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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.

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? 

Be the first person to answer the question!

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