ISEE Upper Level Quantitative Reasoning - How to find the answer from a table

The following is a portion of the menu at a coffee shop:

$\begin{matrix} \textrm{\underline{Item}}& \textrm{\underline{Price}}\ \textrm{Latte} & $2.89\ \textrm{Americano} &$2.49 \ \textrm{Cappucino} & $2.79\ \textrm{Espresso} & $3.19\ \textrm{Turkish} & $ 3.09 \end{matrix}$

A boss treats her employees to coffee at this coffee shop. She orders three lattes, three Americanos, two espressos, a cappucino, and a Turkish coffee. The tax is . The boss hands the cashier a bill. How much change will she get back?

Explanation

Add the prices of the ten items:

$\begin{matrix} $2.89 \ \ 2.89\ \2.89\ \2.49\ \2.49\ \2.49\ \3.19\ \3.19\ \2.79\ \underline{\3.09}\28.40 \end{matrix}$

of this is $$ 28.40 \times 0.07 = 1.988 \approx 1.99$ , so the tax is

The price of the beverages after tax is .

The change out of a bill is .

Classroom table

Jefferson Elementary School has seven eighth-grade teachers; each teacher has the number of boys and girls listed above.

How many teachers have classes in which at least 40% of the students are boys?

Six

Five

Seven

Four

Explanation

Five teachers each have 30 students, and 40% of 30 is

$30 \times 40 % = 30 \times 0.4 = 12$ .

Two teachers each have 29 students, and 40% of 29 is

$2 9 \times 40 % = 30 \times 0.4 = 11.6$ .

Therefore, to have a class that is at least 40% boys, a teacher must have 12 boys at minimum. Only Mr. Georghiou does not have at least 12 boys, so the correct response is six.

Classroom table

Washington Elementary School has seven eighth-grade teachers; each teacher has the number of boys and girls listed above.

An eighth-grade girl has transferred from another school. It is desired that no teacher have more than thirty students overall or eighteen girls in his or her class. Of the seven teachers, how many could accept the girl into his or her class?

One

Two

Six

Seven

Explanation

We can eliminate Cermak and Georghiou immediately since each has eighteen girls in his class. Of the other five:

Adams has students;

Boyer has students;

Donovan has students;

Esterhaus has students;

Finnegan has students.

Only Mrs. Finnegan's class could accept the new girl without going against the wishes of the school. The correct response is one.

Pie_graph

Refer to the above circle graph. There are voters registered as independents in Smith County; to the nearest hundred, how many voters in all are registered?

It is impossible to tell from the information given.

Explanation

Set to the number of voters total. of them are independent - these number , so we can set up the equation:

$0.4 V \div 0.4= 3,471 \div 0.4$

$V\approx 8,678$ , so the correct choice is .

Scrabble

A popular word game uses one hundred tiles, each of which is marked with a letter or a blank. The distribution of the tiles is shown above, with each letter paired with the number of tiles marked with that letter. Notice that there are two blank tiles.

All of the consonant tiles are placed in a box. It is desired to place just enough of the vowel tiles so that the probability of drawing a vowel is $\frac{1}{3}$ . How many vowels must be placed in the box?

Note: for purposes of this question, "Y" is a consonant.

Explanation

There are nine "A" tiles, twelve "E" tiles, nine "I" tiles, eight "O" tiles, and four "U" tiles. This is a total of

There are also two blanks, so the number of tiles marked with consonants is

For the probability of drawing a vowel tile to be $\frac{1}{3}$ , the ratio of consonant tiles to vowel tiles must be

$\frac{3-1}{1} = \frac{2}{1}$ - that is, 2 to 1.

If we let stand for the number of vowel tiles to be added, then

$\frac{56}{V} = \frac{2}{1}$

$\frac{56}{V} \cdot \frac{V}{2} = \frac{2}{1} \cdot \frac{V}{2}$

vowel tiles.

High and low

Refer to the above graph, which shows the high and low temperatures for Kingdom City over a one-week period. The temperatures at left are given in degrees Fahrenheit.

Temperatures given in degrees Fahrenheit can be converted to the Celsius scale using the formula

$C= \frac{5}{9}(F-32)$

Express the highest temperature of the week in degrees Celsius (nearest whole degree).

$26 ^{\circ } C$

$16 ^{\circ } C$

$21 ^{\circ } C$

$31 ^{\circ } C$

Explanation

As can be seen below, the highest temperature for the week was 78 degrees Fahrenheit, on Tuesday.

High and low 2

To convert this to degrees Celsius, set and substitute in the given formula:

$C= \frac{5}{9}(F-32)$

$C= \frac{5}{9}(78-32) = \frac{5}{9} \cdot 46= 25 \frac{5}{9}^{\circ }C$ . The correct choice is $26 ^{\circ } C$ .

Nine students are running for student council; each member of the student body will vote for four. Freida's boyfriend Greg is running and she wants to vote for him. How many ways can she cast a ballot so that she can include Greg among her choices?

Explanation

Since Freida has already chosen one of the nine candidates, she will choose three of the remaining eight, Since order is unimportant, the number of ways to do this is the number of combinations of three chosen from eight.

$C (8,3) = \frac{8!}{(8-3)!; 3!}= \frac{8!}{5!; 3!} = \frac{40,320}{120 \cdot 6 } = 56$

Temperature

Refer to the above graph, which shows the high temperatures in the town of Smithville over seven days.

On how many days that week did Smithville see a peak temperature 75 degrees or greater?

Explanation

There were four days that saw a peak temperature of 75 degrees or greater:

Monday: 76 degrees

Tuesday: 80 degrees

Wednesday: 77 degrees

Friday: 78 degrees

The beverage menu from a restaurant reads as follows:

$\begin{matrix} \textrm{\underline{Beverage}} & \textrm{\underline{Price}} \ \textrm{Soda}& $1.29 \ \textrm{Iced Tea} & $1.39 \ \textrm{Coffee} & $1.69 \ \textrm{Hot Tea} & $1.59 \ \textrm{Milk} & $1.49 \end{matrix}$

Ten friends go out for drinks. They order four sodas, two coffees, two iced teas, a milk, and a hot tea. One of the ten agrees to leave the entire amount of the tip, which is to be 20% of the check. What is the amount of the tip (round to the nearest dime)?

Explanation

The costs of the beverages will be as follows:

$\begin{matrix} \textrm{4 Sodas}& \4 \times $1.29 = $5.16 \ \textrm{2 Iced Teas} & 2 \times $1.39 = $2.78 \ \textrm{2 Coffees} &2 \times $1.69 = $3.38 \ \textrm{1 Hot Tea} & $1.59 \ \textrm{1 Milk} & $1.49 \end{matrix}$

Add these amounts:

$\begin{matrix} ; $5.16\ ; ; 2.78\ ; ; 3.38\ ; ; 1.59\; ; \underline{1.49}\ $14.40 \end{matrix}$

20% of $14.40 is $14.40 \times 0.20 = 2.88$ , or $2.90 when rounded to the nearest dime.

Temperature

Refer to the above graph, which shows the high temperatures in the town of Smithville over seven days.

Which day of this week saw the highest peak temperature?

Tuesday

Wednesday

Thursday

Monday

Friday

Explanation

The highest point on the line graph is located at Tuesday.

How to find the answer from a table

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