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SSAT Middle Level Math : How to find the answer from a table

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

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Example Questions

Example Question #1 : Tables

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 Jones will face each other in a runoff.

Mills won the election outright.

Jones and King will face each other in a runoff.

Jones won the election outright.

Mills and King 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.

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Example Question #1 : Tables

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

$\begin{matrix} \textrm{\underline{Candidate}} & \textrm{\underline{Votes}} \\ \textrm{Allen } & 4,128 \\ \textrm{Carter } & 2,177 \\ \textrm{Johnson } & 5,813 \\ \textrm{Wayne } & 1,578 \end{matrix}$ $\displaystyle \begin{matrix} \textrm{\underline{Candidate}} & \textrm{\underline{Votes}} \\ \textrm{Allen } & 4,128 \\ \textrm{Carter } & 2,177 \\ \textrm{Johnson } & 5,813 \\ \textrm{Wayne } & 1,578 \end{matrix}$

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

Possible Answers:

$\displaystyle 20$ %

$\displaystyle 40$ %

$\displaystyle 10$ %

$\displaystyle 30$ %

$\displaystyle 50$ %

Correct answer:

$\displaystyle 40$ %

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:

$\displaystyle 4,178 + 2,177 + 5,813 + 1,578$

$\approx 4,000 + 2,000 + 6,000 + 2,000 = 14,000$ $\displaystyle \approx 4,000 + 2,000 + 6,000 + 2,000 = 14,000$

Johnson's share of the vote is about 6,000 of those approximately 14,000 votes, or $\frac{6,000}{14,000} = \frac{6}{14} = \frac{3}{7}$ $\displaystyle \frac{6,000}{14,000} = \frac{6}{14} = \frac{3}{7}$

As a percent, $\frac{3}{7}$ $\displaystyle \frac{3}{7}$ is equal to:

$\frac{3}{7} \cdot 100 = \frac{300}{7}$ $\displaystyle \frac{3}{7} \cdot 100 = \frac{300}{7}$

$300 \div 7 \approx 43$ $\displaystyle 300 \div 7 \approx 43$

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

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Example Question #1 : Tables

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:

$\displaystyle 5$ %

$\displaystyle 40$ %

$\displaystyle 20$ %

$\displaystyle 10$ %

$\displaystyle 30$ %

Correct answer:

$\displaystyle 10$ %

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.

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Example Question #11 : Analyzing Graphs And Figures

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:

Johnson won outright.

A runoff will be held between Johnson and Carter.

Allen won outright.

A runoff will be held between Allen and Carter.

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:

$\displaystyle 4,128 + 2,177 + 1,578 = 7,883$

Johnson won 5,813 votes. Since $\displaystyle 5,813 < 7,883$, he did not win a majority, and he will face the second highest vote-getter, Allen, in a runoff.

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Example Question #1 : How To Find The Answer From A Table

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

$\begin{matrix} \textrm{\underline{Candidate}} & \textrm{\underline{Votes}} \\ \textrm{Boatwright} & 8,542 \\ \textrm{Delmar} & 3,176 \\ \textrm{Stephens} & 1,753 \\ \textrm{Van Owen} & 2,578 \end{matrix}$ $\displaystyle \begin{matrix} \textrm{\underline{Candidate}} & \textrm{\underline{Votes}} \\ \textrm{Boatwright} & 8,542 \\ \textrm{Delmar} & 3,176 \\ \textrm{Stephens} & 1,753 \\ \textrm{Van Owen} & 2,578 \end{matrix}$

Possible Answers:

Delmar won the election outright.

Boatwright won the election outright.

Boatwright and Delmar will face each other in a runoff.

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

Boatwright and Stephens will face each other in a runoff.

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:

$\displaystyle 3,176 + 1,753 + 2,578 = 7,507$

Boatwright won 8,542 votes. Since $\displaystyle 8,542 > 7,507$, Boatwright won a majority, and thus won the election outright.

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Example Question #5 : Analyzing Graphs And Figures

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

$\begin{matrix} \textrm{\underline{Student}} &\textrm{\underline{Votes}} \\ \textrm{Phillips}\; & 105\\ \textrm{Young}\; \; \;& 83\\ \textrm{Harris}\; \; \; &64 \\ \textrm{McCain}\;& 45\\ \textrm{Zimmer}\; \; & 39 \end{matrix}$ $\displaystyle \begin{matrix} \textrm{\underline{Student}} &\textrm{\underline{Votes}} \\ \textrm{Phillips}\; & 105\\ \textrm{Young}\; \; \;& 83\\ \textrm{Harris}\; \; \; &64 \\ \textrm{McCain}\;& 45\\ \textrm{Zimmer}\; \; & 39 \end{matrix}$

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

Possible Answers:

$56.0 \%$ $\displaystyle 56.0 \%$

$21.3 \%$ $\displaystyle 21.3 \%$

$36.8 \%$ $\displaystyle 36.8 \%$

$78.7 \%$ $\displaystyle 78.7 \%$

$44.0 \%$ $\displaystyle 44.0 \%$

Correct answer:

$44.0 \%$ $\displaystyle 44.0 \%$

Explanation:

$\displaystyle 105+83+64+45+39 = 336$ students voted; of those students, $\displaystyle 64+45+39 = 148$ voted for a candidate other than Phillip or Young. To convert this to a percent, use this proportion and solve for $\displaystyle p$ :

