ISEE Lower Level Quantitative Reasoning - How to find the part from the whole

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

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

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

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.

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.

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}=$10$

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.

Brianna's favorite song is 2 and a half minutes. There is a drum solo that begins one third of the way into the song and lasts for 24 seconds. How many seconds into the song does the drum solo end?

Explanation

If a song is 2 and a half minutes long, it is 150 seconds long. If the drum solo starts one third of the way into the song, it will begin at the 50 second mark, since 50 is one third of 150.

Since the drum solo lasts for 24 seconds, it will end at the 74 second mark. Therefore, 74 is the correct answer.

Kevin has 80 marbles and wants to give his brother 40% of them. How many will he keep?