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ISEE Middle Level Quantitative : ISEE Middle Level (grades 7-8) Quantitative Reasoning

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 #22 : Equations

How many elements of the set $\left \{ -2, -1, 0, 1, 2 \right \}$ can be substituted for to make the inequality $-9y \geq 18$ a true statement?

Possible Answers:

None

Five

Two

Four

One

Correct answer:

One

Explanation:

$-9y \geq 18$

$-9y \div (-9) \leq 18\div (-9)$ (Note that the inequality symbol switches here)

$y\leq -2$

Of the elements of $\left \{ -2, -1, 0, 1, 2 \right \}$ , only fits this criterion.

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Example Question #23 : Equations

If y = 4 , then how many integers can be substituted for to make the equation 4xy = 0 a true statement?

Possible Answers:

It cannot be determined from the information given

Two

Infinitely many

One

Zero

Correct answer:

One

Explanation:

If y = 4 , the equation can be rewritten and solved as follows:

4xy = 0

$4x \cdot 4 = 0$

16x = 0

$16x \div 16 = 0 \div 16$

x = 0

This is the only number that makes this statement true, so the correct choice is "one".

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Example Question #24 : Equations

If x = -8 , then how many integers can be substituted for to make the equation $x^{2} + y^{3} = 0$ a true statement?

Possible Answers:

Three

Two

Zero

Six

One

Correct answer:

One

Explanation:

If x = -8 , then the equation can be rewritten and solved as follows:

$x^{2} + y^{3} = 0$

$(-8)^{2} + y^{3} = 0$

$64 + y^{3} = 0$

$64 + y^{3} -64 = 0-64$

$y^{3} = -64$

The only integer that can be cubed to yield the result is , so the correct response is "one".

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Example Question #25 : Equations

If y = 12 , then how many integers can be substituted for to make the equation $x^{2} - y^{2} = 0$ a true statement?

Possible Answers:

One

Zero

Two

Infinitely many

It cannot be determined from the information given

Correct answer:

Two

Explanation:

If y = 12 , the equation can be restated and solved as follows:

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

$x^{2} - 12^{2} = 0$

$x^{2} -144 = 0$

$x^{2} -144 + 144 = 0 + 144$

$x^{2} = 144$

Both x = 12 and x = -12 make this true, so both make the original statement true. "Two" is the correct choice.

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Example Question #26 : Equations

How many elements of the set $\left \{ -2, -1, 0, 1, 2 \right \}$ can be substituted for to make the inequality $y + 3\frac{1}{2} < 2 \frac{1}{4}$ a true statement?

Possible Answers:

Four

Five

One

Two

Three

Correct answer:

One

Explanation:

$y + 3\frac{1}{2} < 2 \frac{1}{4}$

$y + 3\frac{1}{2} - 3\frac{1}{2} < 2 \frac{1}{4} - 3\frac{1}{2}$

$y < 2 \frac{1}{4} - 3\frac{1}{2}$

$y < -\left ( 3\frac{1}{2} - 2 \frac{1}{4} \right )$

$y <- 1 \frac{1}{4}$

Of the elements of the set $\left \{ -2, -1, 0, 1, 2 \right \}$ , only fits this criterion, making "one" the correct choice.

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Example Question #27 : Equations

$\frac{c}{-6 } = 25$

$\frac{d}{-9} = 20$

Which is the greater quantity?

(A)

(B)

Possible Answers:

(A) and (B) are equal

(B) is greater

(A) is greater

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

Correct answer:

(A) is greater

Explanation:

$\frac{c}{-6 } = 25$

$\frac{c}{-6 }\times (-6) = 25 \times (-6)$

c= -150

$\frac{d}{-9} = 20$

$\frac{d}{-9}\times (-9) = 20 \times (-9)$

d = -180

Since 150 < 180 , -150 > -180 .

c > d , so (A) is greater.

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Example Question #28 : Equations

If x = 0 , then how many integers can be substituted for to make the equation 9xy = 0 a true statement?

Possible Answers:

Infinitely many

Four

Zero

One

Two

Correct answer:

Infinitely many

Explanation:

If x = 0 , this can be rewritten as

9xy = 0

$9 \cdot 0 \cdot y =0$

0 y =0

However, since zero multiplied by any number yields a product of zero, this is a true statement for all values of . This makes "infinitely msny" correct.

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Example Question #31 : Equations

4A + 30 = 76 - 4B

Evaluate A + B .

Possible Answers:

$11 \frac{1}{2}$

$26 \frac{1}{2}$

$-26 \frac{1}{2}$

It is impossible to evaluate A + B from the information given

$-11 \frac{1}{2}$

Correct answer:

$11 \frac{1}{2}$

Explanation:

We will not be able to solve for the values of and ; instead, we need to group them together by reorganizing the equation.

4A + 30 = 76 - 4B

Start by adding and subtracting on each side. This will allow both variables to be on the left and both whole numbers to be on the right.

4A + 30 + 4B - 30 = 76 - 4B + 4B - 30

4A + 4B = 76 - 30

4A + 4B = 46

can be factored out of the left side.

$4\left ( A + B \right )= 46$

Divide both sides by .

$4\left ( A + B \right ) \div 4 = 46\div 4$

$A + B = 11 \frac{1}{2}$

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Example Question #151 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Divide 1,000 by 30. The quotient is ; the remainder is . Which is the greater quantity?

(A)

(B)

Possible Answers:

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

(A) is greater

(B) is greater

(A) and (B) are equal

Correct answer:

(A) is greater

Explanation:

First, divide:

$1,000 \div 30 = 33 \textrm{ R } 10$

Q = 33 and R = 10 , so Q > R .

(A) is greater.

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Example Question #154 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

A + 9 = B - 7

Evaluate A + B .

Possible Answers:

{2}

It is impossible to evaluate A + B from the information given

Correct answer:

It is impossible to evaluate A + B from the information given

Explanation:

We cannot solve for and on their own. Instead, we need to reorganize the equation to find A + B .

A + 9 = B - 7

A+9-B-9=B-7-B-9

A-B=-7-9

It quickly becomes clear that we cannot solve for A + B with certainty.

If A = 2 and B = 18 , then

A + 9 = B - 7 , since

2 + 9 = 18 - 7 = 11

This makes A + B = 2 + 18= 20

If A = 3 and B = 19 , then

A + 9 = B - 7 , since

3 + 9 = 19 - 7 = 12

This makes A + B = 3+ 19 = 22

Therefore, A + B cannot be evaluated with certainty.

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All ISEE Middle Level Quantitative Resources

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ISEE Middle Level Quantitative : ISEE Middle Level (grades 7-8) Quantitative Reasoning

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

All ISEE Middle Level Quantitative Resources

Example Questions

Example Question #22 : Equations

Example Question #23 : Equations

Example Question #24 : Equations

Example Question #25 : Equations

Example Question #26 : Equations

Example Question #27 : Equations

Example Question #28 : Equations

Example Question #31 : Equations

Example Question #151 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Example Question #154 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

All ISEE Middle Level Quantitative Resources

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