Display Problems

Imagination is more important than knowledge... Albert Einstein

Guess is more important than calculation --- Knowhowacademy.com

Numbers - Percentage

For COMPETITION
Number of Total Problems: 11.
FOR PRINT ::: (Book)

Problem Num : 1

From : NCTM

Type: Application

Section:Numbers

Theme:Manipulation
Adjustment# :

Difficulty: 2

Category Percentage

Analysis

Solution/Answer

Problem Num : 2

From : AMC10B

Type:

Section:Numbers

Theme:
Adjustment# : 0

Difficulty: 1

'
Each day, Jenny ate $20\%$ of the jellybeans that were in her jar at the beginning of that day. At the end of the second day, $32$ remained. How many jellybeans were in the jar originally?
$mathrm{(A) 40 } qquad mathrm{(B) 50 } qquad mathrm{(C) 55 } qquad mathrm{(D) 60 } qquad mathrm{(E) 75 }$
'

Category Percentage

Analysis

Solution/Answer
Since Jenny eats $20\%$ of her jelly beans per day, $80\%=frac{4}{5}$ of her jelly beans remain after one day.
Let $x$ be the number of jelly beans in the jar originally.
$frac{4}{5}cdotfrac{4}{5}cdot x=32$
$frac{16}{25}cdot x=32$
$x=frac{25}{16}cdot32= 50 Rightarrow oxed{B}$

Answer:

Problem Num : 3

From : AMC10

Type:

Section:Numbers

Theme:
Adjustment# : 0

Difficulty: 1

'
A solid box is $15$ cm by $10$ cm by $8$ cm. A new solid is formed by removing a cube $3$ cm on a side from each corner of this box. What percent of the original volume is removed?
$mathrm{(A) } 4.5\%qquad mathrm{(B) } 9\%qquad mathrm{(C) } 12\%qquad mathrm{(D) } 18\%qquad mathrm{(E) } 2...$
'

Category Percentage

Analysis

Solution/Answer
The volume of the original box is $15cdot10cdot8=1200$
The volume of each cube that is removed is $3cdot3cdot3=27$
Since there are $8$ corners on the box, $8$ cubes are removed.
So the total volume removed is $8cdot27=216$ .
Therefore, the desired percentage is $frac{216}{1200}cdot100 = oxed{mathrm{(D)} 18\%}$

Answer:

Problem Num : 4

From : AMC10B

Type:

Section:Numbers

Theme:
Adjustment# : 0

Difficulty: 1

'
A positive number $x$ has the property that $x\%$ of $x$ is $4$ . What is $x$ ?
$mathrm{(A)} 2 qquadmathrm{(B)} 4 qquadmathrm{(C)} 10 qquadmathrm{(D)} 20 qquadmathrm{(E)} 4...$
'

Category Percentage

Analysis

Solution/Answer
$0.01x cdot x=4 Rightarrow x^2 = 400 Rightarrow x = oxed{20}.$

Answer:

Problem Num : 5

From : AMC10

Type:

Section:Numbers

Theme:
Adjustment# : 0

Difficulty: 1

'
At Euclid High School, the number of students taking the AMC 10 was $60$ in 2002, $66$ in 2003, $70$ in 2004, $76$ in 2005, $78$ and 2006, and is $85$ in 2007. Between what two consecutive years was there the largest percentage increase?
$ext{(A)} 2002 ext{and} 2003 qquad ext{(B)} 2003 ext{and} 2004 qquad ext{(C)} 2004 ext{and} 2005 qquad...$
'

Category Percentage

Analysis

Solution/Answer
We compute the percentage increases:

$frac{66 - 60}{60} = 10\%$
$frac{70 - 66}{66} approx 6\%$
$frac{76-70}{70} approx 8.6\%$
$frac{78-76}{76} approx 2.6\%$
$frac{85-78}{78} approx 9\%$

The answer is $mathrm{(A)}$ .
In fact, the answer follows directly from examining the differences between each year. The largest differences are $6,6,7$ , and it is easy to see that due to the decreased starting number of students in 2002 that that will be our answer.

Answer:

Problem Num : 6

From : AMC10

Type:

Section:Numbers

Theme:
Adjustment# : 0

Difficulty: 1

'
Last year Mr. Jon Q. Public received an inheritance. He paid $20\%$ in federal taxes on the inheritance, and paid $10\%$ of what he had left in state taxes. He paid a total of $\text{[math]}$ 10500 for both taxes. How many dollars was his inheritance?
$(mathrm {A}) 30000 qquad (mathrm {B}) 32500 qquad(mathrm {C}) 35000 qquad(mathrm {D}) 37500 qquad(mathrm {E}) 4...$
'

Category Percentage

Analysis

Solution/Answer
After paying his taxes, he has $0.8*0.9=0.72$ of the inheritance left. Since $10500$ is $0.28$ of the inheritance, the whole inheritance is $frac{10500}{0.28}=37500 mathrm{(D)}$ .

