Understanding two-part analyses - GMAT Data Insights

Card 0 of 20

Question

Over a seven-year period, from 2002 to 2009, the number of babies born to married couples increased despite a decrease in marriages from 17,000 marriages in 2002.

In the given expression, and represent the percent change in the babies and marriages, respectively. represents the number of babies per married couple in 2002. The percent change in a quantity is calculated by the formula:

$\left(\frac{X_{new}-X_{old}}{X_{old}} \right )\times 100$

Identify the following with the given information,

I. The expression that represents the number of babies born in 2002.

II. The expression of the number of babies born per family in 2009.

Answer

To identify,

I. The expression that represents the number of babies born in 2002.

Recall the given information in this particular question.

It is known that in 2002 there are 17,000 marriages and represents $\frac{\text{Babies}}{\text{Marriage}}$ .

Using this information to create a mathematical expression is as follows.

$17,000 \text{ marriages}\times \frac{\text{babies}}{\text{marriage}}\Rightarrow17,000 \text{ marriages}\times I=17,000I$

Now to identify,

II. The expression of the number of babies born per married couple in 2009.

Use the formula given

$\left(\frac{X_{new}-X_{old}}{X_{old}} \right )\times 100$

This part of the problem is asking for a ratio, but the variables that are given are percents.

Therefore, the 100’s are there because M and B are percent quantitie_s._ They are both added because M is a negative number.

So the number in the numerator is the percentage of babies that exist in 2009 compared to 2002 (a number that will be less than 100). The denominator is the percentage of the 2002 marriages that exists in 2009 (a number greater than 100).

Thus the solution is,

$\left( \frac{100+B}{100+M}\right)\times I$

Compare your answer with the correct one above

Question

A high-school music department is putting together a two-day music festival to highlight the students' talents. The schedule for the two days will adhere to the following rules:

1. Five musical performances are scheduled for each day.

2. The majority of the performances on one of the days will be composed of woodwind instruments (clarinets, flutes, saxophones, oboes, or bassoons)

3. The other day will primarily feature solo performances.

Currently, 8 of the performances (4 each day) have been scheduled. The music department must add one additional performance on each day:

Day 1

Smooth Jazz Group (10th Grade, Saxophone Trio)

Rock Your Socks Off (12th Grade, Vocal Group)

Dustin & Karen (11th Grade, Flute Duo)

James (11th Grade, Trumpet Solo)

Day 2

Adam (10th Grade, Vocal Solo)

John (11th Grade, Clarinet Solo)

Rachel (12th Grade, Brass Solo)

4 Blind Mice (9th Grade, Woodwind Quartet)

The music department must add one additional performance on each day.

Based on the rules above, identify a performance that following:

I. A performance that can be scheduled on either day.

II. A performance that cannot be scheduled on either day.

Answer

Recall the criteria for this particular problem.

Five musicians are scheduled to play each day. To feature the departments strengths, the majority of the musicians on one of the days will be composed of woodwind instruments (clarinets, flutes, saxophones, oboes, bassoons) and the other day will be primarily solo musicians.

Looking at day one it is clear that represents the woodwind day and day two represents the solo day.

Therefore, for someone to be able to play either day that student must play a woodwind instrument and be doing a solo. For a musician(s) to play neither day it must be a group that is composed of instruments other than woodwind.

Also recall that violins are string instruments, trumpets are brass instruments, and vocal is ones voice.

Keeping all of this in mind, the correct answer is,

I. Susan (12th Grade, Flute Solo)

II. James & Jimmy (10th Grade, Vocal Duo)

Compare your answer with the correct one above

Question

Over a seven-year period, from 2002 to 2009, the number of babies born to married couples increased despite a decrease in marriages from 17,000 marriages in 2002.

In the given expression, and represent the percent change in the babies and marriages, respectively. represents the number of babies per married couple in 2002. The percent change in a quantity is calculated by the formula:

$\left(\frac{X_{new}-X_{old}}{X_{old}} \right )\times 100$

Identify the following with the given information,

I. The expression that represents the number of babies born in 2002.

II. The expression of the number of babies born per family in 2009.

Answer

To identify,

I. The expression that represents the number of babies born in 2002.

Recall the given information in this particular question.

It is known that in 2002 there are 17,000 marriages and represents $\frac{\text{Babies}}{\text{Marriage}}$ .

Using this information to create a mathematical expression is as follows.

