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

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Question

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

Answer

40% of 80 can be calculated as

,

so Kevin will give his brother 32 marbles and keep

marbles.

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Question

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?

Answer

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.

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Question

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?

Answer

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.

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Question

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)?

Answer

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

Calculate the average:

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Question

Find % of of .

Answer

First, we need to find of . Multiply to get .

Then, we need to find of . Multiply to get .

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Question

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

Answer

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.

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Question

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?

Answer

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.

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Question

If the probability of Ms. Jones calling on a male student during class is , and there are students in the class, how many students are female?

Answer

There are students in Ms. Jones' class. Since the probability of her calling on a male student is , we must first find of .

Now we must reduce by dividing both the top and bottom by .

is the same as , so there are male students in Ms. Jones' class. In order to find the number of female students in Ms. Jones' class, we must subtract from the total number of students in the class, which is .

There are female students in Ms. Jones' class.

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Question

What is 62% of 23? Round to the nearest tenths place.

Answer

To find the part from the whole, you will need to multiply the whole (23) by the percent. In order to do this, first change the percent to a decimal (62% becomes 0.62).

The question askes you to round to the nearest tenths place: 14.26 becomes 14.3.

Therefore, 62% of 23 is 14.3.

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Question

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?

Answer

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 of the class, voted for other sports.

When we reduce to simplest form (divide the numerator and denominator by two), we get the fraction .

Therefore, of the students voted for other sports.

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Question

What is of ?

Answer

of can be rewritten as

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Question

What is of ?

Answer

of can be rewritten as

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Question

What is of ?

Answer

of can be rewritten as

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Question

If Barbara's eyeshadow costs 15 dollars after being discounted 25%, what was the original price?

Answer

25% of 20 is equal to . Therefore, if the eyeshadow cost $20, it would be discounted by $5 (the equivalent of 25% off).

Given that , the correct answer is .

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Question

In the number , in what place is the 6?

Answer

The number 6 is the thousand's place because is written in words as seventy-six thousand, four hundred, thirty-five.

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Question

Brett and Bob love to ski. They planned on a 5 day ski trip together, but Brett decided to stay 40% longer than they had originally planned. How many extra days did Brett stay?

Answer

If Bob and Brett planned a 5 day ski trip, then 2 days would make the trip 40 percent longer.

This is because 2 extra days out of 5 is equal to . The percent equivalent of .4 is 40 percent. Therefore, 2 is the correct answer.

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Question

If there are 15 cookies in a tin, and Rebecca gives 5 of the cookies to her mother and one fifth of the remaining cookies to her father, how many cookies remain?

Answer

If there are 15 cookies in a tin, and Rebecca gives 5 of the cookies to her mother, then 10 cookies remain. She gives one fifth of them, or 2 cookies, to her father.

Therefore, 8 cookies remain.

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Question

If Rebecca has watched 6 and a half minutes of a video that is one hour and five minutes long, what percentage of the video has she watched?

Answer

Rebecca has watched 6 and a half minutes of a video that is one hour and five minutes long, which can also be written as 6.5 minutes of a video that is 65 minutes long.

Given that , Rebecca has watched 10% of the video.

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Question

A pizza contains 12 slices. Becky eats of the pizza. How many slices does she eat?

Answer

Becky eats of a pizza, which contains 12 pieces. You can find the total number that she eats by multiplying the fraction by the whole:

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Question

Jamie and Austin share a large pizza. The pizza is sliced up into 12 equal pieces. If Jamie eats 1/4 of the pizza and Austin eats twice as many slices as Jamie eats, how many slices of pizza are remaining?

Answer

Begin with the amount of pizza that Jamie eats. Because there are 12 slices in a whole pizza, Jamie eats 3 slices, or 1/4 of the entire pizza.

1/4 of 12 slices =

1/4 x 12 =

3 slices

If Austin eats twice as much as Jamie, that means that he eats

3 x 2

6 slices

To find how many slices are remaining,

we would subtract 3 and 6 from 12.

12 – 3 – 6 = 3

3 pizza slices are remaining.

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