GRE Math : How to evaluate algebraic expressions

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #21 : How To Evaluate Algebraic Expressions

Quantitative Comparison

Quantity A: 

Quantity B: 

Possible Answers:

Quantity B is greater.

Quantity A is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

Correct answer:

The relationship cannot be determined from the information given.

Explanation:

If x = 0, (x – 5)= 25 and (x + 5)2 = 25, so the quantities are equal.

If x = 1, (x – 5)2 = (–4)2 = 16 and (x + 5)= 62 = 36, so B is greater.

This is a contradiction, so the answer cannot be determined.

Example Question #341 : Algebra

Ten years ago, when Molly was born, Ginny was twice as old as Lily. Now Ginny is twice as old as Molly. How old is Lily now? 

Possible Answers:

Correct answer:

Explanation:

If Molly was born 10 years ago, she is now 10 years old. If Ginny is twice Molly's age now, she is 20 years old, which made her 10 years old when Molly was born. If Ginny was 10 years old when Molly was born and was twice as old as Lily, Lily must have been 5 years old. If Lily was 5 years old 10 years ago, she must be 15 years old currently.

Example Question #342 : Algebra

If the average (arithmetic mean) of the above terms is , what is the median?

Possible Answers:

Correct answer:

Explanation:

Since we know the mean is 7, and the number of terms is 5, we can first find the value of x:

((x – 2)+ (x) + (x + 1) + (x + 4) + (x + 7))/5 = (5x + 10)/5 = 7

x = 5

Since the terms are already listed in order, we can simpy plug in x = 5 to the middle value to get 5 + 1 = 6 as the median term. 

Example Question #24 : How To Evaluate Algebraic Expressions

How many square tiles, each with an area of 49 square inches, must be used to completely cover a floor with a width of 98 inches and a length of 49 inches. 

Possible Answers:

98

7

14

2

84

Correct answer:

98

Explanation:

The answer is 98.

If the area of each square tile is 49 then each side of the tile is 7. The width of the floor is 98 so 14 tiles would fit across. The length of the floor is 49 so 7 tiles would fit down.

14 tiles * 7 tiles = 98 tiles total

Example Question #25 : How To Evaluate Algebraic Expressions

Quantitative Comparison

 

A

---

 

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:

The two quantities are equal

Explanation:

Since both values are negative, in both situations the final result of the fraction will be positive regardless of the absolute value sign. Additionally, the definition of the exponent "–1" means the value is becoming its reciprocal. Thus, "x" → "1/x" and "1/y" → "y", equating to y/x.

Example Question #26 : How To Evaluate Algebraic Expressions

Fran has eight more chickens that Jan. If Fran gives two of her chickens to Jan, Fran will have twice as many chickens as Jan. How many chickens does Fran currently have (before giving two away to Jan)?

Possible Answers:

Correct answer:

Explanation:

Set up two different equations:

 and

Note the importance in the second equation of accounting for the exchange of 2 chickens for both quantities: Jan loses the two that she gives to Fran, and Fran gains the two that she receives.

Solve for  by substituting  for \dpi{100} \small j in the second equation:

Solving for  results in .

Example Question #27 : How To Evaluate Algebraic Expressions

Find the algebraic expression to represent the following statement.

The square of  multiplied by , the result has  subtracted from it and the final result divided by .

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem we must go through the statement step by step to determine the correct algebraic expression.

The first part of the problem states "The square of x". Therefore we are certain the the expression contains . Following that, it says "multiplied by three", therefore we simply multiply the square of x by three, obtaining .

 

The statement then says, "the result subtracted by 18". This means that we take whatever we had previously, in this case,  and subtract 18, resulting in .

 

The final part of the statement says "the final result divided by 15". Therefore we once again take what we had previously,  and divide the entire thing by 15. Thus our final expression is .

 

Example Question #28 : How To Evaluate Algebraic Expressions

The difference between two positive integers is . The larger number is  times larger than the smaller number. What is the smaller number?

Possible Answers:

Correct answer:

Explanation:

To solve this problem, we must work step by step through the information given to us.

 

The first part of the problem states "The difference between two positive integers is 9". If we assign variables  and  to the two integers, we can express the statement as . In this expression,  is the smaller variable.

 

The second part of the problem states "The larger number is 4 times larger than the smaller number". Using the same variables we can express this statement as .

 

Plugging in  into the equation obtained from the first part of the statement, , we find  or . Therefore the value of the smaller integer is .

Example Question #29 : How To Evaluate Algebraic Expressions

Compare  and determine which is larger.

:

 

Assume .

Possible Answers:

Correct answer:

Explanation:

To solve this problem, we must simplify each quantity to its simpliest form, then compare the two.

Quantity A: 

Quantity B:

 

After simplifying, we can tell that Quantity A will always be larger than Quantity B when .

Example Question #30 : How To Evaluate Algebraic Expressions

 houses have a total valuation of  in 2014.  In 2015, two of the houses decreased in value by , one of the houses increased in value by  and the rest of the houses remained the same price.

Compare  and determine which is larger.

: The mean value of the houses in 2015.

: The mean value of the houses in 2014.

Possible Answers:

Correct answer:

Explanation:

The mean value of the houses can be determined by summing up all the values of the houses and dividing by the total number of houses. In 2014, the  houses were worth a total of .  This means the mean value is .

 

In 2015, two houses decreased in price by  while one house increased in price by .  This means the net value of the  houses is still .  This means that the mean value of the  houses did not change from 2014-2015 meaning the two quantities are equal.

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