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ISEE Middle Level Quantitative : Algebraic Concepts

Study concepts, example questions & explanations for ISEE Middle Level Quantitative

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All ISEE Middle Level Quantitative Resources

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Example Questions

Example Question #31 : Equations

Divide 200 by 17. The quotient is ; the remainder is . Which is the greater quantity?

(A)

(B)

Possible Answers:

(A) and (B) are equal

(A) is greater

It is impossible to tell which is greater from the information given

(B) is greater

Correct answer:

(B) is greater

Explanation:

$200 \div 17 = 11 \textrm{ R }13$

A = 11 and B = 13 .

B > A and (B) the greater quantity.

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Example Question #34 : Equations

If y = -7 , then how many integers can be substituted for to make the equation $x^{2} + y^{2} = 0$ a true statement?

Possible Answers:

Zero

One

Two

Infinitely many

It cannot be determined from the information given

Correct answer:

Zero

Explanation:

If y = -7 , the equation can be restated and solved as follows:

$x^{2} + y^{2} = 0$

$x^{2} + (-7)^{2} = 0$

$x^{2} + 49 = 0$

$x^{2} + 49 - 49 = 0 - 49$

$x^{2} = - 49$

However, no integer can be squared to yield a negative result; therefore, there is no solution, and the correct response is "zero."

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Example Question #32 : Equations

How many elements of the set $\left \{ 1, 2, 3, 4, 5 \right \}$ can be substituted for to make the inequality 4y < 15 a true statement?

Possible Answers:

None

Two

Three

One

Four

Correct answer:

Three

Explanation:

4y < 15

$4y \div 4 < 15 \div 4$

$y < 3 \frac{3}{4}$

Three elements of the set—1, 2, and 3—fit this criterion.

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Example Question #33 : Equations

-7K = 91

-6M = 72

Which is greater?

(A)

(B)

Possible Answers:

It is impossible to determine which is greater from the information given

(A) is greater

(B) is greater

(A) and (B) are equal

Correct answer:

(B) is greater

Explanation:

-7K = 91

$-7K\div (-7) = 91 \div (-7)$

K= -13

-6M = 72

$-6M \div (-6) = 72 \div (-6)$

M = -12

13 > 12 , so -12 > -13 .

Therefore M > K , so (B) is greater.

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Example Question #33 : Equations

How many elements of the set $\left \{ -2, -1, 0, 1, 2 \right \}$ can be substituted for to make the inequality -6y > 12 a true statement?

Possible Answers:

One

Four

Five

Two

None

Correct answer:

None

Explanation:

-6y > 12

$-6y \div (-6) < 12 \div (-6)$ (Note that the inequality symbol switches here.)

y < -2

None of the elements of $\left \{ -2, -1, 0, 1, 2 \right \}$ fit this criterion.

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Example Question #37 : Equations

If y = 3 , then how many integers can be substituted for to make the equation $x^{3} + y^{3} = 0$ a true statement?

Possible Answers:

Three

Zero

One

Infinitely many

Two

Correct answer:

One

Explanation:

If y = 3 , then the equation can be rewritten and solved as follows:

$x^{3} + y^{3} = 0$

$x^{3} + 3^{3} = 0$

$x^{3} + 27= 0$

$x^{3} + 27- 27 = 0 - 27$

$x^{3} = - 27$

The only integer that can be substituted for to make this true is x = -3 , so the correct response is "one".

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Example Question #34 : Equations

If a and b are complementary angles, what is the value of a if b is equal to 33 degrees?

Possible Answers:

Correct answer:

Explanation:

Complementary angles add up to 90 degrees. Therefore, a+b=90 .

Given that b is equal to 33 degrees, the equation is:

a+33=90

Next, 33 should be subtracted from each side of the equation.

a=57

Therefore, 57 is the correct answer.

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Example Question #165 : Algebraic Concepts

Angles g and h are supplementary. Angle g is 3 times as big as angle h. What is the value of angle h?

Possible Answers:

135

Correct answer:

Explanation:

If angles g and h are supplementary, then they will add up to 180 degrees.

g+h=180

Given that angle g is 3 times as big as angle h, then:

g=3h

Therefore,

3h+h=180

4h=180

h=45

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Example Question #166 : Algebraic Concepts

Solve for .

3x - 6 = 18

Possible Answers:

Correct answer:

Explanation:

3x - 6 = 18

In order to solve an equation, you first want to get like terms on the same sides: variables should be on one side and whole numbers on the other. To do this, you must add 6 to both sides of the equation.

3x - 6 =18

The equation will then look like this:

3x = 24

In order to solve for , you must make it so that there is only one of the variable . Since the 3 is multiplied times the variable, you must divide by 3 on both sides of the equation to remove it.

$\frac{3x}{3}=\frac{24}{3}$

$x=\frac{24}{3}=8$

The result you are left with is x=8 .

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Example Question #161 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

If x and y are angles that are equal to each other and are also complementary, what is the value of x?

Possible Answers:

Correct answer:

Explanation:

If two angles are complementary, then they add up to 90 degrees.

Therefore, x+y=90 .

Given that x and y are equal to each other, x=y .

Thus, x+x=90 .

2x=90

x=45

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All ISEE Middle Level Quantitative Resources

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ISEE Middle Level Quantitative : Algebraic Concepts

Study concepts, example questions & explanations for ISEE Middle Level Quantitative

All ISEE Middle Level Quantitative Resources

Example Questions

Example Question #31 : Equations

Example Question #34 : Equations

Example Question #32 : Equations

Example Question #33 : Equations

Example Question #33 : Equations

Example Question #37 : Equations

Example Question #34 : Equations

Example Question #165 : Algebraic Concepts

Example Question #166 : Algebraic Concepts

Example Question #161 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

All ISEE Middle Level Quantitative Resources

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