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

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Example Questions

Example Question #701 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

The slope of a line is 2; the line does not pass through the origin.

Which is the greater quantity?

(a) The -coordinate of the -intercept

(b) The -coordinate of the -intercept

Possible Answers:

(a) and (b) are equal.

(a) is greater.

It is impossible to tell from the information given.

(b) is greater.

Correct answer:

It is impossible to tell from the information given.

Explanation:

Let (b,0),(0,a) be the - and -intercepts, respectively. We know that the line does not pass through the origin - so $a,b \neq 0$ .

Then the slope is:

$m = \frac{a-0}{0-b} = \frac{a}{-b} = - \frac{a}{b}$

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

a = -2b

Either or can be the greater. For example, if b = 1 , then a = -2 , and if b =- 1 , then a = 2 .

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Example Question #702 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

$6^{3x}= 36 ^{x+ 3}$ .

Which is the greater quantity?

(a)

(b)

Possible Answers:

It is impossible to tell from the information given.

(a) is greater.

(b) is greater.

(a) and (b) are equal.

Correct answer:

(a) and (b) are equal.

Explanation:

$36 = 6^{2}$ , so substitute and use the power of a power rule.

$6^{3x}= 36 ^{x+ 3}$

$6^{3x}=\left ( 6^{2} \right )^{x+ 3}$

$6^{3x}= 6^{2(x+ 3)}$

$6^{3x}= 6^{2x + 6}$

3x = 2x + 6

3x -2x= 2x-2x + 6

x = 6

This makes (a) and (b) equal.

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Example Question #701 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Which is the greater quantity?

(a) The slope of the line of the equation y = 5x + 4

(b) The slope of the line of the equation y = 4x + 5

Possible Answers:

(a) is greater.

(a) and (b) are equal.

(b) is greater.

It is impossible to tell from the information given.

Correct answer:

(a) is greater.

Explanation:

Both equations are in slope-intercept form, so compare the coefficients of . The coefficients in (a) and (b) are 5 and 4, respectively, so these are the slopes of the lines. The line in (a) has the greater slope.

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

y = 2x + 1

Which is the greater quantity?

(a)

(b)

Possible Answers:

(a) and (b) are equal.

It is impossible to tell from the information given.

(a) is greater.

(b) is greater.

Correct answer:

It is impossible to tell from the information given.

Explanation:

Using two different cases, we show that it is impossible to tell which is greater.

Case 1: x = 1 . Then $y = 2x + 1 = 2 \cdot 1+ 1 = 2 + 1 = 3$ , and y > x .

Case 2: x = -3 . Then $y = 2x + 1 = 2 \cdot (-3)+ 1 = -6+ 1 = -5$ , and y < x .

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Example Question #26 : Algebraic Concepts

x + y = 10

2x - y = 14

Which is the greater quantity?

(a)

(b)

Possible Answers:

(a) and (b) are equal.

(a) is greater.

It is impossible to tell from the information given.

(b) is greater.

Correct answer:

(a) is greater.

Explanation:

To solve the system of equations, add the left and right sides of the equation separately:

x + y = 10

$\underline{2x - y = 14}$

$3x\; \; \; \; \; \; = 24$

Divide:

$3x \div 3 = 24\div 3$

x=8

Substitute to get :

x+y = 10

8+y = 10

8-8+y = 10-8

y = 2

is greater.

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Example Question #30 : How To Find The Solution To An Equation

t + 1 = |u|

Which is the greater quantity?

(a)

(b)

Possible Answers:

(a) is greater

It is impossible to tell from the information given

(a) and (b) are equal

(b) is greater

Correct answer:

It is impossible to tell from the information given

Explanation:

We show that it is possible for either or to be the greater by giving one of each case.

Case 1: u = 1 . Then $t + 1 = \left | 1\right | = 1$ , so t = 0

Case 2: u = -1 . Then $t + 1 = \left | -1\right | = 1$ , so t = 0

In Case 1, t < u ; in Case 2, t > u

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Example Question #31 : How To Find The Solution To An Equation

x + 3y = 28

3x + 2y = 35

Which is the greater quantity?

(a)

(b)

Possible Answers:

(a) is greater

(a) and (b) are equal

(b) is greater

It is impossible to tell from the information given

Correct answer:

(a) and (b) are equal

Explanation:

Multiply both sides of the top equation by 3, and subtract both sides of the second equation.

x + 3y = 28

$3\left ( x + 3y \right )= 3 \cdot 28$

$3 x + 9y \right )= 84$

$\underline{3x + 2y = 35}$

7y = 49

$7y \div 7= 49 \div 7$

y = 7

Now substitute to find :

x + 3y = 28

$x + 3 \cdot 7 = 28$

x + 21= 28

x + 21-21= 28-21

x = 7

The two are equal.

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Example Question #32 : How To Find The Solution To An Equation

4x +y = 20

2x + 3y = 30

Which is the greater quantity?

(a)

(b)

Possible Answers:

(a) is greater

(a) and (b) are equal

It is impossible to tell from the information given

(b) is greater

Correct answer:

(b) is greater

Explanation:

Triple both sides of the top equation, and subtract both sides of the bottom equation:

4x +y = 20

$3 \left ( 4x +y \right ) = 3\left ( 20\right )$

12x +3y = 60

$\underline{2x + 3y = 30}$

10x =30

$10x \div 10 = 30 \div 10$

x = 3

Now substitute to find :

4x +y = 20

$4 \cdot 3 +y = 20$

12 +y = 20

12 +y -12= 20 -12

y = 8

This makes y > x

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Example Question #33 : How To Find The Solution To An Equation

t = |u - 1|

Which is the greater quantity?

(a)

(b)

Possible Answers:

(a) and (b) are equal

(b) is greater

It is impossible to tell from the information given

(a) is greater

Correct answer:

It is impossible to tell from the information given

Explanation:

We show that it cannot be determined which of and , if either, is greater, by showing one case in which t > u and one case in which t < u .

Case 1: u = 0 . Then

t = |u - 1| = |0 - 1| = | - 1| = 1

and t > u .

Case 2: u = 1 . Then

t = |u - 1| = |1 - 1| = | 0| = 0

and t < u .

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Example Question #34 : How To Find The Solution To An Equation

t = |u + 1|

Which is the greater quantity?

(a)

(b)

Possible Answers:

(b) is greater

(a) and (b) are equal

It is impossible to tell from the information given

(a) is greater

Correct answer:

(a) is greater

Explanation:

If u < 0 , then, since is nonnegative, t > u .

If $u \geq 0$ , then $u + 1 \geq 1 > 0$ , so the equation becomes t = u + 1 . Therefore, t > u .

Either way, (a) is greater.

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All ISEE Upper Level Quantitative Resources

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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 #701 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #702 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #701 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

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

Example Question #26 : Algebraic Concepts

Example Question #30 : How To Find The Solution To An Equation

Example Question #31 : How To Find The Solution To An Equation

Example Question #32 : How To Find The Solution To An Equation

Example Question #33 : How To Find The Solution To An Equation

Example Question #34 : How To Find The Solution To An Equation

All ISEE Upper Level Quantitative Resources

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