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ISEE Middle Level Quantitative : Equations

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 #51 : How To Find The Solution To An Equation

4t + 13 = 72

3u + 13 = 54

Which is the greater quantity?

(a)

(b)

Possible Answers:

(b) is the greater quantity

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

(a) and (b) are equal

(a) is the greater quantity

Correct answer:

(a) is the greater quantity

Explanation:

Solving both equations:

4t + 13 = 72

4t + 13 - 13 = 72 - 13

4t = 59

$4t \div 4 = 59 \div 4$

$t = 14 \frac{3}{4}$

3u + 13 = 54

3u + 13- 13 = 54 - 13

3u = 41

$3u \div 3 = 41 \div 3$

$u = 13\frac{2}{3}$

t > u .

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Example Question #171 : Algebraic Concepts

B + (-40 ) = 100 - A

Which is the greater quantity?

(a) A + B

(b) 60

Possible Answers:

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

(a) and (b) are equal

(b) is the greater quantity

(a) is the greater quantity

Correct answer:

(a) is the greater quantity

Explanation:

B + (-40 ) = 100 - A

B + (-40 ) + A + 40 = 100 - A + A + 40

A+ B + (-40 ) + 40 = 100 + 40- A + A

A + B = 140 , which is greater than 60.

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Example Question #53 : How To Find The Solution To An Equation

A + (-30) = B + 50

Evaluate B - A .

Possible Answers:

B - A = 80

B - A = -80

B - A = -20

B - A = 20

Correct answer:

B - A = -80

Explanation:

A + (-30) = B + 50

A + (-30) - A - 50 = B + 50 - A - 50

A - A + (-30) - 50 = B - A + 50 - 50

B - A = (-30) - 50 = - 30 + (-50) = -(30+50) = -80 .

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Example Question #53 : How To Find The Solution To An Equation

m + (-45) = 77

n +45 = - 77

Which is the greater quantity?

(a)

(b)

Possible Answers:

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

(b) is the greater quantity

(a) is the greater quantity

(a) and (b) are equal

Correct answer:

(a) is the greater quantity

Explanation:

m + (-45) = 77

m + (-45) - (-45) = 77 - (-45)

m = 77 + 45 = 122

n +45 = - 77

n +45 - 45 = - 77 - 45

n = - 77 +( - 45) = -(77+45) = -122

m > n

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Example Question #54 : How To Find The Solution To An Equation

Solve for :

$- \frac{1}{4}r - (-3)=34$

Possible Answers:

r = -148

r = 124

r = 148

r = -124

Correct answer:

r = -124

Explanation:

$- \frac{1}{4}r - (-3)=34$

$- \frac{1}{4}r - (-3) + (-3) =34 + (-3)$

$- \frac{1}{4}r =34 -3$

$- \frac{1}{4}r =31$

$- \frac{1}{4}r \div \left ( - \frac{1}{4} \right ) =31 \div \left ( - \frac{1}{4} \right )$

$r =31 \cdot \left ( - 4 \right )$

r = -124

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Example Question #55 : How To Find The Solution To An Equation

Solve the equation:

18 + 8t = 132

Possible Answers:

t = 14.75

t = 14.25

t = 15 .25

t= 15.75

Correct answer:

t = 14.25

Explanation:

To solve to the equation isolate the variable on one side of the equation with all other constants on the other side. To accomplish this perform opposite operations to manipulate the equations.

18 + 8t = 132

First subtract 18 from both sides.

18 + 8t- 18 = 132 - 18

8t = 114

Now divide by 8 on both sides.

$8t \div 8 = 114 \div 8$

t = 14.25

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Example Question #56 : How To Find The Solution To An Equation

A + 25 = -B + 75

Which is the greater quantity?

(a) A + B

(b) A - B

Possible Answers:

(a) and (b) are equal

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

(a) is the greater quantity

(b) is the greater quantity

Correct answer:

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

Explanation:

A + 25 = -B + 75

A + 25 + B - 25 = -B + 75 + B - 25

A + B = 50

However, without further information, we cannot determine whether this is greater than A -B . For example,

A = 25 , B = 25 is consistent with the information, and A -B = 25 - 25 = 0 < 50 .

A = 75, B = - 25 is consistent with the information, and 75 -B = 75 -( - 25 )= 100 >50 .

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Example Question #57 : How To Find The Solution To An Equation

A + (-45) = -30 + B

A + 45= 30 - B

Which is the greater quantity?

(a) A + B

(b) A - B

Possible Answers:

(b) is the greater quantity

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

(a) is the greater quantity

(a) and (b) are equal

Correct answer:

(b) is the greater quantity

Explanation:

It is not necessary to find and to answer this question.

A + (-45) = -30 + B

A + (-45) - B + 45 = -30 + B - B + 45

A - B = -30 + 45 = + (45-30) = 15

A + 45= 30 - B

A + 45+ B - 45 = 30 - B + B - 45

A + B = 30 - 45 = 30 + (-45) = - (45-30 )= -15

A - B > A + B .

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Example Question #58 : Equations

is positive.

A+ B =100

A + C = 200

Which is the greater quantity?

(a)

(b)

Possible Answers:

(a) is the greater quantity

(a) and (b) are equal

(b) is the greater quantity

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

Correct answer:

(b) is the greater quantity

Explanation:

A+ B =100 ,

B = 100 - A

and

$2 B = 2\left (100 - A \right ) = 200 - 2A$

A + C = 200 ,

C= 200 - A

If A > 0 , then, since 1 < 2 ,

A < 2 A

-A > - 2 A

200 -A >200 - 2 A

and

C > 2B .

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Example Question #58 : How To Find The Solution To An Equation

m - (-28) = -57

n - (-27) = -58

Which is the greater quantity?

(a)

(b)

Possible Answers:

(b) is the greater quantity

(a) is the greater quantity

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

(a) and (b) are equal

Correct answer:

(a) and (b) are equal

Explanation:

m - (-28) = -57

m - (-28) + (-28) = -57 + (-28)

m = -(57+28) = -85

n - (-27) = -58

n - (-27) + (-27) = -58 + (-27)

n = -(58+27) = -85

m = n

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All ISEE Middle Level Quantitative Resources

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

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ISEE Middle Level Quantitative : Equations

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

All ISEE Middle Level Quantitative Resources

Example Questions

Example Question #51 : How To Find The Solution To An Equation

Example Question #171 : Algebraic Concepts

Example Question #53 : How To Find The Solution To An Equation

Example Question #53 : How To Find The Solution To An Equation

Example Question #54 : How To Find The Solution To An Equation

Example Question #55 : How To Find The Solution To An Equation

Example Question #56 : How To Find The Solution To An Equation

Example Question #57 : How To Find The Solution To An Equation

Example Question #58 : Equations

Example Question #58 : How To Find The Solution To An Equation

All ISEE Middle Level Quantitative Resources

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