ISEE Middle Level Quantitative : How to find a ratio
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All ISEE Middle Level Quantitative Resources
Example Questions
Example Question #1 : How To Find A Ratio
On Katy's facebook page, she has 
Katy has 
Example Question #1 : How To Find A Ratio
Mike drove 120 miles to his mother's house. He finished the trip in two hours and 15 minutes. It took him one hour to drive the first 50 miles.
Which is the greater quantity?
(a) Mike's average speed over the first 50 miles
(b) Mike's average speed over the last 70 miles
It is impossible to tell from the information given
(a) and (b) are equal
(a) is greater
(b) is greater
(b) is greater
We can compare miles per hour.
(a) 50 miles over a one-hour period is 50 miles per hour.
(b) 70 miles over a one-and-one-fourth-hour period is
Mike drove an average of 56 miles per hour over the last 70 miles, making (b) greater.
Example Question #2 : How To Find A Ratio
Travis took 45 minutes to drive a total of 40 miles.
Which is the greater quantity?
(a) 55 miles per hour
(b) The average rate at which Travis drove
(b) is greater
It is impossible to tell from the information given
(a) and (b) are equal
(a) is greater
(a) is greater
Travis drove 40 miles in three-fourths of an hour, so we can divide:
which is less than 55.
Example Question #4 : How To Find A Ratio
The distance between Wilsonville and Coleman is 320 miles and is represented by six inches on a map. The distance between Wilsonville and Garrett is 120 miles.
Which is the greater quantity?
(a) The distance between Coleman and Garrett on the map
(b)
(b) is greater
(a) and (b) are equal
(a) is greater
It is impossible to tell from the information given
It is impossible to tell from the information given
The closest that Coleman and Garrett can be to each other is 200 miles (if Garrett is between Wilsonville and Coleman); the farthest is 440 miles (if Wilsonville is between Coleman and Garrett).
Call the map distance between Coleman and Garrett 
The two extremes of 
The minimum:
The maximum:
It is therefore unclear whether the map distance is greater than or less than 5 inches.
Example Question #1 : How To Find A Ratio
There are fifteen boys in a room and twelve girls. Five more girls enter. What is the ratio of girls to total students in the room after this change occurs?
After the new girls enter the room, you have 
Example Question #2 : How To Find A Ratio
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 #3 : How To Find A Ratio
In a given neighborhood, there are 200 vehicles. Half of these are cars, a quarter are SUVs, five percent are motorcycles, and the remaining amount are trucks. If the number of trucks are doubled, what is the ratio of motorcycles to total vehicles?
You just need to work this through step-by-step.
We know that half of the vehicles are cars; therefore, 
Now, if this is doubled, we have 
Therefore, the ratio of motorcycles to total vehicles will be:
Reducing this, you get:
Example Question #8 : How To Find A Ratio
The ratios 125 to 
Which is the greater quantity?
(a) is the greater quantity
(a) and (b) are equal
(b) is the greater quantity
It is impossible to determine which is greater from the information given
It is impossible to determine which is greater from the information given
The ratios 125 to 
By the cross-product property,
Without any futher information, however, it cannot be determined which of 
Example Question #9 : How To Find A Ratio
The ratios 20 to
Which is the greater quantity?
(a)
(b)
(b) is the greater quantity
(a) is the greater quantity
It is impossible to determine which is greater from the information given
(a) and (b) are equal
It is impossible to determine which is greater from the information given
The ratios 20 to
By the cross-product property,
Without any futher information, however, it cannot be determined which of 
Example Question #10 : How To Find A Ratio
(a)
(b)
It is impossible to determine which is greater from the information given
(a) is the greater quantity
(b) is the greater quantity
(a) and (b) are equal
(b) is the greater quantity
The cross products of two equivalent fractions are themselves equivalent, so if
then
Multiply by 6:
Since 
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All ISEE Middle Level Quantitative Resources
