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ISEE Upper Level Math : Algebraic Concepts

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All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #21 : Equations

Consider the following system: x-y=5 and 2x+y=4 . What is the sum of and ?

Possible Answers:

-1

-2

Correct answer:

Explanation:

We first need to line up the equations and solve for . If we add the equations together we get:

x-y=5

+ 2x+y=4

_______________

3 x=9

From this, we have x=3 . Now we plug into either equation to find that y=-2 . Thus, x+y= 3+(-2)= 1 .

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Example Question #21 : Equations

$x=\frac{1}{3}$ ; $y= \frac{1}{2}$

Find the value of 2x+3y .

Possible Answers:

13/6

1/2

2/3

2/5

Correct answer:

13/6

Explanation:

When plugging in the values for and , we find that the answer is 13/6 :

$2(\frac{1}{3})+3(\frac{1}{2})=\frac{2}{3}+\frac{3}{2}=\frac{13}{6}$

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Example Question #31 : How To Work With Percentages

A class has 25 students. If 60% of them are boys, how many students are girls?

Possible Answers:

Correct answer:

Explanation:

We know that 40% of the class are girls because 60% are boys. To express 40% as a fraction of the 25 total students, we set up a proportion to find the number of girls in the class.

$\frac{40}{100} = \frac{x}{25}$

$\frac{2}{5}=\frac{x}{25}$

5x=50

x=10

When solving for , we find that there are 10 girls in the class.

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Example Question #2 : How To Do Work Problems

Machine A can produce 4 books in 2 days. Machine B can produce 20 books in 4 days. How many books can machines A and B, working together, produce in 40 days?

Possible Answers:

280

120

200

960

Correct answer:

280

Explanation:

Through simplification, we can see that machine A produces 2 books a day and that machine B produces 5 books a day. If we multily each by 40 days and add them together, we find that together they can produce 280 books in 40 days:

$(2+5)\times 40=7\times 40=280$

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Example Question #1 : How To Add And Subtract Fractions

Adam has 3 siblings. When his mother bakes a cake, each of the 4 children is given ¼ of the cake. Adam only finished 1/3 of his share of cake. If the original cake had 12 slices, how many slices did Adam eat?

Possible Answers:

Correct answer:

Explanation:

Each of the children gets 1/4 of the cake. Taking 1/4 of 12 shows that each child gets 3 slices. If Adam finishes 1/3 of his share, then he has eaten one out of the 3 slices.

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Example Question #21 : Algebraic Concepts

Solve for :

$\frac{1}{3}x-14=7$

Possible Answers:

Correct answer:

Explanation:

We first add 14 to both sides to get by itself. This leaves us with $\frac{1}{3}x=21$ . Divide both sides by 1/3 to see that the answer is x=63.

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Example Question #22 : Algebraic Concepts

Solve for :

$\frac{x}{3}+22=45$

Possible Answers:

Correct answer:

Explanation:

Subtract 22 from both sides, then multiply by 3 to solve for :

x+66=135

x=69

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Example Question #23 : Algebraic Concepts

What percent of 60 is 45?

Possible Answers:

75%

80%

25%

50%

45%

Correct answer:

75%

Explanation:

We need to set up a proportion to find out what percent of 60 is 45. When solving the proportion, we find that the answer is 75%.

$\frac{x}{100}=\frac{45}{60}$

$\frac{x}{100}=\frac{3}{4}$

x=75

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Example Question #28 : Algebraic Concepts

Solve the set of equations

3x+4y=-5

2x-y=4

Possible Answers:

x=-1;y=-2

x=1;y=-2

x=-1;y=2

x=1;y=2

Correct answer:

x=1;y=-2

Explanation:

3x+4y=-5

2x-y=4

Solve the second equation for y:

y=2x-4

Substitute into the first equation:

3x+4(2x-4)=-5

3x+8x-16=-5

11x-16+16=-5+16

11x=11

x=1

Substitute into the first equation:

3(1)+4y=-5

Solve for y:

3-3+4y=-5-3

4y=-8

y=-2

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Example Question #29 : Algebraic Concepts

Solve for .

4x+8=-4

Possible Answers:

x=-3

x=-6

x=6

x=3

Correct answer:

x=-3

Explanation:

4x+8=-4

4x+8-8=-4-8

4x=-12

$\frac{4x}{4}=\frac{-12}{4}$

x=-3

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All ISEE Upper Level Math Resources

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ISEE Upper Level Math : Algebraic Concepts

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

Example Question #21 : Equations

Example Question #21 : Equations

Example Question #31 : How To Work With Percentages

Example Question #2 : How To Do Work Problems

Example Question #1 : How To Add And Subtract Fractions

Example Question #21 : Algebraic Concepts

Example Question #22 : Algebraic Concepts

Example Question #23 : Algebraic Concepts

Example Question #28 : Algebraic Concepts

Example Question #29 : Algebraic Concepts

All ISEE Upper Level Math Resources

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