$17,000 \text{ marriages}\times \frac{\text{babies}}{\text{marriage}}\Rightarrow17,000 \text{ marriages}\times I=17,000I$

Now to identify,

II. The expression of the number of babies born per married couple in 2009.

Use the formula given

$\left(\frac{X_{new}-X_{old}}{X_{old}} \right )\times 100$

This part of the problem is asking for a ratio, but the variables that are given are percents.

Therefore, the 100’s are there because M and B are percent quantitie_s._ They are both added because M is a negative number.

So the number in the numerator is the percentage of babies that exist in 2009 compared to 2002 (a number that will be less than 100). The denominator is the percentage of the 2002 marriages that exists in 2009 (a number greater than 100).

Thus the solution is,

$\left( \frac{100+B}{100+M}\right)\times I$

Compare your answer with the correct one above

Question

A high-school music department is putting together a two-day music festival to highlight the students' talents. The schedule for the two days will adhere to the following rules:

1. Five musical performances are scheduled for each day.

2. The majority of the performances on one of the days will be composed of woodwind instruments (clarinets, flutes, saxophones, oboes, or bassoons)

3. The other day will primarily feature solo performances.

Currently, 8 of the performances (4 each day) have been scheduled. The music department must add one additional performance on each day:

Day 1

Smooth Jazz Group (10th Grade, Saxophone Trio)

Rock Your Socks Off (12th Grade, Vocal Group)

Dustin & Karen (11th Grade, Flute Duo)

James (11th Grade, Trumpet Solo)

Day 2

Adam (10th Grade, Vocal Solo)

John (11th Grade, Clarinet Solo)

Rachel (12th Grade, Brass Solo)

4 Blind Mice (9th Grade, Woodwind Quartet)

The music department must add one additional performance on each day.

Based on the rules above, identify a performance that following:

I. A performance that can be scheduled on either day.

II. A performance that cannot be scheduled on either day.

Answer

Recall the criteria for this particular problem.

Five musicians are scheduled to play each day. To feature the departments strengths, the majority of the musicians on one of the days will be composed of woodwind instruments (clarinets, flutes, saxophones, oboes, bassoons) and the other day will be primarily solo musicians.

Looking at day one it is clear that represents the woodwind day and day two represents the solo day.

Therefore, for someone to be able to play either day that student must play a woodwind instrument and be doing a solo. For a musician(s) to play neither day it must be a group that is composed of instruments other than woodwind.

Also recall that violins are string instruments, trumpets are brass instruments, and vocal is ones voice.

Keeping all of this in mind, the correct answer is,

I. Susan (12th Grade, Flute Solo)

II. James & Jimmy (10th Grade, Vocal Duo)

Compare your answer with the correct one above

Question

A Shark XI is a new model remote aircraft. Under ideal flying conditions the Shark XI's fuel is nautical miles per liter $\left(F\frac{\text{nautical miles}}{L} \right )$ when flying speed is constant at nautical miles per hour $\left(S(\text{knots}) \right )$ where knots is the abbreviation for nautical miles per hour.

Identify the following statements in terms of and .

I. Liters of fuel in one hour.

II. Liters of fuel in 80 nautical miles.

Answer

To identify,

I. Liters of fuel in one hour.

Recall the given information,

A Shark XI is a new model remote aircraft. Under ideal flying conditions the Shark XI's fuel is nautical miles per liter $\left(F\frac{\text{nautical miles}}{L} \right )$ when flying speed is constant at nautical miles per hour $\left(S(\text{knots}) \right )$ where knots is the abbreviation for nautical miles per hour.

$F\frac{\text{nautical miles}}{L}; S\frac{\text{nautical miles}}{\text{hour}}$

To get liters per hour:

$\frac{\frac{\text{nautical miles}}{\text{hour}}}{\frac{\text{nautical miles}}{L}}=\frac{\text{nautical miles}}{\text{hour}}\times \frac{L}{\text{nautical miles}}$

the nautical miles cancel out and the solution is

$\frac{L}{\text{hours}}=\frac{S}{F}$

II. Liters of fuel in 80 nautical miles.

$F=\frac{\text{nautical miles}}{L}\Rightarrow F=\frac{80}{L}$

Now solving for liters results in the correct answer,

$\L\cdot F=\frac{80}{L}\cdot L \\\frac{LF}{F}=\frac{80}{F} \\L=\frac{80}{F}$

Compare your answer with the correct one above

Question

Over a seven-year period, from 2002 to 2009, the number of babies born to married couples increased despite a decrease in marriages from 17,000 marriages in 2002.

