How to find the percent of increase - GRE Quantitative Reasoning
Card 1 of 96
Harry and Gerry each own equal shares in a gardening company. Their partner, Izzy, owns 40% of the company. What is the percentage increase of the sum of Harry's and Gerry's shares above Izzy's share in the company?
Harry and Gerry each own equal shares in a gardening company. Their partner, Izzy, owns 40% of the company. What is the percentage increase of the sum of Harry's and Gerry's shares above Izzy's share in the company?
Tap to reveal answer
This basic percentage problem asks you to determine by what percentage the sum of Harry's and Gerry's share of the company is greater than ("exceeds") Izzy's share. Harry's and Gerry's share's are equal, and the sum is 60% of the company (100% – Izzy's 40% = 60%). 60% is 50% greater than 40% (0.40 * 1.5 = 0.60). Examinees may be tempted to go too far with the problem and mistake their task by finding how much greater Izzy's share is than either Harry's or Gerry's. Be careful to read instructions and translate keywords appropriately.
You may think the answer is 20% (60% – 40%), but this is the difference in terms of total shares in the company, not in terms of Izzy's shares, which is what the question is asking.
This basic percentage problem asks you to determine by what percentage the sum of Harry's and Gerry's share of the company is greater than ("exceeds") Izzy's share. Harry's and Gerry's share's are equal, and the sum is 60% of the company (100% – Izzy's 40% = 60%). 60% is 50% greater than 40% (0.40 * 1.5 = 0.60). Examinees may be tempted to go too far with the problem and mistake their task by finding how much greater Izzy's share is than either Harry's or Gerry's. Be careful to read instructions and translate keywords appropriately.
You may think the answer is 20% (60% – 40%), but this is the difference in terms of total shares in the company, not in terms of Izzy's shares, which is what the question is asking.
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A city originally had a 
sales tax, but increased it to 
. Assuming that the rate of consumption in the city does not change, what was the total amount of sales tax collected when the rate was 
if the increase in tax brought in an additional 
in revenue?
A city originally had a
Tap to reveal answer
One way to solve this is by considering that the increase in taxes is a linear addition of 2%. Therefore we can ask the question, 2% of what amount yields $150,000? This can be represented in the following equation:
0.02 * x = 150,000
Solve for x: $7,500,000
Therefore, the total at the old rate is 7,500,000 * 0.06 = $450,000.
One way to solve this is by considering that the increase in taxes is a linear addition of 2%. Therefore we can ask the question, 2% of what amount yields $150,000? This can be represented in the following equation:
0.02 * x = 150,000
Solve for x: $7,500,000
Therefore, the total at the old rate is 7,500,000 * 0.06 = $450,000.
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What is the percent change in the area of a circle if its circumference increases from 20 to 45?
What is the percent change in the area of a circle if its circumference increases from 20 to 45?
Tap to reveal answer
The circumference of a circle increases linearly with its radius. Therefore, an increase in circumference from 20 to 45 represents an increase of (45 – 20) / 20 = 25 / 20 = 125% increase. This means that if the radius was r, it is now r + 1.25r = 2.25r.
Now, the original area, supposing r as our radius, would be πr2
The new area would be π(2.25r)2 = 5.0625πr2
The percent change would be: (5.0625πr2 - πr2) / πr2 = (4.0625πr2) / πr2 = 4.0625 or 406.25%
The circumference of a circle increases linearly with its radius. Therefore, an increase in circumference from 20 to 45 represents an increase of (45 – 20) / 20 = 25 / 20 = 125% increase. This means that if the radius was r, it is now r + 1.25r = 2.25r.
Now, the original area, supposing r as our radius, would be πr2
The new area would be π(2.25r)2 = 5.0625πr2
The percent change would be: (5.0625πr2 - πr2) / πr2 = (4.0625πr2) / πr2 = 4.0625 or 406.25%
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According to the graph above, what was the percent change in the sales of camcorders from 2002-2006?
According to the graph above, what was the percent change in the sales of camcorders from 2002-2006?
Tap to reveal answer
For this problem, pay attention only to the values between 2002 and 2006 - each of which is 17 (thousand) and 22 (thousand). Note that the decrease within this range does not need to be accounted for, as the question asks only for values relative to 2002 and 2006.
