SSAT Middle Level Math : Data Analysis and Probability

Study concepts, example questions & explanations for SSAT Middle Level Math

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Example Questions

Example Question #31 : How To Find The Missing Part Of A List

Assorted 2

Refer to the above diagram. The top row gives a sequence of figures. Which figure on the bottom row comes next?

Possible Answers:

Figure (b) 

Figure (a)

Figure (d)

Figure (c)

Correct answer:

Figure (b) 

Explanation:

The figures alternate between lines with squares and lines with circles, so the next figure must be a line with a square. This eliminates Figures (c) and (d) and leaves Figures (a) and (b).

If we only look at every other figure - the ones with the squares - we note that each figure is the previous one rotated one quarter turn clockwise. The next figure in the sequence is therefore the figure resulting from a one-quarter turn of the fifth figure - this is Figure (b).

Example Question #192 : Data Analysis And Probability

What number replaces the square in the sequence below?

Possible Answers:

Correct answer:

Explanation:

The way to get from one entry of the sequence to the next alternates between multiplying by four and subtracting one, as follows:

Continuing the pattern:

, the correct choice.

Example Question #191 : Data Analysis And Probability

Assorted 1

On the top row in the above diagram is a sequence of figures. Which of the figures in the bottom row is the next one in the sequence?

Possible Answers:

Figure (b)

Figure (a)

Figure (d)

Figure (c)

Correct answer:

Figure (c)

Explanation:

Each figure is obtained by rotating the previous figure one-eighth of a turn clockwise, with the position of the letter and the number also so changed. Also, the number increases by two, and the letter, which is always in the opposite corner, is the letter corresponding to the number (A = 1, C = 3, etc...).

The next number in the pattern is 13; the thirteenth letter in the alphabet is "M"; and, to continue the pattern of rotating one-eighth of a turn clockwise each time, the "M" must be at the very bottom, with the "13" being at the top. This means that Figure 3 is the next figure in the sequence.

Example Question #602 : Ssat Middle Level Quantitative (Math)

Pie_graph

 

Four candidates ran for mayor of Jackson City; the above circle graph shows the share of the vote that each won.

According to a city ordinance, a candidate must win more than 50% of the vote to win the election; if this does not happen, the two candidates who win the most votes will face each other in a runoff election. Based on the above graph, which of the following is the outcome of the vote?

Possible Answers:

Mills and King will face each other in a runoff.

Mills won the election outright.

Jones won the election outright.

Jones and King will face each other in a runoff.

Mills and Jones will face each other in a runoff.

Correct answer:

Mills and Jones will face each other in a runoff.

Explanation:

By comparing the sizes of the sectors, it can be seen that Mills won the largest share of the vote - but not at least one half of it - and Jones won the second-largest share. Therefore, they will face each other in a runoff.

Example Question #3 : Analyzing Graphs And Figures

Four candidates ran for mayor of Johnston City. The results are below.

Which of the following is the best estimate of the percent of the vote won by Johnson?

Possible Answers:

 %

 %

 %

 %

 %

Correct answer:

 %

Explanation:

Since we are asking for an estimate, one way to work this problem is to round each candidate's vote tally to the nearest thousand, then adding the rounded numbers:

Johnson's share of the vote is about 6,000 of those approximately 14,000 votes, or 

As a percent,  is equal to:

Therefore, 40% is the best estimate of the choices we are given.

Example Question #4 : Analyzing Graphs And Figures

Pie_graph

Five candidates ran for mayor of Madison City; the above circle graph shows the share of the vote that each won. Which of the following would be the most reasonable estimate of the percent of the vote Lyle won?

Possible Answers:

 %

 %

 %

 %

 %

Correct answer:

 %

Explanation:

The sector representing Lyle is roughly one-tenth to one-eighth of the circle - in other words, 10-12 % of it. This is the approximate percent of the vote won by Lyle.

Example Question #1 : Tables

Four candidates ran for mayor of Johnston City. The results are below.

According to a city ordinance, a candidate must win more than 50% of the vote to win the election; if this does not happen, the two candidates who win the most votes will face each other in a runoff election. Based on the above table, which of the following is the outcome of the vote?

Possible Answers:

A runoff will be held between Johnson and Carter.

A runoff will be held between Allen and Carter.

Allen won outright.

Johnson won outright.

A runoff will be held between Johnson and Allen.

Correct answer:

A runoff will be held between Johnson and Allen.

Explanation:

We can determine whether the highest vote-getter, Johnson, won the election outright by comparing Johnson's votes to the sum of the votes of his opponents. The votes won by his opponents sum up to:

Johnson won 5,813 votes. Since ,  he did not win a majority, and he will face the second highest vote-getter, Allen, in a runoff.

Example Question #2 : Tables

Four candidates ran for mayor of Monroe City. The results are below.

According to a city ordinance, a candidate must win more than 50% of the vote to win the election; if this does not happen, the two candidates who win the most votes will face each other in a runoff election. Based on the above graph, which of the following is the outcome of the vote?

Possible Answers:

Boatwright and Van Owen will face each other in a runoff.

Boatwright and Stephens will face each other in a runoff.

Delmar won the election outright.

Boatwright and Delmar will face each other in a runoff.

Boatwright won the election outright.

Correct answer:

Boatwright won the election outright.

Explanation:

We can determine whether the highest vote-getter, Boatwright, won the election outright by comparing Boatwright's votes to the sum of the votes of his opponents. The votes won by his opponents sum up to:

Boatwright won 8,542 votes. Since ,  Boatwright won a majority, and thus won the election outright.

Example Question #3 : Tables

Below is the list of candidates for Student Council president, along with the number of votes each won:

What percent of the students voted for neither Phillips nor Young (nearest tenth)?

Possible Answers:

Correct answer:

Explanation:

 students voted; of those students,  voted for a candidate other than Phillip or Young. To convert this to a percent, use this proportion and solve for  :

 

Example Question #612 : Ssat Middle Level Quantitative (Math)

Below is the list of candidates for Student Council president, along with the number of votes each won:

What percent of the students voted for Jarrow (nearest tenth)?

Possible Answers:

Correct answer:

Explanation:

 students total voted. Out of those, 29 voted for Jarrow. To convert this to a percent, use this proportion and solve for  :

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