### All ISEE Middle Level Quantitative Resources

## Example Questions

### Example Question #1 : Ratio And Proportion

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?

**Possible Answers:**

**Correct answer:**

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 #2 : 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

**Possible Answers:**

(b) is greater

It is impossible to tell from the information given

(a) is greater

(a) and (b) are equal

**Correct answer:**

(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

**Possible Answers:**

(a) is greater

(a) and (b) are equal

(b) is greater

It is impossible to tell from the information given

**Correct answer:**

(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 : Ratio And Proportion

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)

**Possible Answers:**

(b) is greater

It is impossible to tell from the information given

(a) is greater

(a) and (b) are equal

**Correct answer:**

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 #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?

**Possible Answers:**

**Correct answer:**

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 #3 : How To Find A Ratio

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:**

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 #4 : 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?

**Possible Answers:**

**Correct answer:**

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 #1 : How To Find A Ratio

and are positive.

The ratios 125 to and to 125 are equvalent.

Which is the greater quantity?

**Possible Answers:**

It is impossible to determine which is greater from the information given

(b) is the greater quantity

(a) is the greater quantity

(a) and (b) are equal

**Correct answer:**

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)

**Possible Answers:**

(a) and (b) are equal

(a) is the greater quantity

(b) is the greater quantity

It is impossible to determine which is greater from the information given

**Correct answer:**

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 : Ratio And Proportion

and are positive. Which is the greater quantity?

(a)

(b)

**Possible Answers:**

(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

**Correct answer:**

(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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