To calculate percent change, take it as a fraction: 22/17 = 1.294; this represents approximately 129% of the actual value or a 29% increase in sales across these 4 years.
For this problem, pay attention only to the values between 2002 and 2006 - each of which is 17 (thousand) and 22 (thousand). Note that the decrease within this range does not need to be accounted for, as the question asks only for values relative to 2002 and 2006.
To calculate percent change, take it as a fraction: 22/17 = 1.294; this represents approximately 129% of the actual value or a 29% increase in sales across these 4 years.
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Alex had an investment worth $1500. If the total investment increased 25% the first year and decreased 10% the next year, what is the final worth of the investment.
Alex had an investment worth $1500. If the total investment increased 25% the first year and decreased 10% the next year, what is the final worth of the investment.
Tap to reveal answer
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Book sales increased by 50% from April 1st to 30th and then decreased by 50% from May 1st to May 31st. Determine the greater quanity.
Book sales increased by 50% from April 1st to 30th and then decreased by 50% from May 1st to May 31st. Determine the greater quanity.
Tap to reveal answer
If book sales were 100/day then an increase by 50% means they would reach 150/day (by the end of April). A decrease at that point means a 50% decrease in 150/day which would lower book sales to 75/day. Thus sales were higher at the beginning of April than at the end of May.
If book sales were 100/day then an increase by 50% means they would reach 150/day (by the end of April). A decrease at that point means a 50% decrease in 150/day which would lower book sales to 75/day. Thus sales were higher at the beginning of April than at the end of May.
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A college student takes out a loan of $8,000 per Quarter. A college student's average living cost is represented by the chart below.
Suppose tution is increased by 8%. What is the increase in the percentage of the loan that is spent on tutition and books?
A college student takes out a loan of $8,000 per Quarter. A college student's average living cost is represented by the chart below.
Suppose tution is increased by 8%. What is the increase in the percentage of the loan that is spent on tutition and books?
Tap to reveal answer
The original percentage of the loan spent on tutition and books is 57.09%. After the 8% increase in tutition, the percentage of the loan is 60.97%
Thus, the increase in percentage is 
.
The original percentage of the loan spent on tutition and books is 57.09%. After the 8% increase in tutition, the percentage of the loan is 60.97%
Thus, the increase in percentage is
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By what percentage did the total book sales of the three stores increase from 2005 to 2010?
By what percentage did the total book sales of the three stores increase from 2005 to 2010?
Tap to reveal answer
Find the total number of books sold in 2005: 8 + 12 + 10 = 30 thousand
Find the total number of books sold in 2010: 11 + 13 + 12 = 36 thousand
Find the total number of books sold in 2005: 8 + 12 + 10 = 30 thousand
Find the total number of books sold in 2010: 11 + 13 + 12 = 36 thousand
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Which of the following is 
greater than 
?
Which of the following is
Tap to reveal answer
The value of 
.
In scientific notation, this is 
.
The value of
In scientific notation, this is
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A new painting company, Paintz, reported a profit of six thousand dollars in 2011. In 2012, Paintz reported $10,000 more profit than 2011. What was the percentage increase in profit for Paintz between 2011 and 2012?
A new painting company, Paintz, reported a profit of six thousand dollars in 2011. In 2012, Paintz reported $10,000 more profit than 2011. What was the percentage increase in profit for Paintz between 2011 and 2012?
Tap to reveal answer
The formula for percentage increase is the difference in profit divided by the original profit multiplied by 100. Here the difference in profit between 2011 and 2012 is 10,000 and the original profit in 2012 is 6000, therefore the percentage increase is 
.
The formula for percentage increase is the difference in profit divided by the original profit multiplied by 100. Here the difference in profit between 2011 and 2012 is 10,000 and the original profit in 2012 is 6000, therefore the percentage increase is
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In 2014, approximately 
of Americans were considered charming. In 2013 approximately 27.1% of Americans were deemed charming. If the population of America in 2013 was 
people and the population of America in 2014 was roughly 
people, what is the percent increase/decrease of charming people from 2013-2014? Round to the nearest tenth.
