ISEE Upper Level Math : ISEE Upper Level (grades 9-12) Mathematics Achievement

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

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Example Questions

Example Question #451 : Isee Upper Level (Grades 9 12) Mathematics Achievement

What is the sum of all of the factors of 60?

Possible Answers:

Correct answer:

Explanation:

60 has twelve factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

Their sum is .

Example Question #452 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Give the prime factorization of 135.

Possible Answers:

Correct answer:

Explanation:

3 and 5 are both primes, so this is as far as we can go. Rearranging, the prime factorization is 

.

Example Question #453 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Which of the following digits can go into the box to form a three-digit number divisible by 3?

Possible Answers:

Correct answer:

Explanation:

Place each of these digits into the box in turn. Divide each of the numbers formed and see which quotient yields a zero remainder:

Only 627 is divisible by 3 so the correct choice is 2.

Example Question #454 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Which of the following digits can go into the box to form a three-digit number divisible by 4?

Possible Answers:

None of the other choices is correct.

Correct answer:

None of the other choices is correct.

Explanation:

For a number to be divisible by 4, the last two digits must form an integer divisible by 4. 2 (02), 22, 62, and 82 all yield remainders of 2 when divided by 4, so none of these alternatives make the number a multiple of 4.

Example Question #7 : Other Factors / Multiples

Which of the following is divisible by ?

Possible Answers:

Correct answer:

Explanation:

Numbers that are divisble by 6 are also divisble by 2 and 3. Only even numbers are divisible by 2, therefore, 72165 is excluded. The sum of the digits of numbers divisible by 3 are also divisible by 3. For example,

Because 18 is divisible by 3, 63,072 is divisible by 3.

Example Question #13 : Factors / Multiples

Let  be the set of all integers  such that  is divisible by  and . How many elements are in ?

Possible Answers:

Correct answer:

Explanation:

The elements are as follows:

This can be rewritten as

.

Therefore, there are elements in .

Example Question #9 : Other Factors / Multiples

Let  be the set of all integers  such that is divisible by three and . How many elements are in ?

Possible Answers:

Correct answer:

Explanation:

The elements are as follows:

This can be rewritten as

.

Therefore, there are elements in .

Example Question #21 : Numbers And Operations

Add the factors of 19.

Possible Answers:

Correct answer:

Explanation:

19 is a prime number and has 1 and 19 as its only factors. Their sum is 20.

Example Question #21 : Factors / Multiples

How many integers from 51 to 70 inclusive do not have 2, 3, or 5 as a factor?

Possible Answers:

None

Correct answer:

Explanation:

We can eliminate the ten even integers right off the bat, since, by definition, all have  as a factor. Of the remaining (odd) integers, we eliminate  and , as they have  as a factor. What remains is: 

We can now eliminate the multiples of . This leaves

.

The correct choice is .

Example Question #455 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Add the factors of .

Possible Answers:

Correct answer:

Explanation:

The factors of  are: 

Their sum is .

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