ISEE Lower Level Quantitative Reasoning - Whole and Part

Amanda and Adriana each ran four laps around the track in twelve minutes. At the same rate of speed, how long would they need to run twenty-eight laps?

$84\ {minutes}$

$28\ {minutes}$

$36\ {minutes}$

$120\ {minutes}$

Explanation

To solve this problem, one must first determine how long it takes to run one lap. Since it takes twelve minutes to run four laps, divide twelve by four.

$12\div4=3$

It takes three minutes to run one lap.

To determine how long it will take to run twenty-eight laps, multiply the original rate of speed by the new distance.

$3\times28=84$

It will take eighty-four minutes to run twenty-eight laps if each lap is run in three minutes.

What is $\frac{1}{10} %$ of $\frac{1}{10}$ ?

$\frac{1}{10,000}$

$\frac{1}{1,000}$

$\frac{1}{100}$

$\frac{1}{10 }$

Explanation

$\frac{1}{10} %$ of $\frac{1}{10}$ can be rewritten as

$\frac{\frac{1}{10}}{100} \times \frac{1}{10}$

$= \frac{1}{10} \times \frac{1}{100} \times \frac{1}{10} = \frac{1}{10 \times 100 \times 10} = \frac{1}{10,000}$

Jonathan ate $\dpi{100} \frac{1}{4}$ of a carton of ice cream. This is equal to 1 pound of ice cream. How many pounds of ice cream were in the carton of ice cream before Jonathan started eating?

$\dpi{100} 4\ pounds$

$\dpi{100} 1\ pound$

$\dpi{100} 16\ pounds$

$\dpi{100} 2\ pounds$

Explanation

The fraction $\dpi{100} \frac{1}{4}$ means that Jonathan has eaten 1 part out of a possible 4 parts of the carton of ice cream. So we can multiply the amount that he ate (1 pound) by 4 to see that there are 4 pounds of ice cream in a carton.

What is 3.4 rounded to the nearest whole number?

Explanation

A whole number is one in which the one's place is the smallest unit. Therefore, in a whole number, there is no decimal. While any number that ends in a .5 decimal or greater rounds up, anything that is smaller than .5 rounds down. Therefore, would round down to .

A classroom contains 30 students, and there are the same number of boys as girls. If $\frac{1}{5}$ of the boys in the classroom are wearing sandals , how many boys are wearing sandals?

Explanation

If the classroom of 30 students has an equal number of boys and girls, then there are 15 girls and 15 boys.

If $\frac{1}{5}$ of the boys are wearing sandals, then $\frac{1}{5}\cdot15=3$ boys are wearing sandals.

If yoga mats are on buy one get one free, and each mat is priced at $20, what is the average price of a mat, in dollars, if Beth buys four mats?

Explanation

If mats are $20 each but also buy one get one free, each mat will be $10 on average, as long as an even number of yoga mats are purchased. Given that four is an even number, the average price of a yoga mat is $10.

If you buy two books, the third is half off. All books cost $12. What is the average cost of a book if 3 books are purchased (in dollars)?

Explanation

The three books will cost $12, $12, and $6.

Calculate the average:

$\frac{12+12+6}{3}=$10$

Twenty students voted on their favorite sports. Eight students voted for tennis, four voted for basketball, and two voted for swimming. What fraction of the students voted for other sports?

$\frac{3}{10}$

$\frac{6}{14}$

$\frac{10}{12}$

$\frac{3}{20}$

Explanation

To solve this problem, begin by finding the total number of students that voted for tennis, basketball, or swimming.

We are told there are twenty students in the class, and now we know that fourteen of those twenty voted for the three sports mentioned. The remaining students voted for other sports.

Six out of the twenty students, or $\frac{6}{20}$ of the class, voted for other sports.

When we reduce $\frac{6}{20}$ to simplest form (divide the numerator and denominator by two), we get the fraction $\frac{3}{10}$ .

Therefore, $\frac{3}{10}$ of the students voted for other sports.

There are 24 slices of bread in a loaf of bread. If Karl eats $\dpi{100} \frac{1}{3}$ of the loaf of bread, how many slices of bread has he eaten?

$\dpi{100} 8$

$\dpi{100} 12$

$\dpi{100} 24$

$\dpi{100} 10$

Explanation

Karl has eaten 1 part out of a possible 3 parts of the loaf of bread. To find out how big each part is, we divide 24 by the number of parts (3).

$\dpi{100} 24\div 3=8$

So each part would be 8 slices of bread. Karl ate 1 part, so he has eaten 8 slices of bread.

Which of the following numbers is NOT a prime factor of ?

Explanation

All of the answer choices are factors of seventy, but only one is not prime.

A prime number is a number greater than one that has only one and itself as divisors.

Thirty-five is not a prime number, because in addition to being divisible by one and itself, it is also divisible by five and seven. Therefore, the answer is thirty-five.

Whole and Part

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