In 2014, approximately
Tap to reveal answer
To solve this problem, we must understand that we can't simply use the percentage change from 2013-2014 in order to solve this problem. Because the populations change, simply using the percentage change in order to is invalid. Therefore we must find the amount of people that were charming in each year to solve for this problem.
In 2013, 
of the 
people in America were considered charming, this means that the number of charming people in America in 2013 is 
people.
In 2014, 
of the 
people in America were considered charming, this means that the number of charming people in America in 2014 is 
people.
Therefore to find the percent increase of charming people, we simply find the difference in charming people from 2013-2014 and divide by the number of charming people in 2013. 
or a 
increase in charming people.
To solve this problem, we must understand that we can't simply use the percentage change from 2013-2014 in order to solve this problem. Because the populations change, simply using the percentage change in order to is invalid. Therefore we must find the amount of people that were charming in each year to solve for this problem.
In 2013,
In 2014,
Therefore to find the percent increase of charming people, we simply find the difference in charming people from 2013-2014 and divide by the number of charming people in 2013.
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Harry and Gerry each own equal shares in a gardening company. Their partner, Izzy, owns 40% of the company. What is the percentage increase of the sum of Harry's and Gerry's shares above Izzy's share in the company?
Harry and Gerry each own equal shares in a gardening company. Their partner, Izzy, owns 40% of the company. What is the percentage increase of the sum of Harry's and Gerry's shares above Izzy's share in the company?
Tap to reveal answer
This basic percentage problem asks you to determine by what percentage the sum of Harry's and Gerry's share of the company is greater than ("exceeds") Izzy's share. Harry's and Gerry's share's are equal, and the sum is 60% of the company (100% – Izzy's 40% = 60%). 60% is 50% greater than 40% (0.40 * 1.5 = 0.60). Examinees may be tempted to go too far with the problem and mistake their task by finding how much greater Izzy's share is than either Harry's or Gerry's. Be careful to read instructions and translate keywords appropriately.
You may think the answer is 20% (60% – 40%), but this is the difference in terms of total shares in the company, not in terms of Izzy's shares, which is what the question is asking.
This basic percentage problem asks you to determine by what percentage the sum of Harry's and Gerry's share of the company is greater than ("exceeds") Izzy's share. Harry's and Gerry's share's are equal, and the sum is 60% of the company (100% – Izzy's 40% = 60%). 60% is 50% greater than 40% (0.40 * 1.5 = 0.60). Examinees may be tempted to go too far with the problem and mistake their task by finding how much greater Izzy's share is than either Harry's or Gerry's. Be careful to read instructions and translate keywords appropriately.
You may think the answer is 20% (60% – 40%), but this is the difference in terms of total shares in the company, not in terms of Izzy's shares, which is what the question is asking.
← Didn't Know|Knew It →
A city originally had a sales tax, but increased it to . Assuming that the rate of consumption in the city does not change, what was the total amount of sales tax collected when the rate was if the increase in tax brought in an additional in revenue?
A city originally had a
Tap to reveal answer
One way to solve this is by considering that the increase in taxes is a linear addition of 2%. Therefore we can ask the question, 2% of what amount yields $150,000? This can be represented in the following equation:
0.02 * x = 150,000
Solve for x: $7,500,000
Therefore, the total at the old rate is 7,500,000 * 0.06 = $450,000.
One way to solve this is by considering that the increase in taxes is a linear addition of 2%. Therefore we can ask the question, 2% of what amount yields $150,000? This can be represented in the following equation:
0.02 * x = 150,000
Solve for x: $7,500,000
Therefore, the total at the old rate is 7,500,000 * 0.06 = $450,000.
← Didn't Know|Knew It →
What is the percent change in the area of a circle if its circumference increases from 20 to 45?
What is the percent change in the area of a circle if its circumference increases from 20 to 45?
Tap to reveal answer
The circumference of a circle increases linearly with its radius. Therefore, an increase in circumference from 20 to 45 represents an increase of (45 – 20) / 20 = 25 / 20 = 125% increase. This means that if the radius was r, it is now r + 1.25r = 2.25r.