In the given expression, and represent the percent change in the babies and marriages, respectively. represents the number of babies per married couple in 2002. The percent change in a quantity is calculated by the formula:

$\left(\frac{X_{new}-X_{old}}{X_{old}} \right )\times 100$

Identify the following with the given information,

I. The expression that represents the number of babies born in 2002.

II. The expression of the number of babies born per family in 2009.

Answer

To identify,

I. The expression that represents the number of babies born in 2002.

Recall the given information in this particular question.

It is known that in 2002 there are 17,000 marriages and represents $\frac{\text{Babies}}{\text{Marriage}}$ .

Using this information to create a mathematical expression is as follows.

$17,000 \text{ marriages}\times \frac{\text{babies}}{\text{marriage}}\Rightarrow17,000 \text{ marriages}\times I=17,000I$

Now to identify,

II. The expression of the number of babies born per married couple in 2009.

Use the formula given

$\left(\frac{X_{new}-X_{old}}{X_{old}} \right )\times 100$

This part of the problem is asking for a ratio, but the variables that are given are percents.

Therefore, the 100’s are there because M and B are percent quantitie_s._ They are both added because M is a negative number.

So the number in the numerator is the percentage of babies that exist in 2009 compared to 2002 (a number that will be less than 100). The denominator is the percentage of the 2002 marriages that exists in 2009 (a number greater than 100).

Thus the solution is,

$\left( \frac{100+B}{100+M}\right)\times I$

Compare your answer with the correct one above

Question

A high-school music department is putting together a two-day music festival to highlight the students' talents. The schedule for the two days will adhere to the following rules:

1. Five musical performances are scheduled for each day.

2. The majority of the performances on one of the days will be composed of woodwind instruments (clarinets, flutes, saxophones, oboes, or bassoons)

3. The other day will primarily feature solo performances.

Currently, 8 of the performances (4 each day) have been scheduled. The music department must add one additional performance on each day:

Day 1

Smooth Jazz Group (10th Grade, Saxophone Trio)

Rock Your Socks Off (12th Grade, Vocal Group)

Dustin & Karen (11th Grade, Flute Duo)

James (11th Grade, Trumpet Solo)

Day 2

Adam (10th Grade, Vocal Solo)

John (11th Grade, Clarinet Solo)

Rachel (12th Grade, Brass Solo)

4 Blind Mice (9th Grade, Woodwind Quartet)

The music department must add one additional performance on each day.

Based on the rules above, identify a performance that following:

I. A performance that can be scheduled on either day.

II. A performance that cannot be scheduled on either day.

Answer

Recall the criteria for this particular problem.

Five musicians are scheduled to play each day. To feature the departments strengths, the majority of the musicians on one of the days will be composed of woodwind instruments (clarinets, flutes, saxophones, oboes, bassoons) and the other day will be primarily solo musicians.

Looking at day one it is clear that represents the woodwind day and day two represents the solo day.

Therefore, for someone to be able to play either day that student must play a woodwind instrument and be doing a solo. For a musician(s) to play neither day it must be a group that is composed of instruments other than woodwind.

Also recall that violins are string instruments, trumpets are brass instruments, and vocal is ones voice.

Keeping all of this in mind, the correct answer is,

I. Susan (12th Grade, Flute Solo)

II. James & Jimmy (10th Grade, Vocal Duo)

Compare your answer with the correct one above

Question

Over a seven-year period, from 2002 to 2009, the number of babies born to married couples increased despite a decrease in marriages from 17,000 marriages in 2002.

In the given expression, and represent the percent change in the babies and marriages, respectively. represents the number of babies per married couple in 2002. The percent change in a quantity is calculated by the formula:

$\left(\frac{X_{new}-X_{old}}{X_{old}} \right )\times 100$

Identify the following with the given information,

I. The expression that represents the number of babies born in 2002.

II. The expression of the number of babies born per family in 2009.

Answer

To identify,

I. The expression that represents the number of babies born in 2002.

Recall the given information in this particular question.

It is known that in 2002 there are 17,000 marriages and represents $\frac{\text{Babies}}{\text{Marriage}}$ .

Using this information to create a mathematical expression is as follows.

