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ISEE Middle Level Quantitative : ISEE Middle Level (grades 7-8) Quantitative Reasoning

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

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All ISEE Middle Level Quantitative Resources

6 Diagnostic Tests 110 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #5 : Squares / Square Roots

$Q^{2} = 49$ $\displaystyle Q^{2} = 49$

Which is the greater quantity?

(A) $\displaystyle Q$

(B) $\displaystyle -8$

Possible Answers:

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

(B) is greater

(A) and (B) are equal

(A) is greater

Correct answer:

(A) is greater

Explanation:

If $Q^{2} = 49$ $\displaystyle Q^{2} = 49$, then one of two things is true - either Q=7 $\displaystyle Q=7$ or Q=- 7 $\displaystyle Q=- 7$. Since 7 > -8 $\displaystyle 7 > -8$ and -7 > -8 $\displaystyle -7 > -8$, Q > -8 $\displaystyle Q > -8$ either way, so (A) is greater.

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Example Question #201 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Which is the greater quantity?

(A) $\sqrt{9} + \sqrt{25}$ $\displaystyle \sqrt{9} + \sqrt{25}$

(B) $\sqrt{34}$ $\displaystyle \sqrt{34}$

Possible Answers:

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

(B) is greater

(A) is greater

(A) and (B) are equal

Correct answer:

(A) is greater

Explanation:

$\sqrt{9} + \sqrt{25} = 3 + 5 = 8$ $\displaystyle \sqrt{9} + \sqrt{25} = 3 + 5 = 8$

since $8^{2} = 8 \times 8 = 64$ $\displaystyle 8^{2} = 8 \times 8 = 64$, $8 = \sqrt{64}$ $\displaystyle 8 = \sqrt{64}$.

Since 64 > 34 $\displaystyle 64 > 34$, $\sqrt{64} > \sqrt{34}$ $\displaystyle \sqrt{64} > \sqrt{34}$, and (A) is greater

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Example Question #202 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Which is the greater quantity?

(A) $\sqrt{4 \cdot 9 \cdot 25}$ $\displaystyle \sqrt{4 \cdot 9 \cdot 25}$

(B) $2 \cdot 3 \cdot 5$ $\displaystyle 2 \cdot 3 \cdot 5$

Possible Answers:

(A) and (B) are equal

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

(B) is greater

(A) is greater

Correct answer:

(A) and (B) are equal

Explanation:

$\sqrt{4 \cdot 9 \cdot 25} = \sqrt{900} = 30$ $\displaystyle \sqrt{4 \cdot 9 \cdot 25} = \sqrt{900} = 30$

$2 \cdot 3 \cdot 5 = 30$ $\displaystyle 2 \cdot 3 \cdot 5 = 30$

The quantities are equal.

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Example Question #203 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Which is the greater quantity?

(A) $\displaystyle 25$

(B) $\sqrt{600}$ $\displaystyle \sqrt{600}$

Possible Answers:

(B) is greater

(A) and (B) are equal

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

(A) is greater

Correct answer:

(A) is greater

Explanation:

$25 ^{2} = 25 \times 25 = 625$ $\displaystyle 25 ^{2} = 25 \times 25 = 625$, so

$25 = \sqrt{625} > \sqrt{600}$ $\displaystyle 25 = \sqrt{625} > \sqrt{600}$

This makes (A) greater.

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Example Question #202 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Which is the greater quantity?

(A) $\sqrt{100^{4}}$ $\displaystyle \sqrt{100^{4}}$

(B) $100^{2}$ $\displaystyle 100^{2}$

Possible Answers:

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

(B) is greater

(A) is greater

(A) and (B) are equal

Correct answer:

(A) and (B) are equal

Explanation:

$\sqrt{100^{4}} = \sqrt{100 \times 100 \times 100 \times 100} = \sqrt{100,000,000} = 10,000$ $\displaystyle \sqrt{100^{4}} = \sqrt{100 \times 100 \times 100 \times 100} = \sqrt{100,000,000} = 10,000$

$100^{2} = 100 \times 100 = 10,000$ $\displaystyle 100^{2} = 100 \times 100 = 10,000$

The quantities are equal.

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Example Question #203 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Which of the following is equal to $\sqrt{4 \cdot 9 \cdot 16}$ $\displaystyle \sqrt{4 \cdot 9 \cdot 16}$ ?

Possible Answers:

$\displaystyle 9$

$\displaystyle 24$

$\displaystyle 16$

$\displaystyle 22$

$\displaystyle 12$

Correct answer:

$\displaystyle 24$

Explanation:

First, simplify the terms within the square root by multiplying.

$\sqrt{4 \cdot 9 \cdot 16} = \sqrt{36 \cdot 16} = \sqrt{576}$ $\displaystyle \sqrt{4 \cdot 9 \cdot 16} = \sqrt{36 \cdot 16} = \sqrt{576}$

Then, solve the sqaure root.

