GRE Math : How to square a decimal

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Example Questions

Example Question #371 : Arithmetic

Which quantity is greater? When 0<x<1 $\displaystyle 0< x< 1$

Quantity A

x^2 $\displaystyle x^2$

Quantity B

Possible Answers:

The relationship cannot be determined from the information given.

The two quantities are equal.

Quantity B is greater.

Quantity A is greater.

Correct answer:

Quantity B is greater.

Explanation:

X must equal a number between 0 and 1.

If you square any decimal number in this range you will get an answer less than 1. Try $\displaystyle (0.999)^2$= 0.998.

Therefore Quantity B is always larger.

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Example Question #2 : Basic Squaring / Square Roots

Which is greater, when $\small \small \small 0<x<1?$ $\displaystyle \small \small \small 0< x< 1?$

Quantity A

$\small x^2$ $\displaystyle \small x^2$

Quantity B

$\small \frac{x}{2}$ $\displaystyle \small \frac{x}{2}$

Possible Answers:

Quantity A is greater

The two quantities are equal

Quantity B is greater

The relationship cannot be determined from the information given

Correct answer:

The relationship cannot be determined from the information given

Explanation:

When $\small 0<x<1$ $\displaystyle \small 0< x< 1$, $\small x$ $\displaystyle \small x$ must be a decimal. Therefore it will decrease when it is squared. To find this answer we can substitute two values for $\small x$ $\displaystyle \small x$.

$\small x = 0.9$ $\displaystyle \small x = 0.9$ and $\small x = 0.1$ $\displaystyle \small x = 0.1$

When $\small x = 0.9$ $\displaystyle \small x = 0.9$

$\small \small 0.9^2 = 0.81 > \frac{0.9}{2} = 0.45$ $\displaystyle \small \small 0.9^2 = 0.81 > \frac{0.9}{2} = 0.45$

But when $\small x = 0.1$ $\displaystyle \small x = 0.1$

$\small 0.1^2 = 0.01 < \frac{0.1}{2} = 0.05$ $\displaystyle \small 0.1^2 = 0.01 < \frac{0.1}{2} = 0.05$

Therefore we cannot tell which is greater based on the information given.

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Example Question #3 : Basic Squaring / Square Roots

Which is greater, when $\small \small 0<x<1?$ $\displaystyle \small \small 0< x< 1?$

Quantity A

$\small \small x$ $\displaystyle \small \small x$

Quantity B

$\small 2x^2$ $\displaystyle \small 2x^2$

Possible Answers:

Quantity B is greater

Quantity A is greater

The relationship cannot be determined from the information given

The two quantities are equal

Correct answer:

The relationship cannot be determined from the information given

Explanation:

$\small x = 0.9$ $\displaystyle \small x = 0.9$ and $\small x = 0.1$ $\displaystyle \small x = 0.1$

When $\small x = 0.9$ $\displaystyle \small x = 0.9$

$\small \small \small 2\cdot0.9^2 = 1.62 > 0.9$ $\displaystyle \small \small \small 2\cdot0.9^2 = 1.62 > 0.9$

But when $\small x = 0.1$ $\displaystyle \small x = 0.1$

$\small \small 2\cdot0.1^2 = 0.02 < 0.1$ $\displaystyle \small \small 2\cdot0.1^2 = 0.02 < 0.1$

Therefore we cannot tell which is greater based on the information given.

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Example Question #961 : Gre Quantitative Reasoning

Which is greater, when $\small -1<x<0?$ $\displaystyle \small -1< x< 0?$

Quantity A

$\small \left | x\right |$ $\displaystyle \small \left | x\right |$

Quantity B

$\small x^2$ $\displaystyle \small x^2$

Possible Answers:

The relationship cannot be determined from the information given

Quantity B is greater

Quantity A is greater

The two quantities are equal

Correct answer:

Quantity A is greater

Explanation:

When $\small \small -1<x<0$ $\displaystyle \small \small -1< x< 0$, $\small x$ $\displaystyle \small x$ must be a negative decimal. Therefore it will decrease when it is squared and become positive. The first quantity $\small \left | x\right |$ $\displaystyle \small \left | x\right |$ is the distance to 0 from $\small x$ $\displaystyle \small x$, in other words the positive value of $\small x$ $\displaystyle \small x$. The second quantity $\small x^2$ $\displaystyle \small x^2$ will always be positive, but because it is a decimal it will always be less than $\small x$ $\displaystyle \small x$, if $\small x$ $\displaystyle \small x$ was a positive quantity. Since $\small \left | x\right |\equiv x$ $\displaystyle \small \left | x\right |\equiv x$, then $\small \left | x\right |$ $\displaystyle \small \left | x\right |$ wiill always be greater than $\small x^2$ $\displaystyle \small x^2$.

Quantity A is greater.

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Example Question #4 : Basic Squaring / Square Roots

Which is greater, when $\small \small -1<x<0?$ $\displaystyle \small \small -1< x< 0?$

Quantity A

$\small x^2$ $\displaystyle \small x^2$

Quantity B

$\small 1$ $\displaystyle \small 1$

Possible Answers:

The relationship cannot be determined from the information given

Quantity A is greater

The two quantities are equal

Quantity B is greater

Correct answer:

Quantity B is greater

Explanation:

When $\small \small -1<x<0$ $\displaystyle \small \small -1< x< 0$, $\small x$ $\displaystyle \small x$ must be a negative decimal. Therefore it will decrease when it is squared and become positive. Because $\small x$ $\displaystyle \small x$ must be a decimal, $\small x^2$ $\displaystyle \small x^2$ will also be a decimal. Therefore $\small x^2$ $\displaystyle \small x^2$ will never be greater than 1.

Quantity B is greater.

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GRE Math : How to square a decimal

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #371 : Arithmetic

Example Question #2 : Basic Squaring / Square Roots

Example Question #3 : Basic Squaring / Square Roots

Example Question #961 : Gre Quantitative Reasoning

Example Question #4 : Basic Squaring / Square Roots

All GRE Math Resources

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