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HSPT Math : How to do other word problems

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Example Question #107 : Word Problems

Let the universal set be the set of all people.

Let , , and be the set of all people who like The Rolling Stones, Bob Seger, and Alanis Morissette, respectively. If represents John, then how would you represent the statement:

$j \in (R \cap M) \cap S'$

as an English-language sentence?

Possible Answers:

John likes Bob Seger, but he dislikes both The Rolling Stones and Alanis Morissette.

John likes The Rolling Stones and Alanis Morissette, but he dislikes Bob Seger.

John likes either The Rolling Stones, Alanis Morissette, or both, but he dislikes Bob Seger.

John likes Bob Seger, but he dislikes The Rolling Stones, Alanis Morissette, or both.

Correct answer:

John likes The Rolling Stones and Alanis Morissette, but he dislikes Bob Seger.

Explanation:

$(R \cap M) \cap S'$ is the intersection of two sets, $R \cap M$ and . $R \cap M$ itself is the intersection of , the set of persons who like The Rolling Stones, and , the set of persons who like Alanis Morissette. is the set of persons who like Bob Seger, so , the complement of , is the set of persons not in - that is, persons who dislike Bob Seger.

Therefore, anyone in the set $(R \cap M) \cap S'$ likes The Rolling Stones, likes Alanis Morissette, and dislikes Bob Seger. The correct choice is "John likes The Rolling Stones and Alanis Morissette, but he dislikes Bob Seger."

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Example Question #101 : Word Problems

Table

Mr. And Mrs. Jackson have invited six guests to dinner, including Mr. Jackson's brother Steve and Mrs. Jackson's brother Jim. Steve and Jim do not like each other, so it is desired that they not sit in adjacent seats. How many arrangements are possible that conform to this specification?

Possible Answers:

11.520

51,840

28,800

40,320

Correct answer:

28,800

Explanation:

First, we note that the total number of seating arrangements for eight people is

$P (8,8) = 8! = 1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 = 40,320$

The number of arrangements that would have Steve and Jim in adjacent seats would be calculated as follows:

The number of ways to choose two adjacent seats is eight: 1-2, 2-3, and so forth up to 8-1. Multiply this by 2, since each choice has two different orders for Steve and Jim. Multiply this by

$P (6,6) = 6! = 1 \times 2 \times 3 \times 4 \times 5 \times 6 = 720$ ,

the number of ways the remaining six persons can be seated. This makes

$8 \times 2 \times 720 = 11,520$

seating arrangements with Steve and Jim together. Since this is not desired, subtract this from the total number of arrangements:

40,320 - 11, 520 = 28,800

This is the number of arrangments without Steve and Jim together, and it is the correct choice.

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Example Question #109 : Word Problems

Let the universal set be the set of positive integers. Let be the set of prime numbers and be the set of odd numbers. Which of the following is in the set $(P' \cup O') '$ ?

Possible Answers:

Correct answer:

Explanation:

By DeMorgan's Law,

$(P' \cup O') ' = (P')' \cap( O') '$

That is, the complement of the union of two sets is the intersection of their complements.

Also, the complement of a complement of a set is the set itself, so (P')' = P and (O)' = O . Therefore,

$(P' \cup O') ' =P \cap O$ .

Consequently, we are looking for a number that falls in the intersection of and . The number must be both prime and odd. 2 and 4 are eliminated for being even. 1 is not considered a prime number, having only one factor. 3, which has only two factors, 1 and 3, is prime, and is the correct choice.

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Example Question #110 : Word Problems

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

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

Possible Answers:

Correct answer:

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

7-2+A - 0+1-2 = 4+A .

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

A = 0: 4+A = 4+ 0 = 4

A =3: 4+A = 4+ 3 = 7

A =5: 4+5 = 4+5 =9

A =7: 4+A = 4+7 = 11

Only in the case A = 7 is the alternating sum divisible by 11, so this is the correct choice.

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Example Question #1 : Understand The Value Of Positive And Negative Numbers: Ccss.Math.Content.6.Ns.C.5

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?