$17,000 \text{ marriages}\times \frac{\text{babies}}{\text{marriage}}\Rightarrow17,000 \text{ marriages}\times I=17,000I$

Now to identify,

II. The expression of the number of babies born per married couple in 2009.

Use the formula given

$\left(\frac{X_{new}-X_{old}}{X_{old}} \right )\times 100$

This part of the problem is asking for a ratio, but the variables that are given are percents.

Therefore, the 100’s are there because M and B are percent quantitie_s._ They are both added because M is a negative number.

So the number in the numerator is the percentage of babies that exist in 2009 compared to 2002 (a number that will be less than 100). The denominator is the percentage of the 2002 marriages that exists in 2009 (a number greater than 100).

Thus the solution is,

$\left( \frac{100+B}{100+M}\right)\times I$

Compare your answer with the correct one above

Question

A high-school music department is putting together a two-day music festival to highlight the students' talents. The schedule for the two days will adhere to the following rules:

1. Five musical performances are scheduled for each day.

2. The majority of the performances on one of the days will be composed of woodwind instruments (clarinets, flutes, saxophones, oboes, or bassoons)

3. The other day will primarily feature solo performances.

Currently, 8 of the performances (4 each day) have been scheduled. The music department must add one additional performance on each day:

Day 1

Smooth Jazz Group (10th Grade, Saxophone Trio)

Rock Your Socks Off (12th Grade, Vocal Group)

Dustin & Karen (11th Grade, Flute Duo)

James (11th Grade, Trumpet Solo)

Day 2

Adam (10th Grade, Vocal Solo)

John (11th Grade, Clarinet Solo)

Rachel (12th Grade, Brass Solo)

4 Blind Mice (9th Grade, Woodwind Quartet)

The music department must add one additional performance on each day.

Based on the rules above, identify a performance that following:

I. A performance that can be scheduled on either day.

II. A performance that cannot be scheduled on either day.

Answer

Recall the criteria for this particular problem.

Five musicians are scheduled to play each day. To feature the departments strengths, the majority of the musicians on one of the days will be composed of woodwind instruments (clarinets, flutes, saxophones, oboes, bassoons) and the other day will be primarily solo musicians.

Looking at day one it is clear that represents the woodwind day and day two represents the solo day.

Therefore, for someone to be able to play either day that student must play a woodwind instrument and be doing a solo. For a musician(s) to play neither day it must be a group that is composed of instruments other than woodwind.

Also recall that violins are string instruments, trumpets are brass instruments, and vocal is ones voice.

Keeping all of this in mind, the correct answer is,

I. Susan (12th Grade, Flute Solo)

II. James & Jimmy (10th Grade, Vocal Duo)

Compare your answer with the correct one above

Question

A Shark XI is a new model remote aircraft. Under ideal flying conditions the Shark XI's fuel is nautical miles per liter $\left(F\frac{\text{nautical miles}}{L} \right )$ when flying speed is constant at nautical miles per hour $\left(S(\text{knots}) \right )$ where knots is the abbreviation for nautical miles per hour.

Identify the following statements in terms of and .

I. Liters of fuel in one hour.

II. Liters of fuel in 80 nautical miles.

Answer

To identify,

I. Liters of fuel in one hour.

Recall the given information,

A Shark XI is a new model remote aircraft. Under ideal flying conditions the Shark XI's fuel is nautical miles per liter $\left(F\frac{\text{nautical miles}}{L} \right )$ when flying speed is constant at nautical miles per hour $\left(S(\text{knots}) \right )$ where knots is the abbreviation for nautical miles per hour.

$F\frac{\text{nautical miles}}{L}; S\frac{\text{nautical miles}}{\text{hour}}$

To get liters per hour:

$\frac{\frac{\text{nautical miles}}{\text{hour}}}{\frac{\text{nautical miles}}{L}}=\frac{\text{nautical miles}}{\text{hour}}\times \frac{L}{\text{nautical miles}}$

the nautical miles cancel out and the solution is

$\frac{L}{\text{hours}}=\frac{S}{F}$

II. Liters of fuel in 80 nautical miles.

$F=\frac{\text{nautical miles}}{L}\Rightarrow F=\frac{80}{L}$

Now solving for liters results in the correct answer,

$\L\cdot F=\frac{80}{L}\cdot L \\\frac{LF}{F}=\frac{80}{F} \\L=\frac{80}{F}$

Compare your answer with the correct one above

Question

Over a seven-year period, from 2002 to 2009, the number of babies born to married couples increased despite a decrease in marriages from 17,000 marriages in 2002.

