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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 #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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Example Question #61 : Equations

Solve for :

- 0.05 t + (-7) = -44

Possible Answers:

t = 1,020

t = - 740

t = - 1,020

t = 740

Correct answer:

t = 740

Explanation:

Apply the properties of equality to both sides of the equation as follows in order to isolate on the left side, keeping in mind the rules for signed integer arithmetic:

- 0.05 t + (-7) = -44

- 0.05 t + (-7) - (-7) = -44 - (-7)

- 0.05 t = -44+7

- 0.05 t = -(44-7)

- 0.05 t = -37

$- 0.05 t \div (- 0.05) = -37 \div (- 0.05)$

$t = 37 \div 0.05$

Move the decimal points two places right in each of the two numbers, then divide:

$t = 3,700 \div 5$

t = 740

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Example Question #62 : Equations

- 0.04 t = 0.005

- 0.05 u= 0.004

Which is the greater quantity?

(a)

(b)

Possible Answers:

(a) and (b) are equal

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

(a) is the greater quantity

(b) is the greater quantity

Correct answer:

(b) is the greater quantity

Explanation:

Isolate on one side of the first equation by dividing both sides by the coefficient of :

- 0.04 t = 0.005

$- 0.04 t \div (- 0.04) = 0.005 \div (- 0.04)$

$t = - \left ( 0.005 \div 0.04 \right )$

Divide by moving the decimal points right two places in order to make the divisor an integer:

$t = - \left ( 0.5 \div4 \right )$

t = -0.125

Similarly:

- 0.05 u= 0.004

$- 0.05 u\div (- 0.05 ) = 0.004 \div (- 0.05 )$

$u=-( 0.004 \div 0.05 )$

$u= -( 0. 4 \div 5 )$

u= - 0.08

0.08 < 0.125 , so

-0.08 >- 0.125 ;

that is, u > t .

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Example Question #62 : Equations

is a positive number; is the additive inverse of .

Which is the greater quantity?

(a) 7a + 7b

(b) 7ab

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:

(b) is the greater quantity

Explanation:

If is the additive inverse of , then, by definition,

a+ b = 0 .

Therefore, after distribution,

$7a + 7b = 7(a+b) = 7 \cdot 0 = 0$ .

If is a positive number, then its additive inverse, , must be negative. Therefore, , as the product of two numbers of unlike sign, is negative. Multiply this by the positive number 7 and the result is also negative, so

7ab < 0 ,

and

7(a+b) > 7ab .

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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 #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

Example Question #61 : Equations

Example Question #62 : Equations

Example Question #62 : Equations

All ISEE Middle Level Quantitative Resources

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