All ISEE Upper Level Quantitative Resources
Example Questions
Example Question #72 : Factors / Multiples
Which one is greater?
The product of the two greatest prime numbers less than
it is not possible to tell based on the information given.
and are equal
is greater
is greater
is greater
A prime number is a natural number greater than that can be divided only by and itself. The two greatest prime numbers less than are and .
So their product is:
, which is greater than . So is greater than .
Example Question #73 : Numbers And Operations
Which one is greater?
The sum of the prime numbers between and
The sum of the prime numbers between and
and are equal
is greater
it is not possible to tell based on the information given.
is greater
is greater
A prime number is a natural number greater than that can be divided only by and itself.
The prime numbers between and are , so we have:
The prime numbers between and are , so we have:
So is greater than .
Example Question #431 : Isee Upper Level (Grades 9 12) Quantitative Reasoning
Which is the greater quantity?
(A) The sum of the even integers from 21 to 30 inclusive
(B) Three times the sum of the prime integers from 21 to 30 inclusive
(A) is greater
(A) and (B) are equal
It is impossible to determine which is greater from the information given
(B) is greater
(B) is greater
The even integers from 21 to 30 inclusive are 22, 24, 26, 28, and 30; their sum is
The prime integers from 21 to 30 inclusive are 23 and 29. their sum is
and three times this sum is
This makes (B) greater
Example Question #432 : Isee Upper Level (Grades 9 12) Quantitative Reasoning
What is the sum of the prime integers between 75 and 100?
The prime integers between 75 and 100 are
Their sum is
Example Question #433 : Isee Upper Level (Grades 9 12) Quantitative Reasoning
Which is the greater quantity?
(A) The number of composite integers between 41 and 50 inclusive.
(B) The number of prime integers between 41 and 50 inclusive.
(B) is greater
(A) and (B) are equal
It is impossible to determine which is greater from the information given
(A) is greater
(A) is greater
The only prime numbers among the ten in the range 41 through 50 are 41, 43, and 47; this makes three prime numbers and seven composite numbers, so (A) is greater.
Example Question #434 : Isee Upper Level (Grades 9 12) Quantitative Reasoning
Multiply the least and greatest primes between 80 and 100.
The least and greatest primes between 80 and 100 are 83 and 97; their product is
Example Question #435 : Isee Upper Level (Grades 9 12) Quantitative Reasoning
Which of the following is the greater quantity?
(A) The sum of the prime numbers between 80 and 90
(B) The sum of the prime numbers between 90 and 100
(B) is greater
(A) is greater
It is impossible to determine which is greater from the information given
(A) and (B) are equal
(A) is greater
The prime numbers between 80 and 90 are 83 and 89, whose sum is ; the only prime number between 90 and 100 is 97. (A) is the greater quantity.
Example Question #81 : Factors / Multiples
Which is the greater quantity?
(A) Twice the number of prime numbers between 41 and 50 inclusive
(B) The number of composite numbers between 41 and 50 inclusive
(A) is greater
(B) is greater
(A) and (B) are equal
It is impossible to determine which is greater from the information given
(B) is greater
Out of the ten integers from 41 to 50, the prime numbers are 41, 43, and 47 - therefore, there are three prime numbers and seven composite numbers. Since
,
(B) is greater.
Example Question #82 : Factors / Multiples
Which of the following is the greater quantity?
(A) The sum of the prime numbers between 50 and 60
(B) The sum of the odd composite numbers between 50 and 60
(A) and (B) are equal
(A) is greater
(B) is greater
It is impossible to determine which is greater from the information given
(B) is greater
The prime numbers between 50 and 60 are 53 and 59; their sum is . The odd composite numbers between 50 and 60 are 51, 55, and 57; their sum is . Therefore, (B) is greater.
Example Question #31 : Prime Numbers
and are prime integers. and . What is the minimum value of ?
The least prime integer between 60 and 70 is 61, so this is the minimum value of . The least prime integer between 80 and 90 is 83, so this is the minimum value of . Since
and ,
then , by the addition property of inequality,
.