ISEE Lower Level Quantitative Reasoning - Data Analysis

$2,5,11,23,47, \square$

What is the next number in the series?

Explanation

First, determine what the pattern is in the series. The pattern here is to multiply the previous number by 2 and then add 1. Therefore, multiply 47 by 2 (which is 94), and then add 1. The result is 95.

$2,5,11,23,47, \square$

What is the next number in the series?

Explanation

During a basketball game, 3 of the players on a team make 4 baskets each, while the other 2 players only make 1 basket each. What is the mean number of baskets that each player made during the game?

$2\frac{4}{5}$

$2\frac{2}{5}$

$3\frac{4}{5}$

Explanation

The mean is calculated by finding the sum of the numbers in a set, and then dividing that sum by the number of items in the set. Given that 3 of the players made 4 baskets each, while the other 2 players only made only 1 basket each, the equation for finding the mean would look like this (there are 5 players on the team, and so there are 5 items in the set):

$\frac{4+4+4+1+1}{5}$

$\frac{14}{5}$

$2\frac{4}{5}$

Define two sets as follows:

$A = \left { a, b, d, f, h, i, j \right }$

$B = \left { b, c, d, e, h, k, m, p\right }$

How many elements are in $A\cap B$ ?

Explanation

$A\cap B$ is the intersection of sets and - the set of all elements that appear in both sets. As can be seen, those elements are - making 3 the correct choice.

Two teams—one with three boys, one with three girls—are competing to sell the most magazine subscriptions. Below is the table listing the number of subscriptions each student has sold so far.

The boys' team:

$\begin{matrix} \textrm{\underline{Student}}& \textrm{\underline{Sales}}\ \textrm{Brett}; ; ; ; & 14\ \textrm{Jim}; ; ; ;; ;&16\ \textrm{Mike}; ; ; ; & 22 \end{matrix}$

The girls' team:

$\begin{matrix} \textrm{\underline{Student}}& \textrm{\underline{Sales}}\ \textrm{Anne} ; ; ; ; & 15\ \textrm{Jill}; ; ; ; ; ; ; &24 \ \textrm{Rhonda} & 15 \end{matrix}$

Which of the following is true right now?

The girls are leading the boys by 2 subscriptions.

The girls are leading the boys by 4 subscriptions.

The boys are leading the girls by 2 subscriptions.

The boys are leading the girls by 4 subscriptions.

The boys and the girls are tied.

Explanation

The girls have sold subscriptions; the boys have sold subscriptions. The girls are leading by 2.

Define the set $C = \left { 1, 3, 5, 7, 9, 11, 13, 15, 17, 19\right }$

Which of the following is not a subset of ?

$\left { 3, 5, 9, 11, 13, 17, 18\right }$

$\left { 1, 5, 7, 9, 11, 15, 17\right }$

$\left { 5, 7, 9, 11, 15, 17, 19 \right }$

$\left { 19\right }$

$\varnothing$

Explanation

A subset of a set , by definition, is any set that contains no elements not in . All elements in $\left { 1, 5, 7, 9, 11, 15, 17\right }$ , $\left { 5, 7, 9, 11, 15, 17, 19 \right }$ , and $\left { 19\right }$ are contained in and the sets are subsets; also, $\varnothing$ , the empty set, is considered a subset of every set. $\left { 3, 5, 9, 11, 13, 17, 18\right }$ , however, contains element , so

$\left { 3, 5, 9, 11, 13, 17, 18\right } subseteq C$ .

What is the value of in the set below?

Explanation

The pattern in the set is that each number increases by 6. The last number was 24. Therefore, since 6 plus 24 equals 30, would be equal to 30.

What is the next number in this sequence?

Explanation

Notice that the numbers in this list are growing at an increasing rate.

First you add :

Then you add : $\left ( 4+2=6 \right )$

Then you add : $\left ( 6+3=9 \right )$ .

By the time you get to the 18, it is time to add 6:

What number comes next in this sequence?

2, 3, 5, 7, 11, 13, __

Explanation

Looking at this sequence, the most obvious thing may be the string of odd numbers. But as you look more closely, you'll notice that the 9 is missing and that there is a 2 in the list. Whenever you see a 2 in a list of odd numbers, your "prime number sensor" (not a real thing) should be on alert. As this is a list of consecutive prime numbers, the next number in the sequence is 17.

What is the next number: