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ISEE Middle Level Quantitative : How to find the solution to an equation

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

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All ISEE Middle Level Quantitative Resources

6 Diagnostic Tests 110 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #21 : Equations

5x = 35

3y = 24

Which is the greater quantity?

(A)

(B)

Possible Answers:

(A) is greater

(A) and (B) are equal

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

(B) is greater

Correct answer:

(B) is greater

Explanation:

5x = 35

$5x \div 5 = 35 \div 5$

x=7

3y = 24

$3y \div 3 = 24 \div 3$

y = 8

y > x , so (B) is greater.

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Example Question #22 : Equations

$\frac{2}{3} a = 20$

$\frac{3}{5} b = 24$

Which is greater?

(A)

(B)

Possible Answers:

(B) is greater

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

(A) and (B) are equal

(A) is greater

Correct answer:

(B) is greater

Explanation:

$\frac{2}{3} a = 20$

$\frac{3}{2} \cdot \frac{2}{3} a =\frac{3}{2} \cdot 20$

$a = \frac{60}{2} = 30$

$\frac{3}{5} b = 24$

$\frac{5}{3}\cdot \frac{3}{5} b =\frac{5}{3}\cdot 24$

$b =\frac{120}{3} = 40$

b > a , so (B) is the greater quantity.

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Example Question #21 : Equations

How many elements of the set $\left \{ 1, 2, 3, 4, 5 \right \}$ can be substituted for to make the inequality y +8.6 < 3.3 a true statement?

Possible Answers:

One

Two

None

Four

Three

Correct answer:

None

Explanation:

y +8.6 < 3.3

y +8.6 - 8.6 < 3.3 - 8.6

y < 3.3 - 8.6

$y < -\left ( 8.6-3.3 \right )$

y < -5.3

None of choices fit this criterion, so the correct answer is none.

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Example Question #21 : How To Find The Solution To An Equation

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

Four

Five

Two

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 #25 : Equations

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

Possible Answers:

Two

One

It cannot be determined from the information given

Zero

Infinitely many

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 #26 : 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:

One

Two

Three

Zero

Six

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 #27 : 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:

Two

Infinitely many

It cannot be determined from the information given

Zero

One

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 #28 : 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:

Five

Two

One

Three

Four

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 #29 : Equations

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

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

Which is the greater quantity?

(A)

(B)

Possible Answers:

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

(A) is greater

(A) and (B) are equal

(B) is greater

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 #22 : How To Find The Solution To An Equation

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

Possible Answers:

Four

One

Zero

Infinitely many

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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All ISEE Middle Level Quantitative Resources

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ISEE Middle Level Quantitative : How to find the solution to an equation

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

All ISEE Middle Level Quantitative Resources

Example Questions

Example Question #21 : Equations

Example Question #22 : Equations

Example Question #21 : Equations

Example Question #21 : How To Find The Solution To An Equation

Example Question #25 : Equations

Example Question #26 : Equations

Example Question #27 : Equations

Example Question #28 : Equations

Example Question #29 : Equations

Example Question #22 : How To Find The Solution To An Equation

All ISEE Middle Level Quantitative Resources

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