Data Analysis and Probability - ISEE Lower Level Quantitative Reasoning

Card 0 of 1681

Question

Look at the chart below. If we add more apples, how many more apples will we have?

Answer

Looking at the graph, we first need to figure out how many apples we are starting with. We are starting with apples and we are going to add more apples, which means we will have apples.

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Question

Look at the chart below. How many grapes are there?

Answer

In the chart, grapes are shown in the last bar, on the right. That bar goes up to the number , which means there are grapes.

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Question

Kate's class is going to plant flowers outside of their class window. To help decide what flower to plant, her teacher took a class vote.

Use the graph below to help answer the question.

What is the label of the x-axis?

Answer

A graph is made up of an x-axis and a y-axis. The x-axis of a graph is always the horizontal line (a line that runs from left to right) and the y-axis is alway the vertical line (a line that runs from top to bottom)

The x-axis of this graph is labeled "Type of Flower".

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Question

Mrs. Ryan's class had their class election today for their class president. The results are displayed in the chart below.

Use the graph below to help answer the question.

How many people voted for Megan?

Answer

The bar for Megan is the first bar on the left. The bar raises to the number , which means people voted for Megan.

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Question

What is the missing value of w in this sequence?

Answer

In this sequence, every subsequent number is 7 less than the preceding number. Given that the number that precedes w is 71, the value of w is . Therefore, 64 is the correct answer.

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Question

What is the value of n in the sequence below?

Answer

The numbers increase by 5. Given that the number before n is 20, the value of n is .

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Question

Bob recorded the number of red cars he saw out his office window every day. He recorded 15 more cars on Wednesday than on Friday.

According to the chart, how many real life cars does each car picture represent?

Answer

Look at the chart and count how many more car pictures there are on Wednesday than on Friday: three red car pictures.

Divide the actual difference in the number of cars by the difference in the number of car pictures in the table: 15 $\div$ 3 = 5, which is the correct answer.

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Question

Eric has a 2 red shirts, 3 orange shirts, 4 purple shirts, and 1 pink shirt. If Eric randomly chooses a shirt, what are the chances that he selects a pink shirt?

Answer

First, add up all of the shirts.

$\dpi{100} 2+3+4+1=10\ shirts$

We then see that Eric has 1 pink shirt and 10 shirts from which to choose. Build a fraction with the number of pink shirts on top, and the total number of shirts on the bottom, $\dpi{100} \frac{1}{10}$ .

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Question

Ten cards each have a number printed on them. Five have a 1 printed on them, three have a 2, and two have a 3. The cards are shuffled and a card is dealt. What is the probability that the card will not be a 3?

Answer

There are ten cards total, and eight cards that are not threes. This makes the probability of drawing a three

$\frac{8}{10} = \frac{4}{5}$

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Question

Express the probability as a fraction.

Nija has 7 marbles. There are 2 red, 3 blue, and 2 yellow. What is the probablilty that Nija will choose a red marble?

Answer

Probability can be expressed as a fraction:

$\frac{part}{total, possible}$

Our fraction is $\frac{red;marbles}{total;marbles }$ .

Since there are 2 red marbles out of 7 total marbles, the probability of choosing a red marble is $\frac{2}{7}$ .

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Question

A ring toss game has 25 bottles, 5 of which are yellow. If you toss a ring around a yellow bottle, you win the grand prize. What is the probability of winning the grand prize? (Give the fraction in simplest form.)

Answer

To find the probability of an outcome, set up a fraction.

$\frac{part}{total, possible}$

Since there are 5 yellow (part) out of 25 bottles (total possible) the fraction looks like this: $\frac{5}{25}$ .

Reduce the fraction by dividing the top and bottom by 5:

$\frac{5\div5}{25\div5}=\frac{1}{5}$

This is the probability of winning the grand prize.

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Question

A magician holds in his bag 3 green balls, 4 red balls and 7 blue balls. What is the probability of drawing a red ball from the bag?

Answer

Probability = total number of possible outcomes/sample space.