In the given expression, and represent the percent change in the babies and marriages, respectively. represents the number of babies per married couple in 2002. The percent change in a quantity is calculated by the formula:

$\left(\frac{X_{new}-X_{old}}{X_{old}} \right )\times 100$

Identify the following with the given information,

I. The expression that represents the number of babies born in 2002.

II. The expression of the number of babies born per family in 2009.

Answer

To identify,

I. The expression that represents the number of babies born in 2002.

Recall the given information in this particular question.

It is known that in 2002 there are 17,000 marriages and represents $\frac{\text{Babies}}{\text{Marriage}}$ .

Using this information to create a mathematical expression is as follows.

$17,000 \text{ marriages}\times \frac{\text{babies}}{\text{marriage}}\Rightarrow17,000 \text{ marriages}\times I=17,000I$

Now to identify,

II. The expression of the number of babies born per married couple in 2009.

Use the formula given

$\left(\frac{X_{new}-X_{old}}{X_{old}} \right )\times 100$

This part of the problem is asking for a ratio, but the variables that are given are percents.

Therefore, the 100’s are there because M and B are percent quantitie_s._ They are both added because M is a negative number.

So the number in the numerator is the percentage of babies that exist in 2009 compared to 2002 (a number that will be less than 100). The denominator is the percentage of the 2002 marriages that exists in 2009 (a number greater than 100).

Thus the solution is,

$\left( \frac{100+B}{100+M}\right)\times I$

Compare your answer with the correct one above

Question

A high-school music department is putting together a two-day music festival to highlight the students' talents. The schedule for the two days will adhere to the following rules:

1. Five musical performances are scheduled for each day.

2. The majority of the performances on one of the days will be composed of woodwind instruments (clarinets, flutes, saxophones, oboes, or bassoons)

3. The other day will primarily feature solo performances.

Currently, 8 of the performances (4 each day) have been scheduled. The music department must add one additional performance on each day:

Day 1

Smooth Jazz Group (10th Grade, Saxophone Trio)

Rock Your Socks Off (12th Grade, Vocal Group)

Dustin & Karen (11th Grade, Flute Duo)

James (11th Grade, Trumpet Solo)

Day 2

Adam (10th Grade, Vocal Solo)

John (11th Grade, Clarinet Solo)

Rachel (12th Grade, Brass Solo)

4 Blind Mice (9th Grade, Woodwind Quartet)

The music department must add one additional performance on each day.

Based on the rules above, identify a performance that following:

I. A performance that can be scheduled on either day.

II. A performance that cannot be scheduled on either day.

Answer

Recall the criteria for this particular problem.

Five musicians are scheduled to play each day. To feature the departments strengths, the majority of the musicians on one of the days will be composed of woodwind instruments (clarinets, flutes, saxophones, oboes, bassoons) and the other day will be primarily solo musicians.

Looking at day one it is clear that represents the woodwind day and day two represents the solo day.

Therefore, for someone to be able to play either day that student must play a woodwind instrument and be doing a solo. For a musician(s) to play neither day it must be a group that is composed of instruments other than woodwind.

Also recall that violins are string instruments, trumpets are brass instruments, and vocal is ones voice.

Keeping all of this in mind, the correct answer is,

I. Susan (12th Grade, Flute Solo)

II. James & Jimmy (10th Grade, Vocal Duo)

Compare your answer with the correct one above

Question

Over a seven-year period, from 2002 to 2009, the number of babies born to married couples increased despite a decrease in marriages from 17,000 marriages in 2002.

In the given expression, and represent the percent change in the babies and marriages, respectively. represents the number of babies per married couple in 2002. The percent change in a quantity is calculated by the formula:

$\left(\frac{X_{new}-X_{old}}{X_{old}} \right )\times 100$

Identify the following with the given information,

I. The expression that represents the number of babies born in 2002.

II. The expression of the number of babies born per family in 2009.

Answer

To identify,

I. The expression that represents the number of babies born in 2002.

Recall the given information in this particular question.

It is known that in 2002 there are 17,000 marriages and represents $\frac{\text{Babies}}{\text{Marriage}}$ .

Using this information to create a mathematical expression is as follows.

