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ISEE Upper Level Quantitative Reasoning › Tables

Questions 1 - 10

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 $\$50$ bill. How much change will she get back?

$\$19.61$

$\$21.60$

$\$29.61$

$\$31.60$

$\$30.39$

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 $\$1.99.$

The price of the beverages after tax is $\$28.40 + 1.99 = \$30.39$ .

The change out of a $\$50$ bill is .

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

$\$19.61$

$\$21.60$

$\$29.61$

$\$31.60$

$\$30.39$

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 $\$1.99.$

The price of the beverages after tax is $\$28.40 + 1.99 = \$30.39$ .

The change out of a $\$50$ bill is .

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.

Classroom table

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

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.

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

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.

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.

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?