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GRE - Quantitative Reasoning - Algebra

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 I’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.

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

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

(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

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