= $\frac{4}{14}$

= $\frac{2}{7}$

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Question

If there are 2 blue marbles and 18 red marbles in a jar, what is the probability that Jeff will pick out a red marble?

Answer

First, add the total number of marbles, which is . There are 18 red marbles, so you set up a fraction $\frac{18}{20}$ .

If you simplify by dividing the numerator and denominator by 2, you get $\frac{9}{10}$ .

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Question

In a restaurant there are two managers, three workers, and twelve guests. What is the probability that a person chosen at random is a worker?

Answer

The total number of people in the room is the sum of all the different types of people:

The probability of choosing a worker is the number of workers divided by the total number of people. There are three workers and seventeen people in total:

$3\div 17=\frac{3}{17}$

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Question

Find the probability of an outcome. Express the outcome as fraction, reduced to its lowest terms.

Mr. Thomas went to a car lot to buy a new car. Of the 68 cars on the lot, 22 were black, 16 were silver, 8 were white, 12 were blue, and 10 were red. What is the probability that Mr. Thomas will buy a blue car?

Answer

To find the probability of an outcome, set up a fraction:

$\frac{part}{total \ possible}$

Since there are 12 blue cars (part) out of 68 cars in all (total possible) the fraction looks like this:

$\frac{12}{68}$

If you reduce the fraction by 4 (because the numerator and the denominator are both divisible by 4 which makes 4 the GCF (greatest common factor), it becomes:

$\frac{3}{17}$

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Question

There are 10 marbles in a bag:

7 red

2 blue

1 yellow

What is the probability of choosing a red ball out of the bag?

Answer

To find the probability of an outcome, set up a fraction:

$\frac{parts}{total , possible}$

Since there are 7 red marbles (part) out of 10 marbles in all (total possible) the fraction looks like this:

$\frac{7}{10}$

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Question

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

What is the next number in the series?

Answer

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.

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Question

Casey has a bag containing red, yellow, blue, and green beads. There are equal numbers of red and blue beads, which comprise half the bag when combined. If there are 24 beads in the bag, what is the probability that Casey will select a blue bead?

Answer

There are $\small 24$ beads in Casey's bag. We know that the red and blue beads make up half of the bag, so we divide $\small 24$ by $\small 2$ to find the total number of red and blue beads.

$\small 24/2=12$

Since there is an equal number of red and blue beads, we divide $\small 12$ by $\small 2$ .

$\small 12/2=6$

To find probability, we create a fraction with our desired outcome written as the numerator and the total possible outcomes written as the denominator:

$\small \frac{6}{24}$

Since $\small 6$ and $\small 24$ are divisible by $\small 6$ , we must reduce the fraction.

$\small \frac{(6/6)}{(24/6)}=\frac{1}{4}$

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Question

A bag contains red socks and purple socks. What is the chance that I pick a purple sock from the bag?

Answer

To find the probability of picking a purple sock from the bag of socks, we need to set up a fraction like this: $\frac{purple socks}{total socks}$ . The problem tells us that we have purple socks, so we can put that on the top of the fraction. The total number of socks is equal to purple socks + red socks, giving us a sum of (which goes on the bottom of the fraction). That gives us a $\frac{3}{7}$ chance of picking a purple sock from the bag!

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Question

Mikey has a box filled with cookies. He has 6 chocolate chip cookies, 4 sugar cookies, and 2 oatmeal raisin cookies. What is the chance that Mikey picks a sugar cookie out of the box?

Answer

To find the probability of picking a sugar cookie from the bag of cookies, we need to set up a fraction like this:

$\frac{sugar\ cookies}{total\ cookies}$

The problem tells us that Mikey has 4 sugar cookies, so we can put that on the top of the fraction. The total number of cookies is equal to 6 chocolate chip cookies + 4 sugar cookies + 2 oatmeal raisin cookies, giving us a sum of 12 (which goes on the bottom of the fraction). That gives Mikey a $\frac{4}{12}$ chance of picking a sugar cookie!

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