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ISEE Upper Level Quantitative : Algebraic Concepts

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 #61 : Equations

In an aquarium, the ratio of sharks to clown fish is 2:7 . If there are 160 more clown fish than sharks, how many sharks are there?

Possible Answers:

Correct answer:

Explanation:

Set up a proportion, where $\frac{2}{7}= \frac{s}{s+160}$ .

Cross multiply:

2(s+160)=7s

Distribute:

2s+320=7s

Combine like terms:

320=5s

Divide both sides of the equation by 5:

s=64

There are 64 sharks.

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Example Question #62 : How To Find The Solution To An Equation

In June, a company had a profit of $\$3$ million. In July, the company doubled that profit. In August, the company's profits rose by percent. If profits rise by another percent in September, what is the September profit?

Possible Answers:

$\$7.18$ million

$\$10$ million

$\$6.9$ million

$\$7.9$ million

$\$9.3$ million

Correct answer:

$\$7.9$ million

Explanation:

The profit in July is twice the profit in June, or $6 million.

Because profits rise by 15% in August, August's profit is really 115% of July's profit:

$1.15\times \$6\ mil = \$6.9\ million$

Similarly, September's profit is 115% of August's profit:

$1.15\times \$6.9\ mil\approx \$7.9\ million$

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Example Question #63 : How To Find The Solution To An Equation

K + L = 100

3K + 2L = 500

Evaluate .

Possible Answers:

K = -200

K = 100

K = -100

K = 200

K = 300

Correct answer:

K = 300

Explanation:

K + L = 100

$2 \cdot \left (K + L \right )= 2 \cdot 100$

2K + 2 L = 2 00

Subtract expressions:

3K + 2L = 500

$\underline{2K + 2 L = 2 00}$

$1K \; \; \; \; \; \; \; \; = 300$

or K = 300

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Example Question #61 : Equations

If x+ 5 = 17 and y + 5 = 13 , evaluate x + y

Possible Answers:

It is impossible to tell from the information given.

Correct answer:

Explanation:

x+ 5 = 17

x+ 5-5 = 17 -5

x = 12

y + 5 = 13

y + 5 - 5 = 13 - 5

y = 8

x + y = 12 + 8 = 20

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Example Question #61 : How To Find The Solution To An Equation

Solve for :

yt - 3x= 100

Possible Answers:

$t= \frac{100 -y}{3x}$

$t= \frac{100 + 3x}{y}$

$t= \frac{100 -3x}{y}$

$t= \frac{100 +y}{3x}$

$t= \frac{100 -x}{3y}$

Correct answer:

$t= \frac{100 + 3x}{y}$

Explanation:

yt - 3x= 100

yt - 3x+ 3x = 100 + 3x

yt = 100 + 3x

$\frac{yt}{y} = \frac{100 + 3x}{y}$

$t= \frac{100 + 3x}{y}$

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Example Question #61 : Algebraic Concepts

M + N = 1,000

Which is the greater quantity?

(A) 0.01M + 0.01N

(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:

0.01M + 0.01N

=0.01(M + N)

$=0.01 \cdot 1,000$

=10 > 1

This makes (A) greater.

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Example Question #63 : Equations

5x + 9 = 64

4y -7 = 37

Which of the following 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) and (B) are equal

Explanation:

5x + 9 = 64

5x + 9 -9 = 64-9

5x = 55

$5x \div 5 = 55 \div 5$

x = 11

4y -7 = 37

4y -7 + 7 = 37+ 7

4y = 44

$4y \div 4 = 44 \div 4$

y = 11

The quantities are equal.

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Example Question #744 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

If $a\therefore b =a^2-4b$ , then what is $1\therefore 3$ ?

Possible Answers:

Correct answer:

Explanation:

To solve this problem, simply plug the numbers into the equation: 1^2-4(3) . Then, just simplify. This gives you 1-12 , which is -11.

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Example Question #745 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

f(x)=3x^2-1

Column A Column B

f(-2) f(2)

Possible Answers:

The realtionship between the columns cannnot be determined.

The quantity in Column B is greater.

The quantities in both columns are equal.

The quantity in Column A is greater.

Correct answer:

The quantities in both columns are equal.

Explanation:

f(-2) and f(-2) mean that you must plug in what it's inside the parantheses to x in the function. Therefore, when you plug in -2 to the function, you get 3(-2^2)-1 , which is 11. Then, plug in 2 to the function, which gives you 3(2^2)-1 , which is also 11. Therefore, the columns are equal.

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Example Question #62 : Algebraic Concepts

Column A Column B

The slope of The slope of

the line the line perpendicular

y=4x-3 . to the line in Column A.

Possible Answers:

The quantity in Column A is greater.

The quantities are equal.

There can be do relationship determined.

The quantity in Column B is greater.

Correct answer:

The quantity in Column A is greater.

Explanation:

The slope of the line y=4x-3 is 4. You can determine this by remembering the y=mx+b slope-intercept form. "M" is slope, so the number in front of x is the slope. Therefore, it's 4. The slope of a line perpendicular to the line is the negative reciprocal of the first slope. Therefore, if the slope of the first line is 4, then the slope of the perpendicular line is $\frac{-1}{4}$ . Therefore, Column A is greater.

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All ISEE Upper Level Quantitative Resources

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ISEE Upper Level Quantitative : Algebraic Concepts

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

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #61 : Equations

Example Question #62 : How To Find The Solution To An Equation

Example Question #63 : How To Find The Solution To An Equation

Example Question #61 : Equations

Example Question #61 : How To Find The Solution To An Equation

Example Question #61 : Algebraic Concepts

Example Question #63 : Equations

Example Question #744 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #745 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #62 : Algebraic Concepts

All ISEE Upper Level Quantitative Resources

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