# Welcome to the LEAP Q&A Forum

## GRE - Quantitative Reasoning - Algebra

Sahanawaz Khan 2 months ago

### A quant question (more)

QID : 61 - If x + (1/x) = 2, then what is the value of x64 + x121?

Options:
1) 0
2) 1
3) 2
4) – 2

Answer is Option 1) 0

But How?

x+(1/x)=2 x^2-2x+1=0 (x-1)(x-1)=0 x=1 X=1; therefore 1*64 + 1*121 =64+121=185 or Iâ€™m not sure what the question means. In the expression x64 + x121, are the numbers supposed to be exponents? If so, we could evaluate easily: 1^64 + 1^121 = 1+1 = 2.

LEAP Administrator 8 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 8 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 10 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 10 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