All ISEE Middle Level Quantitative Resources
Example Questions
Example Question #1 : How To Find A Ratio
On Katy's facebook page, she has friends who are girls,
friends that are boys,
friends from her home town, and 100 friends that are from Michigan. What is the ratio of girl to friends from Michigan?
Katy has friends that are girls and
friends from Michigan, so the ratio is
. When we divide both numbers by fifty to simplify, the ratio becomes
, since
and
.
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
(a) is greater
(b) is greater
It is impossible to tell from the information given
(a) and (b) are equal
(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 #1 : Ratio And Proportion
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
(a) and (b) are equal
(a) is greater
It is impossible to tell from the information given
(b) is greater
(a) is greater
Travis drove 40 miles in three-fourths of an hour, so we can divide:
miles per hour,
which is less than 55.
Example Question #1 : 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)
(a) is greater
(a) and (b) are equal
It is impossible to tell from the information given
(b) is greater
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 can be calculated using proportion statements.
The minimum:
The maximum:
It is therefore unclear whether the map distance is greater than or less than 5 inches.
Example Question #191 : Numbers And Operations
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 boys and
girls. This means that there is a total of
people in the room. The ratio of girls to boys would be
.
Example Question #192 : 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
Example Question #1 : Ratio And Proportion
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, of them are cars. To find the number of SUVs, multiply
by
(a quarter) and get
SUVs. To find the number of motorcycles, multiply
by
to get
. Finally, there is
% remaining for trucks; therefore, multiply
by
to get
.
Now, if this is doubled, we have trucks. This means that the total number of vehicles is:
vehicles
Therefore, the ratio of motorcycles to total vehicles will be:
Reducing this, you get:
Example Question #2 : How To Find A Ratio
and
are positive.
The ratios 125 to and
to 125 are equvalent.
Which is the greater quantity?
(b) is the greater quantity
(a) and (b) are equal
It is impossible to determine which is greater from the information given
(a) is the greater quantity
It is impossible to determine which is greater from the information given
The ratios 125 to and
to 125 are equvalent, so
By the cross-product property,
Without any futher information, however, it cannot be determined which of and
is the greater. For example,
and
fits the condition, as does the reverse case.
Example Question #1 : How To Find A Ratio
and
are positive.
The ratios 20 to and
to 40 are equvalent.
Which is the greater quantity?
(a)
(b)
It is impossible to determine which is greater from the information given
(a) and (b) are equal
(b) is the greater quantity
(a) is the greater quantity
It is impossible to determine which is greater from the information given
The ratios 20 to and
to 40 are equvalent, so
By the cross-product property,
Without any futher information, however, it cannot be determined which of and
is the greater. For example,
and
fits the condition, as does the reverse case.
Example Question #1 : How To Find A Ratio
and
are positive. 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
(b) is the greater quantity
The cross products of two equivalent fractions are themselves equivalent, so if
then
Multiply by 6:
Since , it follows that
, and by substitution,
.
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All ISEE Middle Level Quantitative Resources
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