct

LEAP Administrator 6 months ago

### If 1+x+x2+x3=60, then the average (arithmetic mean) of x, x2, x3, and x4 is equal to which of the following? (more)

If 1 x x2 x3=60, then the average (arithmetic mean) of x, x2, x3, and x4 is equal to which of the following?

A. 12x
B. 15x
C. 20x
D. 30x
E. 60x

Arithmetic mean of x, x2, x3, and x4 =  (x + x2 + x+ + x4) / 4 = x(1+x+x2+x3)/4

= x*60/4 = x*12

12x

Option A is correct

LEAP Administrator 6 months ago

### x(x-2) / (x-3)(x-4)^2 = 0 (more)

$\frac { x(x-2) }{ (x-3){ (x-4) }^{ 2 } } =\quad 0$

Quantity A: x

Quantity B: -2

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.

The given equation can be written as x(x-2) = 0

either x = 0 or x = 2

in both cases x > -2

hence Quantity A is greater

Option A is correct