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

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

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Example Questions

Example Question #41 : How To Find The Whole From The Part

Last year, Alex could run a mile in 10 minutes. If Alex was able to reduce his mile time by 2 minutes this year, how many miles could he run in 24 minutes?

Possible Answers:

\(\displaystyle 4\)

\(\displaystyle 3\)

\(\displaystyle 4.5\)

\(\displaystyle 3.5\)

Correct answer:

\(\displaystyle 3\)

Explanation:

Given that Alex was previously able to run a mile in 10 minutes, if he improved his time by 2 minutes, that means he could run a mile in 8 minutes. If he had 24 minutes to run, he would be able to run 3 miles, as 24 divided by 8 is 3. 

Example Question #42 : How To Find The Whole From The Part

Ariel bought 18 pieces of fruit. One third of the pieces of fruit she bought were apples. One half of the apples were bruised. How many bruised apples were there?

Possible Answers:

\(\displaystyle 4\)

\(\displaystyle 2\)

\(\displaystyle 3\)

\(\displaystyle 6\)

Correct answer:

\(\displaystyle 3\)

Explanation:

If one third of the fruit that Ariel bought were apples, she bought 6 apples because 6 is one third of 18, the total pieces of fruit that she bought. 

If one half of the 6 apples were bruised, this means that 3 of the apples were bruised. 

Example Question #43 : How To Find The Whole From The Part

How many times can the fraction \(\displaystyle \frac{2}{3}\) go into the number 6?

Possible Answers:

\(\displaystyle 9\)

\(\displaystyle 12\)

\(\displaystyle 25\)

\(\displaystyle 18\)

Correct answer:

\(\displaystyle 9\)

Explanation:

This problem can be solved using mental math. In the number 6, we can find the amount of thirds contained within it by multipling 6 and 3, which gives us 18. 

If there are 18 values of \(\displaystyle \frac{1}{3}\) within 6, then it makes sense that there would be half as many \(\displaystyle \frac{2}{3}\) values, giving us a value of 9. The correct answer is therefore 9. 

Example Question #1035 : Isee Middle Level (Grades 7 8) Mathematics Achievement

A store bought a statue for \(\displaystyle \$90.00\) and decided to sell it for a price \(\displaystyle 50\%\) higher than the price at which it was bought. A customer then purchased the statue. How much profit did the store make in dollars from the sale of the statue?

Possible Answers:

\(\displaystyle \$45.00\)

\(\displaystyle \$35.00\)

\(\displaystyle \$25.00\)

\(\displaystyle \$55.00\)

Correct answer:

\(\displaystyle \$45.00\)

Explanation:

Given that \(\displaystyle 50\%\) of \(\displaystyle 90\) is \(\displaystyle 45\), a \(\displaystyle 50\%\) price increase for a \(\displaystyle \$90.00\) statue would mean that the statue's new, increased price \(\displaystyle \$90.00+\$45.00=\$135.00\)

A customer bought the statue for \(\displaystyle \$135.00\) and the store originally paid \(\displaystyle \$90.00\) for the statue, so the store's total profit equals \(\displaystyle \$135.00-\$90.00=\$45.00\).

 

Example Question #44 : How To Find The Whole From The Part

If you know that male students make up \(\displaystyle 75\)\(\displaystyle \%\) of a class and there are \(\displaystyle 45\) of them, what is to total amount of students?

Possible Answers:

\(\displaystyle 45\)

\(\displaystyle 15\)

\(\displaystyle 60\)

\(\displaystyle 30\)

\(\displaystyle 75\)

Correct answer:

\(\displaystyle 60\)

Explanation:

You can set up a ratio for this problem in fraction form.  

The \(\displaystyle 45\) male students would go over \(\displaystyle x\) amount of total students,\(\displaystyle \frac{45}{x}\).  

\(\displaystyle 75\)\(\displaystyle \%\) would be written as \(\displaystyle \frac{3}{4}\).  

Your ratio would be,

 \(\displaystyle \frac{45}{x}=\frac{3}{4}\) 

and you can cross multiple.  

This would give you \(\displaystyle 180=3x\).  

To solve for \(\displaystyle x\), you would divide each side by \(\displaystyle 3\) and your answer would be \(\displaystyle 180/3=60\)

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