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ISEE Upper Level Quantitative : ISEE Upper Level (grades 9-12) Quantitative Reasoning

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 #4 : How To Factor A Number

What is the sum of all of the factors of 27?

Possible Answers:

Correct answer:

Explanation:

27 has four factors: 1, 3, 9, 27.

Their sum is 1 + 3 + 9 + 27 = 40 .

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Example Question #5 : How To Factor A Number

Add all of the factors of 30.

Possible Answers:

Correct answer:

Explanation:

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. Their sum is

1+2+3+5+ 6+10+15 + 30 = 72 .

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Example Question #6 : Other Factors / Multiples

Which is the greater quantity?

(a) The number of factors of 169

(b) The number of factors of 121

Possible Answers:

It is impossible to tell from the information given

(a) and (b) are equal

(b) is greater

(a) is greater

Correct answer:

(a) and (b) are equal

Explanation:

Each number has only three factors. 121 has 1, 11, and 121 as factors; 169 has 1, 13, and 169 as factors. The answer is that the quantities are equal.

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Example Question #6 : How To Factor A Number

Which is the greater quantity?

(a) The number of factors of 15

(b) The number of factors of 17

Possible Answers:

(a) is greater.

It is impossible to tell from the information given.

(b) is greater.

(a) and (b) are equal.

Correct answer:

(a) is greater.

Explanation:

(a) 15 has four factors, 1, 3, 5, and 15.

(b) 17, as a prime, has two factors, 1 and 17.

Therefore, (a) is greater.

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Example Question #9 : How To Factor A Number

Which is the greater quantity?

(a) The product of the integers between -1,000,000 and inclusive

(b) The sum of the integers between -1,000,000 and inclusive

Possible Answers:

(b) is greater.

It is impossible to tell from the information given.

(a) and (b) are equal.

(a) is greater.

Correct answer:

(a) and (b) are equal.

Explanation:

The quanitites are equal, as both can be demonstrated to be equal to .

(a) One of the integers in the given range is , so one of the factors will be , making the product .

(b) The sum of the numbers will be:

0 + (-1 + 1) + (-2 + 2) + (-3 + 3) + ... + (-1,000,000+ 1,000,000)

0 + 0 + 0+...+0 = 0

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Example Question #7 : How To Factor A Number

Which is the greater quantity?

(a) The sum of the factors of

(b) The sum of the factors of

Possible Answers:

(a) is greater.

It is impossible to tell from the information given.

(a) and (b) are equal.

(b) is greater.

Correct answer:

(b) is greater.

Explanation:

(a) The factors of are 1, 2, 3, 6, 9, 18. Their sum is

1+ 2+3+ 6+ 9+18 = 39 .

(b) The factors of are 1, 2, 4, 5, 10, 20. Their sum is

1+ 2+4+5+10+20 = 42 .

(b) is greater.

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Example Question #11 : Factors / Multiples

Which is the greater quantity?

(a) The sum of all of the two-digit even numbers

(b) 2,500

Possible Answers:

(a) and (b) are equal

It is impossible to tell from the information given

(b) is greater

(a) is greater

Correct answer:

(b) is greater

Explanation:

The sum of the integers from to is equal to $\frac{\left ( n+m \right )\left ( n-m+1 \right )}{2}$ . We take advantage of the fact that the sum of the even numbers from 10 to 98 is equal to twice the sum of the integers from 5 to 49, as seen here:

10+12 + 14+...+98

$=2 \left ( 5+ 6+7+...+49\right )$

$=2\cdot \frac{\left ( 49+5 \right )\left ( 49-5+1 \right )}{2}$

$=54 \times 45 = 2,430 < 2,500$

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Example Question #21 : Numbers And Operations

What is the prime factorization of 16ab^2 ?

Possible Answers:

$2\cdot 2\cdot 2\cdot 2\cdot a\cdot b$

$2\cdot 2\cdot 2\cdot a\cdot b\cdot b$

$2\cdot 2\cdot 2\cdot 2$

$2\cdot 2\cdot 2\cdot 2\cdot 2\cdot a\cdot b\cdot b$

$2\cdot 2\cdot 2\cdot 2\cdot a\cdot b\cdot b$

Correct answer:

$2\cdot 2\cdot 2\cdot 2\cdot a\cdot b\cdot b$

Explanation:

First make a factor tree for 16. Keep breaking it down until you get all prime numbers (for example: $4\times 4$ , which then yields $2\times 2\times 2\times 2$ ). Then, at the end, remember to factor the variables as well. Since the b term is squared, that means there are two of them. Therefore, the final answer is $2\cdot 2\cdot 2\cdot 2\cdot a\cdot b\cdot b$ .

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Example Question #22 : Numbers And Operations

Which one is greater?

(a) number of factors of 100

$(b)\ 10$

Possible Answers:

it is not possible to tell based on the information given.

(a) is greater

(b) is greater

(a) and (b) are equal

Correct answer:

(b) is greater

Explanation:

Factors of 100 are:

$1,2,4,5,10,20,25,50\ and\ 100$ . So it has factors which is less than .

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Example Question #23 : Numbers And Operations

Which one is greater?

(a) The sum of all of the factors of

$(b)\ 200$

Possible Answers:

(a) and (b) are equal

(a) is greater

it is not possible to tell based on the information given.

(b) is greater

Correct answer:

(b) is greater

Explanation:

Factors of are:

$1,2,3,4,6,8,9,12,18,24,36\ and\ 72$ . So we can write:

1+2+3+4+6+8+9+12+18+24+36+72=195

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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 : ISEE Upper Level (grades 9-12) Quantitative Reasoning

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

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #4 : How To Factor A Number

Example Question #5 : How To Factor A Number

Example Question #6 : Other Factors / Multiples

Example Question #6 : How To Factor A Number

Example Question #9 : How To Factor A Number

Example Question #7 : How To Factor A Number

Example Question #11 : Factors / Multiples

Example Question #21 : Numbers And Operations

Example Question #22 : Numbers And Operations

Example Question #23 : Numbers And Operations

All ISEE Upper Level Quantitative Resources

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