ISEE Middle Level Quantitative : How to find a ratio

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

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Example Questions

Example Question #11 : Ratio And Proportion

. Which of the following must be equivalent to the ratio ?

(a) 

(b) 

(c) 

Possible Answers:

(a) only

(b) and (c) only

(b) only

(c) only

Correct answer:

(a) only

Explanation:

Two ratios are equivalent if and only if their cross products are equal. Set  equal to each choice in turn and find their cross products:

(a) 

The cross products are equal, so regardless of the value of , the ratios are equivalent.

 

(b) 

The cross products are equal if and only if , so the ratios are not equivalent.

 

 

(c) 

The cross products are equal if and only if , so the ratios are not equivalent.

 

The correct response is (a) only.

Example Question #201 : Numbers And Operations

In a bowl of  pieces of fruit,  are apples. The rest are kiwis. If the number of apples is doubled, what is the ratio of kiwis to the total number of fruit in the newly enlarged quantity of fruit in the bowl.

Possible Answers:

Correct answer:

Explanation:

We know that  of the total  pieces of fruit are apples. This means that there are:

 apples.

Thus far, we know that we must have:

 apples

and

 kiwis

Now, if we double the apples, we will have:

 apples

and

 kiwis

This means that the proportion of kiwis to total fruit will be:

 or , which can be reduced to 

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