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Questions 1 - 10

On a particular November day, it is $75^\circ F$ and sunny in Tucson, Arizona. On the eastern side of the United States, it is $-31^\circ F$ and sleeting in New Castle, Pennsylvania. How many degrees warmer is it in Tucson than New Castle?

$106^\circ F$

$160^\circ F$

$116^\circ F$

$86^\circ F$

$76^\circ F$

Explanation

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is $31^\circ F$ below zero and in Tucson it is $75^\circ F$ above zero; therefore we can say:

$31+75=106^\circ F$

Also, we can solve this problem by using a number line. New Castle’s temperature is units away from zero and Tucson’s is units away.

Temp3

We can see that Tucson is $106^\circ F$ warmer than New Castle.

On a particular November day, it is $110^\circ F$ and sunny in Tucson, Arizona. On the eastern side of the United States, it is $-15^\circ F$ and sleeting in New Castle, Pennsylvania. How many degrees warmer is it in Tucson than New Castle?

$125^\circ F$

$152^\circ F$

$150^\circ F$

$115^\circ F$

$80^\circ F$

Explanation

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is $15^\circ F$ below zero and in Tucson it is $110^\circ F$ above zero; therefore we can say:

$15+110=125^\circ F$

Also, we can solve this problem by using a number line. New Castle’s temperature is units away from zero and Tucson’s is units away.

Temp10

We can see that Tucson is $125^\circ F$ warmer than New Castle.

On a particular November day, it is $65^\circ F$ and sunny in Tucson, Arizona. On the eastern side of the United States, it is $-23^\circ F$ and sleeting in New Castle, Pennsylvania. How many degrees warmer is it in Tucson than New Castle?

$88^\circ F$

$87^\circ F$

$78^\circ F$

$98^\circ F$

$97^\circ F$

Explanation

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is $23^\circ F$ below zero and in Tucson it is $65^\circ F$ above zero; therefore we can say:

$23+65=88^\circ F$

Also, we can solve this problem by using a number line. New Castle’s temperature is units away from zero and Tucson’s is units away.

Temp1

We can see that Tucson is $88^\circ F$ warmer than New Castle.

A candymaker has two machines. One can turn out one hundred pieces of divinity in one hour; the other, an older machine, can do the same in one hour and twenty minutes. Working together and starting at the same time, how many hours would it take for them to make 10,000 pieces of divinity?

Choose the closest answer.

Explanation

The newer machine can make 100 pieces of divinity per hour. The older machine makes 100 pieces in one hour twenty minutes, or, equivalently, one and one third hours, which is

$100 \div 1 \frac{1}{3} = 100 \div \frac{4}{3} = 100 \times \frac{3}{4} = 75$ pieces per hour.

Together, the machines make pieces per hour.

Divide 10,000 pieces by 175 pieces per hour:

$10,000 \div 175 = 57 \textup{ R }1$ .

The candy can be made in a little over 57 hours. The closest choice is therefore 60 hours.

$88^\circ F$

$87^\circ F$

$78^\circ F$

$98^\circ F$

$97^\circ F$

Explanation

$23+65=88^\circ F$

Also, we can solve this problem by using a number line. New Castle’s temperature is units away from zero and Tucson’s is units away.

Temp1

We can see that Tucson is $88^\circ F$ warmer than New Castle.

Choose the closest answer.

Explanation

The newer machine can make 100 pieces of divinity per hour. The older machine makes 100 pieces in one hour twenty minutes, or, equivalently, one and one third hours, which is

$100 \div 1 \frac{1}{3} = 100 \div \frac{4}{3} = 100 \times \frac{3}{4} = 75$ pieces per hour.

Together, the machines make pieces per hour.

Divide 10,000 pieces by 175 pieces per hour:

$10,000 \div 175 = 57 \textup{ R }1$ .

The candy can be made in a little over 57 hours. The closest choice is therefore 60 hours.

$106^\circ F$

$160^\circ F$

$116^\circ F$

$86^\circ F$

$76^\circ F$

Explanation

$31+75=106^\circ F$

Also, we can solve this problem by using a number line. New Castle’s temperature is units away from zero and Tucson’s is units away.

Temp3

We can see that Tucson is $106^\circ F$ warmer than New Castle.

$125^\circ F$

$152^\circ F$

$150^\circ F$

$115^\circ F$

$80^\circ F$

Explanation

$15+110=125^\circ F$

Also, we can solve this problem by using a number line. New Castle’s temperature is units away from zero and Tucson’s is units away.

Temp10

We can see that Tucson is $125^\circ F$ warmer than New Castle.

On a particular November day, it is $115^\circ F$ and sunny in Tucson, Arizona. On the eastern side of the United States, it is $-10^\circ F$ and sleeting in New Castle, Pennsylvania. How many degrees warmer is it in Tucson than New Castle?

$125^\circ F$

$115^\circ F$

$135^\circ F$

$123^\circ F$

$122^\circ F$

Explanation

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is $10^\circ F$ below zero and in Tucson it is $115^\circ F$ above zero; therefore we can say:

$10+115=125^\circ F$

Also, we can solve this problem by using a number line. New Castle’s temperature is units away from zero and Tucson’s is units away.

Temp11

We can see that Tucson is $125^\circ F$ warmer than New Castle.

Fill in the missing digit to form a number that is divisible by 44:

$72; \underline{ ; ; }; ,012$

Explanation

A number that is divisible by 44 must also be divisible by all factors of 44.

One factor is 4. The number is divisible by 4 if the last two digits form a number itself divisible by 4. Since the last two digits are "12", which is divisible by 4, we know the number to be divisible by 4 regardless of the digit chosen.

Another factor is 11. The number is divisible by 11 if and only of the alternating sum has an absolute value divisible by 11. If is the missing digit, then

We can set each of the choices equal to and see which one works:

Only in the case is the alternating sum divisible by 11, so this is the correct choice.

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