Answer:

Problem Num : 7

From : AMC10B

Type:

Section:Numbers

Theme:
Adjustment# : 0

Difficulty: 1

'
In a certain year the price of gasoline rose by $20\%$ during January, fell by $20\%$ during February, rose by $25\%$ during March, and fell by $x\%$ during April. The price of gasoline at the end of April was the same as it had been at the beginning of January. To the nearest integer, what is $x$
$mathrm{(A)} 12qquadmathrm{(B)} 17qquadmathrm{(C)} 20qquadmathrm{(D)} 25qquadmathrm{(E)} 35$
'

Category Percentage

Analysis

Solution/Answer
Let $p$ be the price at the beginning of January. The price at the end of March was $(1.2)(0.8)(1.25)p = 1.2p.$ Because the price at the of April was $p$ , the price decreased by $0.2p$ during April, and the percent decrease was $x = 100 cdot frac{0.2p}{1.2p} = frac {100}{6} approx 16.7.$ So to the nearest integer $x$ is $oxed{17}$ . The answer is $mathrm{(B)}$ .

Answer:

Problem Num : 8

From : AMC10B

Type:

Section:Numbers

Theme:
Adjustment# : 0

Difficulty: 1

'
Makarla attended two meetings during her $9$ -hour work day. The first meeting took $45$ minutes and the second meeting took twice as long. What percent of her work day was spent attending meetings?
$extbf{(A)} 15 qquad extbf{(B)} 20 qquad extbf{(C)} 25 qquad extbf{(D)} 30 qquad extbf{(E)} 35$
'

Category Percentage

Analysis

Solution/Answer
The percentage of her time spent in meetings is the total amount of time spent in meetings divided by the length of her workday.
The total time spent in meetings is $45 ext{ min} + 2*45 ext{ min} = 2 ext{ hours } 15 ext{ min} = 9/4 ext{ hours}$
Therefore, the percentage is $frac{9/4 ext{ hours} }{9 ext{ hours}} = frac{1}{4} = 25 \% = oxed{ extbf{(C)} 25}$

Answer:

Problem Num : 9

From : AMC10

Type:

Section:Numbers

Theme:
Adjustment# : 0

Difficulty: 1

'
In a collection of red, blue, and green marbles, there are $25\%$ more red marbles than blue marbles, and there are $60\%$ more green marbles than red marbles. Suppose that there are $r$ red marbles. What is the total number of marbles in the collection?
$mathrm{(A)} 2.85rqquadmathrm{(B)} 3rqquadmathrm{(C)} 3.4rqquadmathrm{(D)} 3.85rqquadmathrm{(E)} 4.25r$
'

Category Percentage

Analysis

Solution/Answer
The number of blue marbles is $frac{4}{5}r$ , the number of green marbles is $frac{8}{5}r$ , and the number of red marbles is $r$ .
Thus, the total number of marbles is $frac{4}{5}r+frac{8}{5}r+r=3.4r$ , and the answer is $mathrm{(C)}$ .

Answer:

Problem Num : 10

From : AMC10

Type:

Section:Numbers

Theme:
Adjustment# : 0

Difficulty: 1

'
A carton contains milk that is $2$ % fat, an amount that is $40$ % less fat than the amount contained in a carton of whole milk. What is the percentage of fat in whole milk?
$mathrm{(A)} frac{12}{5}qquadmathrm{(B)} 3qquadmathrm{(C)} frac{10}{3}qquadmathrm{(D)} 38qquadmathrm{(E)} 42$
'

Category Percentage

Analysis

Solution/Answer
Rewording the question, basically we are being asked "2 is 40% less than what number?" If x represents the number we are looking for, then 40% less than the number would be represented by $x-0.4x$ or $0.6x$ . Thus $0.6x=2$ ; solving for x, we get $x=frac{10}{3}$ , $longrightarrow fbox{C}$

Answer:

Array ( [0] => 3730 [1] => 8210 [2] => 7770 [3] => 8028 [4] => 7848 [5] => 7849 [6] => 8110 [7] => 8126 [8] => 7872 [9] => 7887 ) 111 2