$17,000 \text{ marriages}\times \frac{\text{babies}}{\text{marriage}}\Rightarrow17,000 \text{ marriages}\times I=17,000I$

Now to identify,

II. The expression of the number of babies born per married couple in 2009.

Use the formula given

$\left(\frac{X_{new}-X_{old}}{X_{old}} \right )\times 100$

This part of the problem is asking for a ratio, but the variables that are given are percents.

Therefore, the 100’s are there because M and B are percent quantitie_s._ They are both added because M is a negative number.

So the number in the numerator is the percentage of babies that exist in 2009 compared to 2002 (a number that will be less than 100). The denominator is the percentage of the 2002 marriages that exists in 2009 (a number greater than 100).

Thus the solution is,

$\left( \frac{100+B}{100+M}\right)\times I$

Compare your answer with the correct one above

Question

A high-school music department is putting together a two-day music festival to highlight the students' talents. The schedule for the two days will adhere to the following rules:

1. Five musical performances are scheduled for each day.

2. The majority of the performances on one of the days will be composed of woodwind instruments (clarinets, flutes, saxophones, oboes, or bassoons)

3. The other day will primarily feature solo performances.

Currently, 8 of the performances (4 each day) have been scheduled. The music department must add one additional performance on each day:

Day 1

Smooth Jazz Group (10th Grade, Saxophone Trio)

Rock Your Socks Off (12th Grade, Vocal Group)

Dustin & Karen (11th Grade, Flute Duo)

James (11th Grade, Trumpet Solo)

Day 2

Adam (10th Grade, Vocal Solo)

John (11th Grade, Clarinet Solo)

Rachel (12th Grade, Brass Solo)

4 Blind Mice (9th Grade, Woodwind Quartet)

The music department must add one additional performance on each day.

Based on the rules above, identify a performance that following:

I. A performance that can be scheduled on either day.

II. A performance that cannot be scheduled on either day.

Answer

Recall the criteria for this particular problem.

Five musicians are scheduled to play each day. To feature the departments strengths, the majority of the musicians on one of the days will be composed of woodwind instruments (clarinets, flutes, saxophones, oboes, bassoons) and the other day will be primarily solo musicians.

Looking at day one it is clear that represents the woodwind day and day two represents the solo day.

Therefore, for someone to be able to play either day that student must play a woodwind instrument and be doing a solo. For a musician(s) to play neither day it must be a group that is composed of instruments other than woodwind.

Also recall that violins are string instruments, trumpets are brass instruments, and vocal is ones voice.

Keeping all of this in mind, the correct answer is,

I. Susan (12th Grade, Flute Solo)

II. James & Jimmy (10th Grade, Vocal Duo)

Compare your answer with the correct one above

Question

A Shark XI is a new model remote aircraft. Under ideal flying conditions the Shark XI's fuel is nautical miles per liter $\left(F\frac{\text{nautical miles}}{L} \right )$ when flying speed is constant at nautical miles per hour $\left(S(\text{knots}) \right )$ where knots is the abbreviation for nautical miles per hour.

Identify the following statements in terms of and .

I. Liters of fuel in one hour.

II. Liters of fuel in 80 nautical miles.

Answer

To identify,

I. Liters of fuel in one hour.

Recall the given information,

A Shark XI is a new model remote aircraft. Under ideal flying conditions the Shark XI's fuel is nautical miles per liter $\left(F\frac{\text{nautical miles}}{L} \right )$ when flying speed is constant at nautical miles per hour $\left(S(\text{knots}) \right )$ where knots is the abbreviation for nautical miles per hour.

$F\frac{\text{nautical miles}}{L}; S\frac{\text{nautical miles}}{\text{hour}}$

To get liters per hour:

$\frac{\frac{\text{nautical miles}}{\text{hour}}}{\frac{\text{nautical miles}}{L}}=\frac{\text{nautical miles}}{\text{hour}}\times \frac{L}{\text{nautical miles}}$

the nautical miles cancel out and the solution is

$\frac{L}{\text{hours}}=\frac{S}{F}$

II. Liters of fuel in 80 nautical miles.

$F=\frac{\text{nautical miles}}{L}\Rightarrow F=\frac{80}{L}$

Now solving for liters results in the correct answer,

$\L\cdot F=\frac{80}{L}\cdot L \\\frac{LF}{F}=\frac{80}{F} \\L=\frac{80}{F}$

Compare your answer with the correct one above

Question

Over a seven-year period, from 2002 to 2009, the number of babies born to married couples increased despite a decrease in marriages from 17,000 marriages in 2002.

