GMAT Math : GMAT Quantitative Reasoning

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Example Questions

Example Question #5 : Algebra

Whats the value of when x=20 :

6y+7=17+7x

Possible Answers:

Correct answer:

Explanation:

6y+7=17+7x

6y+7=17+7(20)

6y+7=17+140

6y=17+140-7

6y=150

y=25

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Example Question #2 : Algebra

Solve for :

2x+4y=10

Possible Answers:

x=-2y-5

x=2y-5

x=-2y+5

x=2y+5

Correct answer:

x=-2y+5

Explanation:

2x+4y=10

2x=10-4y

$x=\frac{10-4y}{2}$

x=-2y+5

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Example Question #7 : Solving Linear Equations With Two Unknowns

$x^{2}+ y^{2} = 20$

x+ 2y = 10

What is ?

Possible Answers:

y = 8

y = 5

y = 2

y = 4

y = 10

Correct answer:

y = 4

Explanation:

From the second equation:

x+ 2y = 10

x+ 2y - 2y = 10 - 2y

x = 10 - 2y

Substitute into the first, then solve:

$\left ( 10-2y\right )^{2}+ y^{2} = 20$

$10^{2} - 2 \cdot 10 \cdot 2y + \left ( 2y \right )^{2} + y^{2} = 20$

$4y ^{2} + y^{2} - 40y + 100 = 20$

$5 y^{2} - 40y + 100 = 20$

$5 y^{2} - 40y + 100 - 20= 20 - 20$

$5 y^{2} - 40y + 80= 0$

$5 \left ( y^{2} - 8y + 16 \right )= 0$

$5 \left ( y - 4 \right )^{2}= 0$

y - 4 = 0

y = 4

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Example Question #11 : Algebra

Solve the system of equations.

$\dpi{100} \small 4x+3y=7$

$\dpi{100} \small 7x-14y=21$

Possible Answers:

$\dpi{100} \small x=\frac{23}{11}\and\ y=\frac{5}{11}$

$\dpi{100} \small x=\frac{-23}{11}\and\ y=\frac{5}{11}$

$\dpi{100} \small x=\frac{23}{11}\and\ y=\frac{-5}{11}$

x = all real numbers,

y = all real numbers

$\dpi{100} \small x=\frac{-23}{11}\and\ y=\frac{-5}{11}$

Correct answer:

$\dpi{100} \small x=\frac{23}{11}\and\ y=\frac{-5}{11}$

Explanation:

Let's first look at the 2nd equation. All three terms in $\dpi{100} \small 7x-14y=21$ can be divided by 7. Then $\dpi{100} \small x-2y=3$ We can isolate x to get $\dpi{100} \small x=3+2y$

Now let's plug $\dpi{100} \small x=3+2y$ into the 1st equation, $\dpi{100} \small 4x+3y=7:$

$\dpi{100} \small 4\left ( 3+2y \right )+3y=7$

$\dpi{100} \small 12+8y+3y=7$

$\dpi{100} \small 11y=-5$

$\dpi{100} \small y=\frac{-5}{11}$ Now let's plug our y-value into $\dpi{100} \small x=3+2y$ to solve for y:

$\dpi{100} \small x=3+2\left\left ( \frac{-5}{11} \right )=3-\frac{10}{11}=\frac{33}{11}-\frac{10}{11}=\frac{23}{11}$

So $\dpi{100} \small x=\frac{23}{11}\and\ y=\frac{-5}{11}$

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Example Question #12 : Algebra

4x+3y=19

5x+4y = 23

Choose the statement that most accurately describes the system of equations.

Possible Answers:

is positive, is positive.

is negative, is negative.

is negative, is positive.

No unique solution.

is positive, is negative.

Correct answer:

is positive, is negative.

Explanation:

4x+3y=19

5x+4y = 23

Subtract the first equation from the second:

$x+y = 4\Rightarrow y=4-x$

Now we can substitute this into either equation. We'll plug it into the first equation here:

$4x + 3(4-x) = 19\Rightarrow 4x+12-3x = 19\Rightarrow x+12 = 19$

Thus we get x=7 and y=4-(7) = -3 .

Therefore is positive and is negative.

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Example Question #1091 : Gmat Quantitative Reasoning

If 2x + y = 7 and 3x + 2y = 13 ; what is the value of x+y ?

Possible Answers:

Correct answer:

Explanation:

For this problem we can use the elimination method to solve for one of our variables. We do this my multiplying our first equation by -2.

-2(2x+y=7)=-4x-2y=-14

From here we can combine this equation with our second equation given in the question and solve for x.

-4x-2y=-14

+(3x+2y=13)

------------------------------

-x=-1

x=1

Now we plug 1 back into our original equation and solve for y.

3(1)+2y=13

2y=10

y=5

Therefore,

x+y=1+5=6

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Example Question #14 : Algebra

Find the point of intersection of the two lines.

