GRE Math : How to find the square of an integer

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #1 : How To Find The Square Of An Integer

Neither x nor y is equal to 0. 

xy = 4y/x

Quantity A: x

Quantity B: 2

Possible Answers:

The two quantities are equal.

The relationship cannot be determined from the information given.

Quantity A is greater.

Quantity B is greater.

Correct answer:

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.

Example Question #2 : How To Find The Square Of An Integer

Quantity A: x^{2}

Quantity B: 399

Possible Answers:

The two quantities are equal.

The relationship cannot be determined from the information given.

Quantity A is greater.

Quantitiy B is greater.

Correct answer:

The relationship cannot be determined from the information given.

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.

Example Question #2 : Other Squaring / Square Roots

Quantity A: 9

Quantity B: √(25 + 55)

Possible Answers:

Quantity B is greater.

The relationship cannot be determined from the information given.

Quantity A is greater.

The two quantities are equal.

Correct answer:

Quantity A is greater.

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.

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