$\sqrt{576}=24$ $\displaystyle \sqrt{576}=24$

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Example Question #206 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Which of the following is equal to $\sqrt{4^{2} \cdot 3^{2}}$ $\displaystyle \sqrt{4^{2} \cdot 3^{2}}$ ?

Possible Answers:

$\displaystyle 12$

$\displaystyle 10$

$\displaystyle 14$

$\displaystyle 7$

$\displaystyle 9$

Correct answer:

$\displaystyle 12$

Explanation:

First, evalutate the terms under the radical:

$\sqrt{4^{2} \cdot 3^{2}} = \sqrt{16 \cdot 9} =\sqrt{144}$ $\displaystyle \sqrt{4^{2} \cdot 3^{2}} = \sqrt{16 \cdot 9} =\sqrt{144}$

Then, take the square root:

$\sqrt{144}=12$ $\displaystyle \sqrt{144}=12$

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Example Question #17 : Squares / Square Roots

Which is the greater quantity?

(A) $\sqrt{1+ 4+ 9 + 16 + 25 + 36}$ $\displaystyle \sqrt{1+ 4+ 9 + 16 + 25 + 36}$

(B) $\displaystyle 9$

Possible Answers:

(A) and (B) are equal

(A) is greater

(B) is greater

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

Correct answer:

(A) is greater

Explanation:

$\displaystyle 1+ 4+ 9 + 16 + 25 + 36$

$\displaystyle =5 + 9 + 16 + 25 + 36$

$\displaystyle =14 + 16 + 25 + 36$

$\displaystyle =30+ 25 + 36$

$\displaystyle =55 + 36$

=91 $\displaystyle =91$

Therefore, $\sqrt{1+ 4+ 9 + 16 + 25 + 36} = \sqrt{91}$ $\displaystyle \sqrt{1+ 4+ 9 + 16 + 25 + 36} = \sqrt{91}$.

Since $9^{2} = 9 \times 9 = 81$ $\displaystyle 9^{2} = 9 \times 9 = 81$, $9 = \sqrt{81}$ $\displaystyle 9 = \sqrt{81}$.

91 > 81 $\displaystyle 91 > 81$, so $\sqrt{91 }>\sqrt{ 81}$ $\displaystyle \sqrt{91 }>\sqrt{ 81}$, and (A) is greater.

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Example Question #204 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Which of the following is equal to 39?

Possible Answers:

$12\cdot3+3$ $\displaystyle 12\cdot3+3$

$12\cdot2+3$ $\displaystyle 12\cdot2+3$

$12\cdot3+6$ $\displaystyle 12\cdot3+6$

$16\cdot3+3$ $\displaystyle 16\cdot3+3$

Correct answer:

$12\cdot3+3$ $\displaystyle 12\cdot3+3$

Explanation:

$12\cdot3+3$ $\displaystyle 12\cdot3+3$ is equal to:

36+3 $\displaystyle 36+3$

$\displaystyle 39$

Therefore, $12\cdot3+3$ $\displaystyle 12\cdot3+3$ is the correct answer.

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Example Question #19 : Squares / Square Roots

$\displaystyle A$ is a positive integer; $\displaystyle B$ is a negative integer; A +B =1 $\displaystyle A +B =1$.

Which is the greater quantity?

(a) $\sqrt{A^{2}}$ $\displaystyle \sqrt{A^{2}}$

(b) $\sqrt{B^{2}}$ $\displaystyle \sqrt{B^{2}}$

Possible Answers:

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

(b) is the greater quantity

(a) and (b) are equal

(a) is the greater quantity

Correct answer:

(a) is the greater quantity

Explanation:

A +B =1 $\displaystyle A +B =1$, then B = 1-A $\displaystyle B = 1-A$. Since $\displaystyle B$ is negative, let $\displaystyle C$ be the opposite of $\displaystyle B$. Therefore, $\displaystyle C= - B = - ( 1-A) =A-1$.

Two numbers that are each other's opposite have the same square, so

$C^{2} = B^{2}$ $\displaystyle C^{2} = B^{2}$

$\displaystyle C = A-1 < A$, so, since $\displaystyle C$ and $\displaystyle A$ are positive,

$C^{2} < A^{2}$ $\displaystyle C^{2} < A^{2}$

By substitution,

$B^{2}< A^{2}$ $\displaystyle B^{2}< A^{2}$,

and

$\sqrt{B^{2}}<\sqrt{ A^{2}}$ $\displaystyle \sqrt{B^{2}}< \sqrt{ A^{2}}$.

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All ISEE Middle Level Quantitative Resources

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ISEE Middle Level Quantitative : ISEE Middle Level (grades 7-8) Quantitative Reasoning

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

All ISEE Middle Level Quantitative Resources

Example Questions

Example Question #5 : Squares / Square Roots

Example Question #201 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Example Question #202 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Example Question #203 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Example Question #202 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Example Question #203 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Example Question #206 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Example Question #17 : Squares / Square Roots

Example Question #204 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Example Question #19 : Squares / Square Roots

All ISEE Middle Level Quantitative Resources

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