ISEE Middle Level Quantitative : Ratio and Proportion
Study concepts, example questions & explanations for ISEE Middle Level Quantitative
All ISEE Middle Level Quantitative Resources
Example Questions
Example Question #11 : Ratio And Proportion
(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 
(a)
The cross products are equal, so regardless of the value of 
(b)
The cross products are equal if and only if 
(c)
The cross products are equal if and only if 
The correct response is (a) only.
Example Question #11 : Ratio And Proportion
In a bowl of 
We know that 
Thus far, we know that we must have:
and
Now, if we double the apples, we will have:
and
This means that the proportion of kiwis to total fruit will be:
Example Question #1 : How To Find A Proportion
The distance between Carson and Miller is 260 miles and is represented by four inches on a map. The distance between Carson and Davis is 104 miles.
Which is the greater quantity?
(a) The distance between Carson and Davis on the map
(b)
(a) is greater
It is impossible to tell from the information given
(b) is greater
(a) and (b) are equal
(a) is greater
Let 
Solve for 
Carson and Davis are 
Example Question #12 : Ratio And Proportion
The distance between Vandalia and Clark is 250 miles and is represented by six inches on a map. The distance between Vandalia and Ferrell is represented by three and three-fifths inches on a map.
Which is the greater quantity?
(a) The actual distance between Vandalia and Ferrell
(b) 150 miles
(a) is greater
(a) and (b) are equal
(b) is greater
It is impossible to tell from the information given
(a) and (b) are equal
Let 
Solve for 
The actual distance between Vandalia and Ferrell is 150 miles.
Example Question #2 : How To Find A Proportion
Jay has a shelf of books, of which 60% are hardback. The rest are paperback. If 12 are hardback, how many paperbacks are there?
There are a couple different ways to solve this problem. One way is to set up an equation from the given equation. Essentially, you have to find the total number of books before you can find how many paperbacks. An equation for that could be 
Example Question #4 : How To Find A Proportion
A given recipe calls for 
This is an easy case of proportions. To triple the recipe, you merely need to triple each of its component parts; therefore, you will have:
Summing these up, you get:
Example Question #13 : Ratio And Proportion
A witch's brew contains 
To solve this, you need to set up a proportion:
Multiply both sides by 
Simplifying, this gives you:
Example Question #6 : How To Find A Proportion
Isidore could buy 
For this problem, set up a proportion:
To solve this, multiply both sides by 
Example Question #2 : How To Find A Proportion
Refer to the above diagram. How many squares should be shaded in if it is desired that the fraction of the squares that are shaded in should be equivalent to the fraction of the circles that are shaded in?
There are four circles, three of which are shaded; there are eight squares. If we let 
Example Question #14 : Ratio And Proportion
Which is the greater quantity?
(a)
(b)
(b) is the greater quantity
It is impossible to determine which quantity is the greater from the information given
(a) and (b) are equal
(a) is the greater quantity
(a) is the greater quantity
From a property of proportions, if 
All ISEE Middle Level Quantitative Resources
