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ISEE Upper Level Quantitative : ISEE Upper Level (grades 9-12) Quantitative Reasoning

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

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All ISEE Upper Level Quantitative Resources

8 Diagnostic Tests 234 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #75 : Algebraic Concepts

Given the line of the equation $\frac{x}{-3} + \frac{y}{-4} = -2$ , which is the greater quantity?

(A) The -coordinate of the -intercept of the line

(B) The -coordinate of the -intercept of the line

Possible Answers:

(B) is greater

(A) is greater

(A) and (B) are equal

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

Correct answer:

(B) is greater

Explanation:

The -coordinate of the -intercept of the line is 0, so to find the -coordinate, set y = 0 and solve for :

$\frac{x}{-3} + \frac{y}{-4} = -2$

$\frac{x}{-3} + \frac{0}{-4} = -2$

$\frac{x}{-3} +0 = -2$

$\frac{x}{-3} = -2$

$\frac{x}{-3} \cdot (-3) = -2 \cdot (-3)$

x = 6

Similarly, to find the -coordinate of the -intercept, set x= 0 and solve for :

$\frac{x}{-3} + \frac{y}{-4} = -2$

$\frac{0}{-3} + \frac{y}{-4} = -2$

$0 + \frac{y}{-4} = -2$

$\frac{y}{-4} = -2$

$\frac{y}{-4} \cdot (-4) = -2 \cdot (-4)$

y = 8

(B), the -coordinate of the -intercept of the line, is greater.

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Example Question #72 : How To Find The Solution To An Equation

Given the line of the equation 6x+7y = -84 , which is the greater quantity?

(A) The -coordinate of the -intercept of the line

(B) The -coordinate of the -intercept of the line

Possible Answers:

(B) is greater

(A) is greater

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

(A) and (B) are equal

Correct answer:

(B) is greater

Explanation:

The -coordinate of the -intercept of the line is 0, so to find the -coordinate, set y = 0 and solve for :

6x+7y = -84

$6x+7 \cdot 0 = -84$

6x+ 0 = -84

6x = -84

$6x \div 6 = -84 \div 6$

x = -14

Similarly, to find the -coordinate of the -intercept, set x= 0 and solve for :

6x+7y = -84

$6 \cdot 0+7y = -84$

0+7y = -84

7y = -84

$7y \div 7 = -84 \div 7$

y = -12

(B), the -coordinate of the -intercept of the line, is greater.

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Example Question #77 : Algebraic Concepts

Given the line of the equation 4x-5y = -20 , which is the greater quantity?

(A) The -coordinate of the -intercept of the line

(B) The -coordinate of the -intercept of the line

Possible Answers:

(B) is greater

(A) and (B) are equal

(A) is greater

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

Correct answer:

(B) is greater

Explanation:

The -coordinate of the -intercept of the line is 0, so to find the -coordinate, we set y = 0 and solve for :

4x-5y = -20

$4x-5 \cdot 0 = -20$

4x-0 = -20

4x = -20

$4x \div 4 = -20 \div 4$

x = -5

Similarly, to find the -coordinate of the -intercept, we set x= 0 and solve for :

4x-5y = -20

$4 \cdot 0 -5y = -20$

0 -5y = -20

-5y =- 20

$-5y\div (-5) = - 20 \div (-5)$

y= 4

(B), the -coordinate of the -intercept of the line, is greater.

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Example Question #72 : Algebraic Concepts

x + y = 8

x - 2y = -1

Which is the greater quantity?

(A)

(B)

Possible Answers:

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

(A) and (B) are equal

(B) is greater

(A) is greater

Correct answer:

(A) is greater

Explanation:

x + y = 8 so y = 8 - x

Substitute for in the other equation:

$x - 2 \left ( 8 - x \right ) = -1$

x - 16 +2 x = -1

3x - 16 = -1

3x - 16 + 16 = -1 + 16

3x = 15

$3x \div 3 = 15 \div 3$

x= 5

y = 8 - x = 8-5 = 3

x > y so (A) is greater.

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Example Question #751 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

x - y = 2

2x+ y = 12

Which is the greater quantity?

(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:

(A) is greater

Explanation:

The first equation actually provides all of the needed information.

x - y = 2 , so

x = y + 2

making x > y .

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Example Question #73 : Algebraic Concepts

a + b = 1

3a -b =1.2

Which is the greater quantity?

(A)

(B)

Possible Answers:

(A) and (B) are equal

(A) is greater

(B) is greater

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

Correct answer:

(A) is greater

Explanation:

Add both sides of the equations as follows:

a + b = 1

$\underline{3a -b =1.2}$

$4a \; \;\; = 2.2$

$4a \div 4 = 2.2 \div 4$

a = 0.55

a + b = 1 , so

0.55 + b = 1

0.55 + b - 0.55= 1 - 0.55

b = 0.45

a > b , so (A) is greater.