$\frac{p }{100}= \frac{148}{336}$ $\displaystyle \frac{p }{100}= \frac{148}{336}$

$\frac{p }{100} \cdot 100 = \frac{148}{336} \cdot 100$ $\displaystyle \frac{p }{100} \cdot 100 = \frac{148}{336} \cdot 100$

$p = \frac{14,800}{336} \approx 44.0 \%$ $\displaystyle p = \frac{14,800}{336} \approx 44.0 \%$

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Example Question #1 : Tables

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

$\begin{matrix} \textrm{\underline{Student}} &\textrm{\underline{Votes}} \\ \textrm{Kerry}\; \; \; & 95\\ \textrm{Quinn}\; \; \;& 73\\ \textrm{Fellows}\; &54 \\ \textrm{Bester}\; \; & 48\\ \textrm{Jarrow}\; & 29 \end{matrix}$ $\displaystyle \begin{matrix} \textrm{\underline{Student}} &\textrm{\underline{Votes}} \\ \textrm{Kerry}\; \; \; & 95\\ \textrm{Quinn}\; \; \;& 73\\ \textrm{Fellows}\; &54 \\ \textrm{Bester}\; \; & 48\\ \textrm{Jarrow}\; & 29 \end{matrix}$

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

Possible Answers:

$12.4 \%$ $\displaystyle 12.4 \%$

$10.3 \%$ $\displaystyle 10.3 \%$

$9.7 \%$ $\displaystyle 9.7 \%$

$16.1 \%$ $\displaystyle 16.1 \%$

$10.7 \%$ $\displaystyle 10.7 \%$

Correct answer:

$9.7 \%$ $\displaystyle 9.7 \%$

Explanation:

$\displaystyle 95+73+54+48+29= 299$ students total voted. Out of those, 29 voted for Jarrow. To convert this to a percent, use this proportion and solve for $\displaystyle p$ :

$\frac{p }{100}= \frac{29}{299}$ $\displaystyle \frac{p }{100}= \frac{29}{299}$

$\frac{p }{100} \cdot 100= \frac{29}{299}\cdot 100$ $\displaystyle \frac{p }{100} \cdot 100= \frac{29}{299}\cdot 100$

$p= \frac{2,900}{299} \approx 9.7 \%$ $\displaystyle p= \frac{2,900}{299} \approx 9.7 \%$

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Example Question #1 : How To Find The Answer From A Table

Consider the table. On which day of the week is the combined total of Ben and Jason's TV viewing the greatest?

Possible Answers:

Saturday

Thursday

Friday

Sunday

Correct answer:

Sunday

Explanation:

On Sundays, Ben and Jason watch a total of 5.9 hours of TV:

$\displaystyle Total=4.7+1.2=5.9$

They watch less TV on all other days: On Saturdays they watch 5.7 hours, on Fridays they watch 4.5 hours, and on Thursdays they watch 2.4 hours.

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Example Question #1 : Tables

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

What percent of the votes (nearest whole number) were won by the third-place finisher?

Possible Answers:

$19 \%$ $\displaystyle 19 \%$

$31 \%$ $\displaystyle 31 \%$

$13 \%$ $\displaystyle 13 \%$

$25\%$ $\displaystyle 25\%$

$12 \%$ $\displaystyle 12 \%$

Correct answer:

$19 \%$ $\displaystyle 19 \%$

Explanation:

Third place was won by Harris, who won 64 out of $\displaystyle 105+83+64+45+39 = 336$ votes. To rewrite this as a percent, solve this proportion statement for $\displaystyle p$ :

$\frac{p }{100}= \frac{64}{336}$ $\displaystyle \frac{p }{100}= \frac{64}{336}$

$\frac{p }{100} \cdot 100 = \frac{64}{336} \cdot 100$ $\displaystyle \frac{p }{100} \cdot 100 = \frac{64}{336} \cdot 100$

$p= \frac{6,400}{336} \approx 19 \%$ $\displaystyle p= \frac{6,400}{336} \approx 19 \%$

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Example Question #2 : Tables

Graph

The above circle graph shows the results of a school election. According to the rules, the election falls to the student who wins the majority of the votes; if no student wins a majority, the top two vote-getters will face each other in a runoff, with the winner being elected.

Which of the following is the result of this election?

Possible Answers:

Phelps, Creighton, and Wells will face one another in a runoff.

Phelps won the election outright.

None of the other choices is correct.

Phelps and Creighton will face each other in a runoff.

Phelps and Wells will face each other in a runoff.

Correct answer:

Phelps and Creighton will face each other in a runoff.

Explanation:

Since each of the six portions of the graph takes up less than half, no one won a majority. Therefore, there will be a runoff. The two largest portions are light blue (Phelps) and orange (Creighton), so Phelps and Creighton got the most and second-most votes, and they will face each other in a runoff.

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SSAT Middle Level Math : How to find the answer from a table

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #1 : Tables

Example Question #1 : Tables

Example Question #1 : Tables

Example Question #11 : Analyzing Graphs And Figures

Example Question #1 : How To Find The Answer From A Table

Example Question #5 : Analyzing Graphs And Figures

Example Question #1 : Tables

Example Question #1 : How To Find The Answer From A Table

Example Question #1 : Tables

Example Question #2 : Tables

All SSAT Middle Level Math Resources

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