SSAT Middle Level Math : How to find the part from the whole

Study concepts, example questions & explanations for SSAT Middle Level Math

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Example Questions

Example Question #21 : How To Find The Part From The Whole

Sweaters are  each, but they are on sale: when you buy one, you get one free. Rebecca buys one sweater and gets one free. At checkout, she then presents a coupon for an additional  off. What is the average cost of one sweater in dollars (before tax)?

Possible Answers:

Correct answer:

Explanation:

If Rebecca buys a  sweater that is part of a buy one, get one free sale, that means that she will get two sweaters for a total of . A  off discount will mean that Rebecca will save  off of her total because  of  is .

Therefore, the total she will pay is equal to

The average price of a sweater will therefore be .

Example Question #61 : Numbers And Operations

 of the students in a classroom of  students are boys.  of the girls in this classroom wear their hair in pigtails. How many girls wear their hair in pigtails?

Possible Answers:

Correct answer:

Explanation:

If  of the students in a classroom of  students are boys, that means that  students are boys, since . (Alternatively, you could figure this out by realizing that since  of  is  and ,  of  must equal , which is .) If there are  boys in the classroom, there must be  girls, since .

 Given that  of the girls wear their hair in pigtails, and  of  is , it follows that there are  girls in the classroom who wear their hair in pigtails.

Example Question #62 : Numbers And Operations

If the sum of 3 consecutive numbers is 111, what is the value of the middle number?

Possible Answers:

Correct answer:

Explanation:

The sum of  . The easiest way to discover the middle number of this set is to divide 111 by 3:

 

Now that you have the middle number, simply add one to it and subtracy one from it to get your consecutive numbers:

Example Question #24 : How To Find The Part From The Whole

3 brothers weigh 80 pounds, 120 pounds, and 135 pounds. The smallest brother gained 15 pounds over the past year, while the largest brother lost 5 pounds. The middle brother's weight did not change. Based on the brothers' new weights, what is their average weight?

Possible Answers:

Correct answer:

Explanation:

If 3 brothers weigh 80 pounds, 120 pounds and 135 pounds, and the smallest brother gained 15 pounds over the past year, while the largest brother lost 5 pounds, the new weights of the brothers are:

95 pounds, 120 pounds, and 130 pounds.  (The middle brother's weight did not change.)

Given that the average is found by dividing the sum of the numbers in a list by the number of items in that list, the following equation will be used:

Therefore, the new average is 115 pounds. 

Example Question #201 : Whole And Part

If 25 percent of a number is 3, then what would two thirds of the same number be equal to?

Possible Answers:

Correct answer:

Explanation:

If 25 percent of a number is 3, then that means that 100 percent of the number will be equal to 3 times 4, which is 12. Two thirds of the number 12 is 8; therefore, 8 is the correct answer. 

Example Question #31 : How To Find The Part From The Whole

Amanda has 3 more marbles than Jason and 5 fewer marbles than Kate. Together, they all have 17 marbles. How many marbles does Amanda have?

Possible Answers:

4 marbles

7 marbles

5 marbles

6 marbles

Correct answer:

5 marbles

Explanation:

Amanda has 3 more marbles than Jason and 5 fewer marbles than Kate. Together, they all have 17 marbles. 

To solve this problem, we should experiment by picking a number for Amanda. We can pick the number 4. 

If Amanda has 4 marbles, this means that Jason has 1 marble, since Amanda has 3 more. If she has 5 fewer marbles than Kate, that means that Kate must have 9 marbles. 

This leaves us with:

Amanda - 4 marbles 

Jason - 1 marble

Kate - 9 marbles

This adds up to a total of 14 marbles. However, we know that there are a total of 17 marbles. Thus, each child must have 1 more marble than what is stated above. The correct information would be below:

Amanda - 5 marbles 

Jason - 2 marble

Kate - 10 marbles

Here, the sum of the marbles is 17 and Amanda still has 3 more marbles that Jason and 5 fewer marbles that Kate. 

Thus, the correct answer is that Amanda has 5 marbles.

Example Question #21 : Whole And Part

Stephanie needs to drive  miles to meet her family at their vacation home. If she drives at  miles per hour, how many hours will it take Stephanie to arrive?

Possible Answers:

Correct answer:

Explanation:

Divide: 

Answer: It will take Stephanie  hours to arrive.

Example Question #32 : How To Find The Part From The Whole

Eighteen dollars must be shared among  friends. How much money will each friend receive?

Possible Answers:

Correct answer:

Explanation:

Divide:

Answer: Each friend will receive .

Example Question #31 : How To Find The Part From The Whole

Round  to the nearest hundredth.

 

 

Possible Answers:

Correct answer:

Explanation:

When we round a number to the nearest hundredth we look to the thousandths place to tell us if we round up or down.

If the number in our thousandths place is  or greater, we round up. If the number in the thousandths place is  or less, we round down. When we round up, the number in the thousandths place increases by  and all the other numbers to the right become . When we round down, the number in the thousandths place stays the same and all the other numbers to the right become .

In this case,  is greater than  so our rounded number is  or 

Example Question #11 : Round Decimals: Ccss.Math.Content.5.Nbt.A.4

Round  to the nearest hundredth.

 

 

Possible Answers:

Correct answer:

Explanation:

When we round a number to the nearest hundredth we look to the thousandths place to tell us if we round up or down.

If the number in our thousandths place is  or greater, we round up. If the number in the thousandths place is  or less, we round down. When we round up, the number in the thousandths place increases by  and all the other numbers to the right become . When we round down, the number in the thousandths place stays the same and all the other numbers to the right become .

In this case,  is less than  so our rounded number is  or 

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