In the given expression, and represent the percent change in the babies and marriages, respectively. represents the number of babies per married couple in 2002. The percent change in a quantity is calculated by the formula:

$\left(\frac{X_{new}-X_{old}}{X_{old}} \right )\times 100$

Identify the following with the given information,

I. The expression that represents the number of babies born in 2002.

II. The expression of the number of babies born per family in 2009.

Answer

To identify,

I. The expression that represents the number of babies born in 2002.

Recall the given information in this particular question.

It is known that in 2002 there are 17,000 marriages and represents $\frac{\text{Babies}}{\text{Marriage}}$ .

Using this information to create a mathematical expression is as follows.

$17,000 \text{ marriages}\times \frac{\text{babies}}{\text{marriage}}\Rightarrow17,000 \text{ marriages}\times I=17,000I$

Now to identify,

II. The expression of the number of babies born per married couple in 2009.

Use the formula given

$\left(\frac{X_{new}-X_{old}}{X_{old}} \right )\times 100$

This part of the problem is asking for a ratio, but the variables that are given are percents.

Therefore, the 100’s are there because M and B are percent quantitie_s._ They are both added because M is a negative number.

So the number in the numerator is the percentage of babies that exist in 2009 compared to 2002 (a number that will be less than 100). The denominator is the percentage of the 2002 marriages that exists in 2009 (a number greater than 100).

Thus the solution is,

$\left( \frac{100+B}{100+M}\right)\times I$

Compare your answer with the correct one above

Question

A high-school music department is putting together a two-day music festival to highlight the students' talents. The schedule for the two days will adhere to the following rules:

1. Five musical performances are scheduled for each day.

2. The majority of the performances on one of the days will be composed of woodwind instruments (clarinets, flutes, saxophones, oboes, or bassoons)

3. The other day will primarily feature solo performances.

Currently, 8 of the performances (4 each day) have been scheduled. The music department must add one additional performance on each day:

Day 1

Smooth Jazz Group (10th Grade, Saxophone Trio)

Rock Your Socks Off (12th Grade, Vocal Group)

Dustin & Karen (11th Grade, Flute Duo)

James (11th Grade, Trumpet Solo)

Day 2

Adam (10th Grade, Vocal Solo)

John (11th Grade, Clarinet Solo)

Rachel (12th Grade, Brass Solo)

4 Blind Mice (9th Grade, Woodwind Quartet)

The music department must add one additional performance on each day.

Based on the rules above, identify a performance that following:

I. A performance that can be scheduled on either day.

II. A performance that cannot be scheduled on either day.

Answer

Recall the criteria for this particular problem.

Five musicians are scheduled to play each day. To feature the departments strengths, the majority of the musicians on one of the days will be composed of woodwind instruments (clarinets, flutes, saxophones, oboes, bassoons) and the other day will be primarily solo musicians.

Looking at day one it is clear that represents the woodwind day and day two represents the solo day.

Therefore, for someone to be able to play either day that student must play a woodwind instrument and be doing a solo. For a musician(s) to play neither day it must be a group that is composed of instruments other than woodwind.

Also recall that violins are string instruments, trumpets are brass instruments, and vocal is ones voice.

Keeping all of this in mind, the correct answer is,

I. Susan (12th Grade, Flute Solo)

II. James & Jimmy (10th Grade, Vocal Duo)

Compare your answer with the correct one above

Question

Over a seven-year period, from 2002 to 2009, the number of babies born to married couples increased despite a decrease in marriages from 17,000 marriages in 2002.

In the given expression, and represent the percent change in the babies and marriages, respectively. represents the number of babies per married couple in 2002. The percent change in a quantity is calculated by the formula:

$\left(\frac{X_{new}-X_{old}}{X_{old}} \right )\times 100$

Identify the following with the given information,

I. The expression that represents the number of babies born in 2002.

II. The expression of the number of babies born per family in 2009.

Answer

To identify,

I. The expression that represents the number of babies born in 2002.

Recall the given information in this particular question.

It is known that in 2002 there are 17,000 marriages and represents $\frac{\text{Babies}}{\text{Marriage}}$ .

Using this information to create a mathematical expression is as follows.