Now, the original area, supposing r as our radius, would be πr2
The new area would be π(2.25r)2 = 5.0625πr2
The percent change would be: (5.0625πr2 - πr2) / πr2 = (4.0625πr2) / πr2 = 4.0625 or 406.25%
The circumference of a circle increases linearly with its radius. Therefore, an increase in circumference from 20 to 45 represents an increase of (45 – 20) / 20 = 25 / 20 = 125% increase. This means that if the radius was r, it is now r + 1.25r = 2.25r.
Now, the original area, supposing r as our radius, would be πr2
The new area would be π(2.25r)2 = 5.0625πr2
The percent change would be: (5.0625πr2 - πr2) / πr2 = (4.0625πr2) / πr2 = 4.0625 or 406.25%
← Didn't Know|Knew It →
According to the graph above, what was the percent change in the sales of camcorders from 2002-2006?
According to the graph above, what was the percent change in the sales of camcorders from 2002-2006?
Tap to reveal answer
For this problem, pay attention only to the values between 2002 and 2006 - each of which is 17 (thousand) and 22 (thousand). Note that the decrease within this range does not need to be accounted for, as the question asks only for values relative to 2002 and 2006.
To calculate percent change, take it as a fraction: 22/17 = 1.294; this represents approximately 129% of the actual value or a 29% increase in sales across these 4 years.
For this problem, pay attention only to the values between 2002 and 2006 - each of which is 17 (thousand) and 22 (thousand). Note that the decrease within this range does not need to be accounted for, as the question asks only for values relative to 2002 and 2006.
To calculate percent change, take it as a fraction: 22/17 = 1.294; this represents approximately 129% of the actual value or a 29% increase in sales across these 4 years.
← Didn't Know|Knew It →
Alex had an investment worth $1500. If the total investment increased 25% the first year and decreased 10% the next year, what is the final worth of the investment.
Alex had an investment worth $1500. If the total investment increased 25% the first year and decreased 10% the next year, what is the final worth of the investment.
Tap to reveal answer
← Didn't Know|Knew It →
Book sales increased by 50% from April 1st to 30th and then decreased by 50% from May 1st to May 31st. Determine the greater quanity.
Book sales increased by 50% from April 1st to 30th and then decreased by 50% from May 1st to May 31st. Determine the greater quanity.
Tap to reveal answer
If book sales were 100/day then an increase by 50% means they would reach 150/day (by the end of April). A decrease at that point means a 50% decrease in 150/day which would lower book sales to 75/day. Thus sales were higher at the beginning of April than at the end of May.
If book sales were 100/day then an increase by 50% means they would reach 150/day (by the end of April). A decrease at that point means a 50% decrease in 150/day which would lower book sales to 75/day. Thus sales were higher at the beginning of April than at the end of May.
← Didn't Know|Knew It →
A college student takes out a loan of $8,000 per Quarter. A college student's average living cost is represented by the chart below.
Suppose tution is increased by 8%. What is the increase in the percentage of the loan that is spent on tutition and books?
A college student takes out a loan of $8,000 per Quarter. A college student's average living cost is represented by the chart below.
Suppose tution is increased by 8%. What is the increase in the percentage of the loan that is spent on tutition and books?
Tap to reveal answer
The original percentage of the loan spent on tutition and books is 57.09%. After the 8% increase in tutition, the percentage of the loan is 60.97%
Thus, the increase in percentage is .
The original percentage of the loan spent on tutition and books is 57.09%. After the 8% increase in tutition, the percentage of the loan is 60.97%
Thus, the increase in percentage is
← Didn't Know|Knew It →
By what percentage did the total book sales of the three stores increase from 2005 to 2010?
By what percentage did the total book sales of the three stores increase from 2005 to 2010?
Tap to reveal answer
Find the total number of books sold in 2005: 8 + 12 + 10 = 30 thousand
Find the total number of books sold in 2010: 11 + 13 + 12 = 36 thousand
Find the total number of books sold in 2005: 8 + 12 + 10 = 30 thousand
Find the total number of books sold in 2010: 11 + 13 + 12 = 36 thousand
← Didn't Know|Knew It →
Which of the following is greater than ?
Which of the following is
Tap to reveal answer
The value of
.
In scientific notation, this is .
The value of
In scientific notation, this is
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