GRE Math : Algebra

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13 Diagnostic Tests 452 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #431 : Algebra

For all values of x, f(x) = 7x² – 3, and for all values of y, g(y) = 2y + 9. What is g(f(x))?

Possible Answers:

14y² + 3

14x² – 3

7y² – 3

2x + 9

14x² + 3

Correct answer:

14x² + 3

Explanation:

The inner function f(x) is like our y-value that we plug into g(y).

g(f(x)) = 2(7x² – 3) + 9 = 14x² – 6 + 9 = 14x² + 3.

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Example Question #432 : Algebra

Find f(6)

$f(x)=|x^{2}+4x-127|$

Possible Answers:

Correct answer:

Explanation:

Simply plug 6 into the equation and don't forget the absolute value at the end.

=36+24-127=-67

absolute value = 67

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Example Question #433 : Algebra

An outpost has the supplies to last 2 people for 14 days. How many days will the supplies last for 7 people?

Possible Answers:

$\dpi{100} \small 5$

$\dpi{100} \small 7$

$\dpi{100} \small 4$

$\dpi{100} \small 9$

$\dpi{100} \small 10$

Correct answer:

$\dpi{100} \small 4$

Explanation:

Supplies are used at the rate of $\dpi{100} \small \frac{Supplies}{Days\times People}$ .

Since the total amount of supplies is the same in either case, $\dpi{100} \small \frac{1}{14\times 2}=\frac{1}{7\times \ (\&hash;\ of\ days)}$ .

Solve for days to find that the supplies will last for 4 days.

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Example Question #434 : Algebra

Worker $\dpi{100} \small A$ can make a trinket in 4 hours, Worker $\dpi{100} \small B$ can make a trinket in 2 hours. When they work together, how long will it take them to make a trinket?

Possible Answers:

$\dpi{100} \small \frac{1}{2}\ hour$

$\dpi{100} \small 6\ hours$

$\dpi{100} \small \ 1 \frac{1}{2}\ hours$

$\dpi{100} \small \ 1 \frac{1}{3}\ hours$

$\dpi{100} \small 3\ hours$

Correct answer:

$\dpi{100} \small \ 1 \frac{1}{3}\ hours$

Explanation:

The rates are what needs to be added. Rate $\dpi{100} \small A$ is $\dpi{100} \small \frac{1}{4}$ , or one trinket every 4 hours. Rate $\dpi{100} \small B$ is $\dpi{100} \small \frac{1}{2}$ , one per two hours.

$\dpi{100} \small \frac{1}{4}+ \frac{1}{2}=\frac{3}{4}$ , their combined rate in trinkets per hour.

Now invert the equation to get back to hours per trinket, which is what the question asks for: $\dpi{100} \small \frac{4}{3}\ or \ 1 \frac{1}{3}$

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Example Question #2682 : Act Math

$a\ \mho \ b = a(b+1)-3$

Quantity A Quantity B

$1\ \mho\ 1$ $2\ \mho\ 0$

Possible Answers:

Quantity A and Quantity B are equal

Quantity A is greater

The relationship cannot be determined from the information given.

Quantity B is greater

Correct answer:

Quantity A and Quantity B are equal

Explanation:

Since $a\ \mho \ b = a(b+1)-3$ , then we have that

$1\ \mho \ 1=1(1+1)-3=-1$

and

$2\ \mho \ 0=2(0+1)-3=-1$ .

Thus, the two quantities are equal.

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Example Question #435 : Algebra

If the average of two numbers is $\dpi{100} \small 3y$ and one of the numbers is $\dpi{100} \small y+z$ , what is the other number, in terms of $\dpi{100} \small y$ and $\dpi{100} \small z$ ?

Possible Answers:

$\dpi{100} \small 4y-z$

$\dpi{100} \small 3y+z$

$\dpi{100} \small 5y+z$

$\dpi{100} \small 5y-z$

$\dpi{100} \small y+z$

Correct answer:

$\dpi{100} \small 5y-z$

Explanation:

The average is the sum of the terms divided by the number of terms. Here you have $\dpi{100} \small y+z$ and the other number which you can call $\dpi{100} \small x$ . The average of $\dpi{100} \small x$ and $\dpi{100} \small y+z$ is $\dpi{100} \small 3y$ . So $\dpi{100} \small 3y=\frac{(x+y+z)}{2}$

Multiply both sides by 2.

Solve for $\dpi{100} \small x=5y-z$ .

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Example Question #436 : Algebra

Alice is twice as old as Tom, but four years ago, she was three years older than Tom is now. How old is Tom now?

Possible Answers:

$\dpi{100} \small 9$

$\dpi{100} \small 3$

$\dpi{100} \small 21$

$\dpi{100} \small 7$

$\dpi{100} \small 13$

Correct answer:

$\dpi{100} \small 7$

Explanation:

The qustion can be broken into two equations with two unknows, Alice age $\dpi{100} \small (A)$ and Tom's age $\dpi{100} \small (T)$ .

$\dpi{100} \small A=2T$

$\dpi{100} \small A-4=T+3$

$\dpi{100} \small 2T-4=T+3$

$\dpi{100} \small T=7$

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Example Question #437 : Algebra

A jet goes from City 1 to City 2 at an average speed of 600 miles per hour, and returns along the same path at an average speed if 300 miles per hour. What is the average speed, in miles per hour, for the trip?

Possible Answers:

450miles/hour

500miles/hour

400miles/hour

350miles/hour

300miles/hour

Correct answer:

400miles/hour

Explanation:

Chose a number for the distance between City 1 and 2; 1800 works well, as it is a multiple of 600 and 300.

Now, find the time for each trip, the total distance, and the total time.

$t_1=\frac{d_1}{v_1}=\frac{1800}{600}=3$

$t_2=\frac{d_2}{v_2}=\frac{1800}{300}=6$

$total\ t=t_1+t_2=3+6=9$

$total\ d=d_1+d_2=1800+1800=3600$

Now we can find the average speed by dividing the total distance by the total time.

$average speed = \frac{total distance}{total time} = \frac{3600 miles}{9 hours} = 400 miles/hour$

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Example Question #438 : Algebra

$f(x)=3x^{2}-5$

g(x)=9-2x

Find f(g(5)) .

Possible Answers:

131

Correct answer:

Explanation:

Plug 5 into g(x) first:

g(5)=9-2(5)

=-1

Now, plug this answer into f(x) :

$f(-1)=3(-1)^{2}-5$

=3-5

=-2

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Example Question #439 : Algebra

If f(x) = 3x + 7 and g(x) = x^2 - 12 , what is f(g(x)) ?

Possible Answers:

3x^3 - 29

9x^2 - 29

3x^2 - 29

9x^3 + 29

3x^2 + 29

Correct answer:

3x^2 - 29

Explanation:

Plug g(x) into f(x) as if it is just a variable. This gives f(g(x)) = 3(x²– 12) + 7.

Distribute the 3: 3x²– 36 + 7 = 3x²– 29

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GRE Math : Algebra

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #431 : Algebra

Example Question #432 : Algebra

Example Question #433 : Algebra

Example Question #434 : Algebra

Example Question #2682 : Act Math

Example Question #435 : Algebra

Example Question #436 : Algebra

Example Question #437 : Algebra

Example Question #438 : Algebra

Example Question #439 : Algebra

All GRE Math Resources

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