$17,000 \text{ marriages}\times \frac{\text{babies}}{\text{marriage}}\Rightarrow17,000 \text{ marriages}\times I=17,000I$

Now to identify,

II. The expression of the number of babies born per married couple in 2009.

Use the formula given

$\left(\frac{X_{new}-X_{old}}{X_{old}} \right )\times 100$

This part of the problem is asking for a ratio, but the variables that are given are percents.

Therefore, the 100’s are there because M and B are percent quantitie_s._ They are both added because M is a negative number.

So the number in the numerator is the percentage of babies that exist in 2009 compared to 2002 (a number that will be less than 100). The denominator is the percentage of the 2002 marriages that exists in 2009 (a number greater than 100).

Thus the solution is,

$\left( \frac{100+B}{100+M}\right)\times I$

Compare your answer with the correct one above

Question

A high-school music department is putting together a two-day music festival to highlight the students' talents. The schedule for the two days will adhere to the following rules:

1. Five musical performances are scheduled for each day.

2. The majority of the performances on one of the days will be composed of woodwind instruments (clarinets, flutes, saxophones, oboes, or bassoons)

3. The other day will primarily feature solo performances.

Currently, 8 of the performances (4 each day) have been scheduled. The music department must add one additional performance on each day:

Day 1

Smooth Jazz Group (10th Grade, Saxophone Trio)

Rock Your Socks Off (12th Grade, Vocal Group)

Dustin & Karen (11th Grade, Flute Duo)

James (11th Grade, Trumpet Solo)

Day 2

Adam (10th Grade, Vocal Solo)

John (11th Grade, Clarinet Solo)

Rachel (12th Grade, Brass Solo)

4 Blind Mice (9th Grade, Woodwind Quartet)

The music department must add one additional performance on each day.

Based on the rules above, identify a performance that following:

I. A performance that can be scheduled on either day.

II. A performance that cannot be scheduled on either day.

Answer

Recall the criteria for this particular problem.

Five musicians are scheduled to play each day. To feature the departments strengths, the majority of the musicians on one of the days will be composed of woodwind instruments (clarinets, flutes, saxophones, oboes, bassoons) and the other day will be primarily solo musicians.

Looking at day one it is clear that represents the woodwind day and day two represents the solo day.

Therefore, for someone to be able to play either day that student must play a woodwind instrument and be doing a solo. For a musician(s) to play neither day it must be a group that is composed of instruments other than woodwind.

Also recall that violins are string instruments, trumpets are brass instruments, and vocal is ones voice.

Keeping all of this in mind, the correct answer is,

I. Susan (12th Grade, Flute Solo)

II. James & Jimmy (10th Grade, Vocal Duo)

Compare your answer with the correct one above

Question

A Shark XI is a new model remote aircraft. Under ideal flying conditions the Shark XI's fuel is nautical miles per liter $\left(F\frac{\text{nautical miles}}{L} \right )$ when flying speed is constant at nautical miles per hour $\left(S(\text{knots}) \right )$ where knots is the abbreviation for nautical miles per hour.

Identify the following statements in terms of and .

I. Liters of fuel in one hour.

II. Liters of fuel in 80 nautical miles.

Answer

To identify,

I. Liters of fuel in one hour.

Recall the given information,

A Shark XI is a new model remote aircraft. Under ideal flying conditions the Shark XI's fuel is nautical miles per liter $\left(F\frac{\text{nautical miles}}{L} \right )$ when flying speed is constant at nautical miles per hour $\left(S(\text{knots}) \right )$ where knots is the abbreviation for nautical miles per hour.

$F\frac{\text{nautical miles}}{L}; S\frac{\text{nautical miles}}{\text{hour}}$

To get liters per hour:

$\frac{\frac{\text{nautical miles}}{\text{hour}}}{\frac{\text{nautical miles}}{L}}=\frac{\text{nautical miles}}{\text{hour}}\times \frac{L}{\text{nautical miles}}$

the nautical miles cancel out and the solution is

$\frac{L}{\text{hours}}=\frac{S}{F}$

II. Liters of fuel in 80 nautical miles.

$F=\frac{\text{nautical miles}}{L}\Rightarrow F=\frac{80}{L}$

Now solving for liters results in the correct answer,

$\L\cdot F=\frac{80}{L}\cdot L \\\frac{LF}{F}=\frac{80}{F} \\L=\frac{80}{F}$

Compare your answer with the correct one above

Tap the card to reveal the answer