Possible Answers:

$78^\circ F$

$97^\circ F$

$98^\circ F$

$88^\circ F$

$87^\circ F$

Correct answer:

$88^\circ F$

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.

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Example Question #1 : Understand The Value Of Positive And Negative Numbers: Ccss.Math.Content.6.Ns.C.5

On a particular November day, it is $70^\circ F$ and sunny in Tucson, Arizona. On the eastern side of the United States, it is $-27^\circ F$ and sleeting in New Castle, Pennsylvania. How many degrees warmer is it in Tucson than New Castle?

Possible Answers:

$98^\circ F$

$77^\circ F$

$97^\circ F$

$89^\circ F$

$79^\circ F$

Correct answer:

$97^\circ F$

Explanation:

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is $27^\circ F$ below zero and in Tucson it is $70^\circ F$ above zero; therefore we can say:

$27+70=97^\circ F$

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.

Temp2

We can see that Tucson is $97^\circ F$ warmer than New Castle.

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Example Question #3 : Understand The Value Of Positive And Negative Numbers: Ccss.Math.Content.6.Ns.C.5

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?

Possible Answers:

$106^\circ F$

$76^\circ F$

$86^\circ F$

$160^\circ F$

$116^\circ F$

Correct answer:

$106^\circ F$

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.

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Example Question #4 : Understand The Value Of Positive And Negative Numbers: Ccss.Math.Content.6.Ns.C.5

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?

Possible Answers:

$113^\circ F$

$130^\circ F$

$131^\circ F$

$122^\circ F$

$103^\circ F$

Correct answer:

$113^\circ F$

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:

$33+80=113^\circ F$

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.

Temp4

We can see that Tucson is $113^\circ F$ warmer than New Castle.

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Example Question #111 : Word Problems

On a particular November day, it is $85^\circ F$ and sunny in Tucson, Arizona. On the eastern side of the United States, it is $-32^\circ F$ and sleeting in New Castle, Pennsylvania. How many degrees warmer is it in Tucson than New Castle?

Possible Answers:

$121^\circ F$

$115^\circ F$

$117^\circ F$

$91^\circ F$

$101^\circ F$

Correct answer:

$117^\circ F$

Explanation:

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is $32^\circ F$ below zero and in Tucson it is $85^\circ F$ above zero; therefore we can say:

$32+85=117^\circ F$

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.

Temp5

We can see that Tucson is $117^\circ F$ warmer than New Castle.

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Example Question #6 : Understand The Value Of Positive And Negative Numbers: Ccss.Math.Content.6.Ns.C.5

On a particular November day, it is $90^\circ F$ and sunny in Tucson, Arizona. On the eastern side of the United States, it is $-25^\circ F$ and sleeting in New Castle, Pennsylvania. How many degrees warmer is it in Tucson than New Castle?

Possible Answers:

$82^\circ F$

$97^\circ F$

$91^\circ F$

$115^\circ F$

$151^\circ F$

Correct answer:

$115^\circ F$

Explanation:

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is $25^\circ F$ below zero and in Tucson it is $90^\circ F$ above zero; therefore we can say:

$25+90=115^\circ F$

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.

Temp6

We can see that Tucson is $115^\circ F$ warmer than New Castle.

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HSPT Math : How to do other word problems

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #107 : Word Problems

Example Question #101 : Word Problems

Example Question #109 : Word Problems

Example Question #110 : Word Problems

Example Question #1 : Understand The Value Of Positive And Negative Numbers: Ccss.Math.Content.6.Ns.C.5

Example Question #1 : Understand The Value Of Positive And Negative Numbers: Ccss.Math.Content.6.Ns.C.5

Example Question #3 : Understand The Value Of Positive And Negative Numbers: Ccss.Math.Content.6.Ns.C.5

Example Question #4 : Understand The Value Of Positive And Negative Numbers: Ccss.Math.Content.6.Ns.C.5

Example Question #111 : Word Problems

Example Question #6 : Understand The Value Of Positive And Negative Numbers: Ccss.Math.Content.6.Ns.C.5

All HSPT Math Resources

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