How to find the square of an integer

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GRE Quantitative Reasoning › How to find the square of an integer

Questions 1 - 3
1

Neither x nor y is equal to 0.

xy = 4y/x

Quantity A: x

Quantity B: 2

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

Explanation

Given xy = 4y/x and x and y not 0.

Therefore you are able to divide both sides by 'y' such that:

x = 4/x

Multiply both sides by x:

x2 = 4 or x = +2 or –2.

Because of the fact that x could equal –2, the relationship cannot be determined from the information given.

2

Quantity A: 9

Quantity B: √(25 + 55)

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

Explanation

In order to determine the relationship between Quantity A and Quantity B, let's convert both to square roots. In order to do this, we must square Quantity A so it becomes √81 which is equivalent to 9. Now to Quantity B, we must simplify by adding the two values together (25 + 55) to get √80.

√81 is greater than the √80 because 81 is greater than 80. Thus Quantity A is greater.

3

Quantity A: x^{2}

Quantity B: 399

The relationship cannot be determined from the information given.

Quantity A is greater.

Quantitiy B is greater.

The two quantities are equal.

Explanation

Since \dpi{100} \small x is between 10 and 20, it can be any real number between 100 and 400. Therefore, the relationship cannot be determined since \dpi{100} \small x could fall anywhere between these two limits, including between 399 and 400.

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