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ISEE Upper Level Quantitative : Exponents

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 #122 : Numbers And Operations

x> 1

Column A Column B

$\frac{x^3}{x^2}$ $\sqrt{x}$

Possible Answers:

The relationship between the columns cannot be 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 quantity in Column A is greater.

Explanation:

You can simplify Column A first. When you're dividing with exponents and bases are the same, subtract the exponents. Therefore, it simplifies to x. We know that x is positive since it is greater than 1. X is greater than $\sqrt{x}$ . Try plugging in a number to test. 25 is greater than $\sqrt{25}$ , which is 5. Even 1.1 is greater than $\sqrt{1.1}$ . Therefore, Column A is greater.

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Example Question #21 : Exponential Operations

Two quantities are given - one in Column A and the other in Column B. Compare the quantities in the two columns.

Assume, in both columns, that $x\neq0$ .

Column A Column B

2x^2+6x^2 11x^2-x^2

Possible Answers:

The quantity in Column A is greater.

The quantities in both columns are equal.

The relationship cannot be determined from the info given.

The quantity in Column B is greater.

Correct answer:

The quantity in Column B is greater.

Explanation:

When you are adding and subtracting terms with exponents, you combine like terms. Since both columns have expressions with the same exponent throughout, you are good to just look at the coefficients. Remember, a coefficient is the number in front of a variable. Therefore, Column A is 8x^2 since 2+6=8 . Column B is 10x^2 since 11-1=10 . We can see that Column B is greater.

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Example Question #21 : Exponents

Add all of the perfect squares between 50 and 100 inclusive.

Possible Answers:

294

The correct answer is not among the other choices.

194

145

245

Correct answer:

245

Explanation:

The perfect squares between 50 and 100 inclusive are

$8^{2} = 64$

$9^{2} = 81$

$10 ^{2} = 100$

Their sum is 64 + 81 + 100 = 245

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Example Question #22 : Exponents

Which is the greater quantity?

(A) The sum of the first ten perfect square integers

(B) The sum of the first five perfect cube integers

Possible Answers:

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

(A) and (B) are equal

(A) is greater

(B) is greater

Correct answer:

(A) is greater

Explanation:

The sum of the first ten perfect square integers:

$\begin{matrix} \;\; \; 1\\ \;\; \; 4\\ \;\; \; 9\\ \;16\\ \;25\\ \;36\\ \;49\\ \;64\\ \;81\\ \underline{100}\\ 385 \end{matrix}$

The sum of the first five perfect cube integers:

$\begin{matrix} \;\; \; 1\\ \;\; \; 8\\ \;27\\ \;64\\ \underline{125}\\ 225 \end{matrix}$

(A) is greater.

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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 : Exponents

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

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #122 : Numbers And Operations

Example Question #21 : Exponential Operations

Example Question #21 : Exponents

Example Question #22 : Exponents

All ISEE Upper Level Quantitative Resources

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