Categoría: GRE

Re: (x + y)(x − y) = 0 xy ≠ 0

sandy wrote:

$$(x + y)(x – y) = 0$$
$$xy \neq 0$$

 Quantity A Quantity B $$\sqrt[6]{\frac{19}{2x^2}}$$ $$\sqrt{\frac{342}{y^2}}$$

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

$$(x + y)(x – y) = 0$$ means either x=y or x=-y or both
since x and y are in the denominator of the fractions, value of 0 for any of them would make the fraction undefined and therefore it is given $$xy \neq 0$$

I am sure ($$\sqrt[6]{\frac{19}{2x^2}}$$) is meant to be ($$6*\sqrt{\frac{19}{2x^2}}$$)

x=y or x=-y or both IMPLIES $$x^2=y^2$$

$$A=\sqrt[6]{\frac{19}{2x^2}}=\sqrt{\frac{36*19}{2x^2}}=\sqrt{\frac{18*19}{y^2}}=\sqrt{\frac{342}{y^2}}=B$$
so equal

C

Re: If A < 0, 10 < B < 30, and 50 < C < 80, what is the relative

Carcass wrote:

If $$A A. \(\frac{1}{A} < \frac{1}{B} < \frac{1}{C}$$

B. $$\frac{1}{A} < \frac{1}{C} < \frac{1}{B}$$

C. $$\frac{1}{C} < \frac{1}{A} < \frac{1}{B}$$

D. $$\frac{1}{C} < \frac{1}{B} < \frac{1}{A}$$

E. $$\frac{1}{B} < \frac{1}{C}< \frac{1}{A}$$

remember the rule
1) if A and B are positive and greater than 1..
A>B means $$\frac{1}{A} < \frac{1}{B}$$

So 1/C < 1/B as C>B
Now A is negative and it’s reciprocal will also be negative and thus 1/A will be the least.
B. $$\frac{1}{A} < \frac{1}{C} < \frac{1}{B}$$

B

A certain standardized test taken by business school applicants demand

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Re: The area of △ABD The area of △BCD

Carcass wrote:

Attachment:

GRE – powerprep The area of △ABD The area of △BCD.jpg

 Quantity A Quantity B The area of $$△ABD$$ The area of $$△BCD$$

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

Explanation:

For the $$△ABD$$ and $$△BCD$$)

AB = BC , i.e. the base of both $$\triangle$$ are equal.

Since both $$\triangle$$ lies within the $$\triangle ADC,$$ therefore the height must be same

Hence the area of $$\triangle ABD$$= area of $$\triangle BCD$$
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When x is divided by 3 the remainder is 2, and when y is divided by 7

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Re: then which of the following are possible values of x?

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Re: If 2x − 3y = 6, then 6y − 4x =

Carcass wrote:

If 2x − 3y = 6, then 6y − 4x =

A. − 12

B. − 6

C. 6

D. 12

E. Cannot be determined

GIVEN: 2x − 3y = 6

We want to determine the value of 6y − 4x

6y − 4x = -4x + 6y
= -2(2x – 3y)
= -2(6)
= -12

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Re: Ray is 2 inches taller than Lin, and Ray is 3 inches taller

Carcass wrote:

Ray is 2 inches taller than Lin, and Ray is 3 inches taller than Sam.

 Quantity A Quantity B The average (arithmetic mean) height of Ray, Lin, and Sam The median height of Ray, Lin, and Sam

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

Let’s write all heights in terms of Ray’s height.

Let R = Ray’s height (in inches)
So, R – 2 = Lin’s height
And R – 3 = Sam’s height

Average height = [R + (R-2) + (R-3)]/3
= [3R – 5]/3
= 3R/3 – 5/3
= R – 5/3

To find the median height, arrange heights in ASCENDING ORDER: R-3, R-2, R
So, the median height = R-2

So, we get:
QUANTITY A: R – 5/3
QUANTITY B: R – 2

Subtract R from both quantities to get:
QUANTITY A: -5/3
QUANTITY B: -2

Since -5/3 is greater than -2, the correct answer is A

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_________________

Brent Hanneson – Creator of greenlighttestprep.com

Re: An empty, cube-shaped swimming pool is filled part way with

sandy wrote:

An empty, cube-shaped swimming pool is filled part way with x cubic feet of water. It is then filled the rest of the way with y cubic feet of chlorine. Which of the following, in feet, expresses the depth of the swimming pool?

A. $$x + y$$
B. $$\frac{x + y}{3}$$
C. $$\sqrt{x + y}$$
D. $$(x + y)^3$$
E. $$\frac{\sqrt[3]{x+y}}{3}$$

Let the sides and also the height be a each, therefore $$V=a^3$$
Volume is also equal to x+y, therefore $$V=a^3=x+y……a=\sqrt[3]{x+y}$$

C is wrongly written, it should be 3rd root.

Maths

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Re: c and d are positive integers.

Carcass wrote:

$$c$$ and $$d$$ are positive integers.

 Quantity A Quantity B $$\frac{c}{d}$$ $$\frac{c+3}{d+3}$$

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

Explanation

We can solve this question using matching operations
Given:
Quantity A: c/d
Quantity B: (c+3)/(d+3)

Since d is POSITIVE, we can safely multiply both quantities by d to get:
Quantity A: c
Quantity B: d(c+3)/(d+3)

Since d is positive, we know that d+3 is POSITIVE. So, can safely multiply both quantities by d+3 to get:
Quantity A: c(d+3)
Quantity B: d(c+3)

Expand both quantities:
Quantity A: cd + 3c
Quantity B: cd + 3d

Subtract cd from both quantities:
Quantity A: 3c
Quantity B: 3d

Divide both quantities by 3:
Quantity A: c
Quantity B: d

Since we aren’t told anything about the relationship between c and d, the correct answer is D

RELATED VIDEO FROM OUR COURSE

_________________

Brent Hanneson – Creator of greenlighttestprep.com

If (2x + 1)(x – 5) = 2 (x^2 – 1), what is the value of x

If $$(2x + 1)(x – 5) = 2 (x^2 – 1)$$, what is the value of x?

A. $$- \frac{1}{3}$$

B. $$- \frac{1}{5}$$

C. $$0$$

D. $$\frac{1}{3}$$

E. $$\frac{1}{2}$$

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c and d are positive integers.

$$c$$ and $$d$$ are positive integers.

 Quantity A Quantity B $$\frac{c}{d}$$ $$\frac{c+3}{d+3}$$

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

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Quant

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If a, b, c, d, and e are integers and the expression (ab^2c^2 )/(d^2)e

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Re: X or Y

Explanation

According to the current diagram, y° is larger than x°. But remember, the figures are not always drawn to scale and you are free to make changes provided you keep the information given as a constant. In this case, the constant is that PS = SR.

So keeping line PR the same, where PS = SR, move Q around to see what happens to x and y:

As you can see, it’s impossible to determine which angle is greater without having more information about point Q.

Hence option D is correct.

Attachments

di new.jpg [ 18.25 KiB | Viewed 7845 times ]

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Sandy
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Re: Calculate cube root

sandy wrote:

$$\sqrt[3]{8 \times 27 \times 64}$$

Useful rule: ∛(xyz) = (∛x)(∛y)(∛z)

So, $$\sqrt[3]{8 \times 27 \times 64}$$ = (∛8)(∛27)(∛64)
= (2)(3)(4)
= 24