2x+6y=3

x+6y=1

Possible Answers:

(0,0)

(3,2)

None of the other answers

$\left(-\frac{1}{6},2\right)$

(1,1)

Correct answer:

None of the other answers

Explanation:

The correct answer is $\left(2,-\frac{1}{6}\right)$

There are a few ways of solving this. The method I will use is the method of elimination.

2x+6y=3 (Start)

x+6y=1

x+0y=2

x+6y=1 (Multiply the 2nd equation by -1 and add the result to the first equation, combining like terms. Now the top equation simplifies to x=2

Now that we have one of the variables solved for, we can plug x=2 into either of the original equations, and we can get our , Let's use the 2nd equation.

(2)+6y=1

6y=-1

$y=-\frac{1}{6}$

Hence the point of intersection of the two lines is $\left(2,-\frac{1}{6}\right)$ .

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Example Question #42 : Systems Of Equations

Julie has coins, all dimes and quarters. The total value of all her coins is $\$7.25$ . How many dimes and quarters does Julie have?

Possible Answers:

quarters and dimes

Correct answer:

quarters and dimes

Explanation:

Let be the number of dimes Julie has and be the numbers of quarters she has. The number of dimes and the number of quarters add up to coins. The value of all quarters and dimes is $\$7.25$ . We can then write the following system of equations:

x+y=35

0.1x+0.25y=7.25

To use substitution to solve the problem, begin by rearranging the first equation so that is by itself on one side of the equals sign:

x=35-y

Then, we can replace in the second equation with 35-y :

0.1(35-y)+0.25y=7.25

Distribute the 0.1 :

3.5-0.1y+0.25y=7.25

Subtract 3.5 from each side of the equation:

0.15y=3.75

Divide each side of the equation by 0.15 :

y=25

Now, we can insert our value for into the first equation and solve for :

x=35-y=35-25=10

Julie has quarters and dimes.

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Example Question #16 : Algebra

Solve the following system of linear equations:

-3y+x=2

4-y=3x

Possible Answers:

$x=\frac{7}{5},y=-\frac{1}{5}$

$x=\frac{1}{5},y=-\frac{7}{5}$

$x=\frac{7}{5},y=\frac{3}{4}$

$x=-\frac{5}{4},y=\frac{3}{4}$

$x=-\frac{3}{4},y=\frac{5}{4}$

Correct answer:

$x=\frac{7}{5},y=-\frac{1}{5}$

Explanation:

To solve a system of two equations with two unknowns, we first solve one of the equations for one of the variables and then substitute that value into the other equation. This allows us to find a solution for one of the variables, which we then plug back into either equation to find the solution for the other variable:

$-3y+x=2\rightarrow x=3y+2$

Substituting the right side of the rearranged equation into the other equation for , we get:

4-y=3x

4-y=3(3y+2)

Now we can solve this equation for .

4-y=9y+6

$-10y=2\rightarrow y=-\frac{1}{5}$

Now that we know the value of , we can plug that value into the other equation for and solve for :

x=3y+2

$x=3(-\frac{1}{5})+2=-\frac{3}{5}+2=-\frac{3}{5}+\frac{10}{5}=\frac{7}{5}$

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Example Question #1094 : Gmat Quantitative Reasoning

f(x) is a linear equation that passes through the points (-6,4) and (14,6) . What is the slope (m) , and y-intercept (b) of f(x) ?

Possible Answers:

$\small \small \small m=-1.5$

$\small b=-20$

$\small m=\frac{1}{10}$

$\small b=4.6$

$\small m=\frac{-1}{10}$

$\small b=-4.6$

$\small m=-10$

$\small b=9.2$

$\small \small m=4.6$

$\small \small b=\frac{1}{10}$

Correct answer:

$\small m=\frac{1}{10}$

$\small b=4.6$

Explanation:

We're told to find the slope and -intercept of a line that passes through the points (-6,4) and (14,6) . To begin, calculate the slope using the following equation:

$\small m=\frac{y-y'}{x-x'}=\frac{6-4}{14--6}=\frac{2}{20}=\frac{1}{10}$

So now that we have our slope, we need to find our -intercept.

Recall the general form for a linear equation:

$\small y=mx+b$

Rearrange to solve for and use our slope and one of the given points to solve:

$\small \small y-mx=b \rightarrow b=y-mx$

$\small b=6-14*\frac{1}{10}{}=6-1.4=4.6$

So, we have our slope, $\frac{1}{10}$ and our -intercept, 4.6 .

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GMAT Math : GMAT Quantitative Reasoning

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #5 : Algebra

Example Question #2 : Algebra

Example Question #7 : Solving Linear Equations With Two Unknowns

Example Question #11 : Algebra

Example Question #12 : Algebra

Example Question #1091 : Gmat Quantitative Reasoning

Example Question #14 : Algebra

Example Question #42 : Systems Of Equations

Example Question #16 : Algebra

Example Question #1094 : Gmat Quantitative Reasoning

All GMAT Math Resources

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