All ISEE Middle Level Quantitative Resources
Example Questions
Example Question #11 : Ratio And Proportion
. Which of the following must be equivalent to the ratio ?
(a)
(b)
(c)
(a) only
(b) and (c) only
(b) only
(c) only
(a) only
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.
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