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ISEE Upper Level Quantitative : How to add exponents

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Example Questions

Example Question #1 : How To Add Exponents

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 $x\neq0$ $\displaystyle x\neq0$.

Column A Column B

$\displaystyle 2x^2+6x^2$ $\displaystyle 11x^2-x^2$

Possible Answers:

The relationship cannot be determined from the info given.

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 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 $\displaystyle 8x^2$ since 2+6=8 $\displaystyle 2+6=8$. Column B is 10x^2 $\displaystyle 10x^2$ since 11-1=10 $\displaystyle 11-1=10$. We can see that Column B is greater.

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Example Question #1 : How To Add Exponents

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

Possible Answers:

145 $\displaystyle 145$

294 $\displaystyle 294$

194 $\displaystyle 194$

245 $\displaystyle 245$

The correct answer is not among the other choices.

Correct answer:

245 $\displaystyle 245$

Explanation:

The perfect squares between 50 and 100 inclusive are

$8^{2} = 64$ $\displaystyle 8^{2} = 64$

$9^{2} = 81$ $\displaystyle 9^{2} = 81$

$10 ^{2} = 100$ $\displaystyle 10 ^{2} = 100$

Their sum is $\displaystyle 64 + 81 + 100 = 245$

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Example Question #2 : How To Add 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:

(A) and (B) are equal

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

(A) is greater

(B) is greater

Correct answer:

(A) is greater

Explanation:

The sum of the first ten perfect square integers:

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

The sum of the first five perfect cube integers:

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

(A) is greater.

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ISEE Upper Level Quantitative : How to add exponents

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

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #1 : How To Add Exponents

Example Question #1 : How To Add Exponents

Example Question #2 : How To Add Exponents

All ISEE Upper Level Quantitative Resources

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