HSPT Math - How to do other word problems

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 $75^\circ F$ 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 $65^\circ F$ 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.

An arithmetic sequence begins

$1, 7, \bigcirc, \square ,...$

What number replaces the square?

Explanation

In an arithmetic sequence, each term is obtained by adding the same number to the previous term - the common difference. Since , 6 is the common difference. The next two terms are:

19 replaces the square and is the correct choice.

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.

What is the prime factorization of 48?

$\dpi{100} 2\cdot 2\cdot 2\cdot 2\cdot 3$

$\dpi{100} 2\cdot 24$

$\dpi{100} 4\cdot 12$

$\dpi{100} 2\cdot 2\cdot 12$

Explanation

We can find the prime factorization of a number by dividing 48 into smaller numbers.

$\dpi{100} 48=2\times 24$

2 is prime

$\dpi{100} 24=2\times 12$

2 is prime

$\dpi{100} 12=2\times 6$

2 is prime

$\dpi{100} 6=2\times 3$

Both 2 and 3 are prime.

So we have four 2's and one 3. Multiply these numbers to get 48.

What is the least common multiple of 6 and 8?

$\dpi{100} 24$

$\dpi{100} 48$

$\dpi{100} 12$

$\dpi{100} 16$

Explanation

One easy way to find the least common multiple is to take the largest of the numbers given to you, and find its multiples.

8: 8, 16, 24, 32, 40, 48...

Now start with 8, and see if any of these numbers is divisible by 6. The first number that is divisible by 6 is the least common multiple of 6 and 8.

8: No

16: No

24: Yes

24 is the least common multiple of 6 and 8.

Consider the sequence

$1, 3, 4, 7, 11, 18, 29, \bigcirc, \square,...$

What number replaces the square?

Explanation

Beginning with the third term, each term is the sum of the previous two:

, the number in the circle;

, the number in the square.

On a particular November day, it is $80^\circ F$ and sunny in Tucson, Arizona. On the eastern side of the United States, it is $-33^\circ F$ and sleeting in New Castle, Pennsylvania. How many degrees warmer is it in Tucson than New Castle?

$113^\circ F$

$103^\circ F$

$130^\circ F$

$131^\circ F$

$122^\circ F$

Explanation

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is $33^\circ F$ below zero and in Tucson it is $80^\circ F$ above zero; therefore we can say: