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

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

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All ISEE Upper Level Quantitative Resources

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Example Questions

Example Question #71 : How To Find The Solution To An Equation

Column A Column B

The price of a $27

$30 jacket that's

on sale for

10% off.

Possible Answers:

There can be no relationship determined.

The quantities in both columns are equal.

The quantity in Column B is greater.

The quantity in Column A is greater.

Correct answer:

The quantities in both columns are equal.

Explanation:

First, calculate the price of the jacket in Column A. If the $30 jacket is on sale for 10% off, that means that it is $3 lower. (10% of $30 is $3). Therefore, the price of the jacket is $27. The quantities in both columns are equal.

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Example Question #72 : Algebraic Concepts

Give the -coordinate of the point on the line of the equation 4x-5y = 20 that has -coordinate 9.

Possible Answers:

$11\frac{1}{5}$

$-3\frac{1}{5}$

None of the other responses is correct.

$3\frac{1}{5}$

$-11\frac{1}{5}$

Correct answer:

$3\frac{1}{5}$

Explanation:

The point $\left ( 9, y\right )$ is on the line of the equation 4x-5y = 20 . Finding the -coordinate of this point is the same as evaluating for x= 9 .. Substitute, and we get:

4x-5y = 20

$4 \cdot 9 -5y = 20$

36 -5y = 20

36 -5y- 36 = 20 - 36

-5y = - 16

$-5y \div (-5) = - 16 \div (-5)$

$y = 3 \frac{1}{5}$

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Example Question #73 : Algebraic Concepts

Given the line of the equation 4x-7y = 15 , 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:

(A) and (B) are equal

Explanation:

The -intercept of any line is the point at which the line intersects the -axis; therefore, its -coordinate is 0. Similarly, the -coordinate of the -intercept is 0. The quantities are equal.

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Example Question #74 : Algebraic Concepts

Given the line of the equation 0.5x+ 0.4y = -400 , 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:

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

(B) is greater

(A) is greater

(A) and (B) are equal

Correct answer:

(A) is greater

Explanation:

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

0.5x+ 0.4y = -400

$0.5x+ 0.4 \cdot 0 = -400$

0.5x+ 0 = -400

0.5x = -400

$0.5x \div 0.5 = -400 \div 0.5$

x = -800

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

0.5x+ 0.4y = -400

$0.5 \cdot 0+ 0.4y = -400$

0+ 0.4y = -400

0.4y = -400

$0.4y \div 0.4 = -400 \div 0.4$

y = -1,000

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

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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 #73 : How To Find The Solution To An Equation

x - y = 2

2x+ y = 12

Which is the greater quantity?

(A)

(B)

Possible Answers:

(A) is greater

(B) is greater

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

(A) and (B) are equal

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

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

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #71 : How To Find The Solution To An Equation

Example Question #72 : Algebraic Concepts

Example Question #73 : Algebraic Concepts

Example Question #74 : Algebraic Concepts

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 #73 : How To Find The Solution To An Equation

Example Question #73 : Algebraic Concepts

All ISEE Upper Level Quantitative Resources

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