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Example Question #81 : How To Find The Solution To An Equation

$b =- a+\frac{1}{2 }$

2a + 2b = 1

Which is the greater quantity?

(A)

(B)

Possible Answers:

(A) is greater

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

(B) is greater

(A) and (B) are equal

Correct answer:

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

Explanation:

The two equations are actually equivalent, as is proved here:

$b =- a+\frac{1}{2 }$

$a + b =a - a+\frac{1}{2 }$

$a + b = \frac{1}{2 }$

$2 \cdot \left (a + b \right )= 2 \cdot \frac{1}{2 }$

2a + 2b = 1

Therefore, we need only test the first equation. However, it can be shown that it is possible for either of the two to be greater or both to be equal; as can be determined from that third equation $a + b = \frac{1}{2 }$ , any two values of and that add up to $\frac{1}{2}$ will solve the system, such as $\left ( 0, \frac{1}{2}\right )$ , $\left ( \frac{1}{4}, \frac{1}{4} \right )$ , or $\left ( \frac{1}{2}, 0\right )$ .

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Example Question #82 : How To Find The Solution To An Equation

$-\frac{3}{4} M =- \frac{6}{7}$

$-\frac{4}{5} N =- \frac{5}{6}$

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

(B) is greater

(A) is greater

Correct answer:

(A) is greater

Explanation:

$-\frac{3}{4} M =- \frac{6}{7}$

$\left ( - \frac{4}{3}\right ) \cdot\left ( -\frac{3}{4} M \right )=\left ( - \frac{4}{3}\right ) \cdot\left ( - \frac{6}{7} \right )$

$M = \frac{24}{21} = \frac{8}{7} = 1 \frac{1}{7}$

$-\frac{4}{5} N =- \frac{5}{6}$

$\left (-\frac{5} {4} \right ) \cdot \left (-\frac{4}{5} N \right )= \left (-\frac{5} {4} \right ) \cdot \left (- \frac{5}{6} \right )$

$N = \frac{25}{24} = 1\frac{1}{24}$

$1 \frac{1}{7} > 1 \frac{1}{24}$ , so M > N , making (A) greater.

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Example Question #81 : Algebraic Concepts

Give the -coordinate of the point on the graph of the equation $\frac{3}{x} + \frac{2}{y} = 5$ that has -coordinate $-\frac{1}{4}$ .

Possible Answers:

$-\frac{2}{7}$

$\frac{17}{2}$

$\frac{2} {17}$

No such point exists.

$-\frac{7}{2}$

Correct answer:

$\frac{2} {17}$

Explanation:

The point $\left ( - \frac{1}{4}, y\right )$ is on the graph of the equation $\frac{3}{x} + \frac{2}{y} = 5$ . Finding the -coordinate of this point is the same as evaluating for $x= -\frac{1}{4}$ . Substitute, and we get:

$\frac{3}{x} + \frac{2}{y} = 5$

$\frac{3}{ -\frac{1}{4}} + \frac{2}{y} = 5$

$-12+ \frac{2}{y} = 5$

$-12+ \frac{2}{y} + 12 = 5 + 12$

$\frac{2}{y} = 17$

$\frac{2}{y}\cdot \frac{y}{17} = 17 \cdot \frac{y}{17}$

$\frac{2} {17} = y$

The -coordinate is therefore $\frac{2} {17}$ .

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Example Question #83 : How To Find The Solution To An Equation

Give the -coordinate of the point on the graph of the equation $2\sqrt{x} + \sqrt{y} = 25$ that has -coordinate 64.

Possible Answers:

No such point exists.

Correct answer:

Explanation:

The point $\left ( 64, y\right )$ is on the graph of the equation $2\sqrt{x} + \sqrt{y} = 25$ . Finding the -coordinate of this point is the same as evaluating for x=64 . Substitute, and we get:

$2\sqrt{x} + \sqrt{y} = 25$

$2\sqrt{64} + \sqrt{y} = 25$

$2 \cdot 8 + \sqrt{y} = 25$

$16+ \sqrt{y} = 25$

$16+ \sqrt{y} - 16 = 25 - 16$

$\sqrt{y} = 9$

$\left (\sqrt{y} \right )^{2} = 9 ^{2}$

y =81

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All ISEE Upper Level Quantitative Resources

8 Diagnostic Tests 234 Practice Tests Question of the Day Flashcards Learn by Concept

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ISEE Upper Level Quantitative : ISEE Upper Level (grades 9-12) Quantitative Reasoning

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

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #75 : Algebraic Concepts

Example Question #72 : How To Find The Solution To An Equation

Example Question #77 : Algebraic Concepts

Example Question #72 : Algebraic Concepts

Example Question #751 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #73 : Algebraic Concepts

Example Question #81 : How To Find The Solution To An Equation

Example Question #82 : How To Find The Solution To An Equation

Example Question #81 : Algebraic Concepts

Example Question #83 : How To Find The Solution To An Equation

All ISEE Upper Level Quantitative Resources

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