All ISEE Upper Level Quantitative Resources
Example Questions
Example Question #41 : How To Factor A Number
Which of the following is NOT a factor of ?
First, we must solve for
While 64 is divisible by 4, 8, and 16, it is not divisible by 7; therefore, 7 is not a factor of 64 and is thus the correct answer.
Example Question #51 : Numbers And Operations
and are distinct odd primes. Which is the greater quantity?
(a) The number of factors of
(b) The number of factors of
(b) is greater
(a) is greater
(a) and (b) are equal
It is impossible to tell which is greater from the information given
It is impossible to tell which is greater from the information given
Since and are distinct primes, the prime factorization of is ; therefore, the factors of are 1, , , and . There are four factors.
We show that may or may not have more factors by example.
Case 1: .
Then , which has four factors: 1, 2, 4, 8.
Case 2:
Then , which has six factors: 1, 2, 3, 4, 6, 12.
Therefore, we have at least one situation in which and have the same number of factors, and at least one in which has more. The given infomation is insufficient.
Example Question #42 : How To Factor A Number
and are distinct odd primes. Which is the greater quantity?
(a) The number of factors of
(b) The number of factors of
It is impossible to tell which is greater from the information given
(b) is greater
(a) and (b) are equal
(a) is greater
(a) is greater
Since and are distinct primes, the prime factorization of is ; therefore, the factors of are 1, , , and . There are four factors.
Since is a prime, the prime factorization of is ; therefore, the factors of are 1, , and . There are three factors.
This makes (a) greater.