ISEE Upper Level (grades 9-12) Quantitative Reasoning - Numbers and Operations

1

Which is the greater quantity?

(a) The number of prime numbers between 1 and 20 inclusive

(b) The number of composite numbers between 21 and 30 inclusive

2

Which is the greater quantity?

(a) The number of factors of 169

(b) The number of factors of 121

3

Which is the greater quantity?

(a) The number of prime numbers between 70 and 110

(b) The number of prime numbers between 80 and 120

4

$\frac{ \left ( 30 -2 \cdot 15\right )^{0}}{\left ( 30 -15\right )^{0}}$

5

Which is the greater quantity?

(a) The number of factors of 169

(b) The number of factors of 121

6

Which is the greater quantity?

(a) The number of prime numbers between 70 and 110

(b) The number of prime numbers between 80 and 120

7

Which is the greater quantity?

(a) The number of prime numbers between 1 and 20 inclusive

(b) The number of composite numbers between 21 and 30 inclusive

8

Define an operation $\bigstar$ as follows:

For all positive integers and

$a \bigstar b = \textup{lcd }(a,b) + \textup{gcf }(a,b)$ .

Evaluate $100 \bigstar 80$ .

9

$\frac{ \left ( 30 -2 \cdot 15\right )^{0}}{\left ( 30 -15\right )^{0}}$

10

$\frac{ \left ( 30 -2 \cdot 15\right )^{0}}{\left ( 30 -15\right )^{0}}$

Numbers and Operations