| Arithmetic | Fractions and Decimals | Percents | Ratios and Proportions | Word Problems |
|---|---|---|---|---|
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2
a can be 1, or 2. Since a is positive, divide both sides of the given inequality by a. Answers can only be integers, so only 1 and 2 are positive integers equal to or less than 2.
For how many positive integers, a, is it true that a² ≤ 2a?
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2/5
Boys over total. 12 over 30 reduced (use 6) is 2/5
A French class has 12 boys and 18 girls. Boys are what fraction of the class?
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$59.85
Cost of the radio was $57 - .95x60. 1.05x57 - 59.85
Charlie bought a $60 radio on sale at 5% off. How much did he pay, including the 5% sales tax?
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1:2
If you have 3 people in the office, 2 are non smokers and 1 is a smoker, so ratio is 1:2
If 2/3 of the workers in an office are non-smokers, what is the ratio of smokers to non-smokers?
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100
For the average to be 84 on 5 tests, the total number of point would be 420. Right now he has (80x4) points - 320. The difference is 100 points.
Justin's average (arithmetic mean) on four tests is 80. What grade does he need on his fifth test to raise his average to 84?
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5 degrees
In the 9 hours between 3am and noon, the temperature rose from -13 to 32 - 45 degrees total. 45/9 - 5.
At 3am the temperature was 13 degrees below zero. By noon it had risen to 32 degrees. What was the average hourly increase in temperature?
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44
Simple! 6/11 is twice as much as 3/11. So double 22 to get 44.
If 3/11 of a number is 22, what is 6/11 of that number?
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84%
21/25 passed, so .84 or 84%
If 25 students took an exam and 4 of them failed, what percent of them passed?
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1:4
20 accepted for every 80 rejected, 20:80 reduced is 1:4
If 80% of the applicants to a program were rejected, what is the ratio of the number accepted to the number rejected?
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78
His last birthday was October 14, 1968. 1968-1890 = 78
Dwight Eisenhower was born on October 14, 1890 and died on March 28, 1969. What was his age, in years, at the time of his death?
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4
I(-2-3) - (2-3)I = I(-5) - (-1)I = I-5+1I = I-4I = 4
What is the value of: I(-2-3) - (2-3)I
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7/12
There are 24 hours in a day, and 7 days in a week, so there are 168 hours in a week. 98/168 reduced is 7/12
What fractional part of a week is 98 hours?
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$88
Divide his earning of the second week by 1.25. $110 ÷ 1.25 = 88.
During his second week on the job, Jason earned $110. This represented a 25% increase over his earning from the previous week. How much did he earn during his first week?
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86.4
72 pages ÷ 60 minutes = 1.2 pages a minute. 1.2 pages a minute x 72 minutes = 86.4
John can read 72 pages per hour. At this rate, how many pages can he read in 72 minutes?
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4/5
Each marble is equally likely to have been removed. The likelihood that yellow is left is 1/5, the likelihood it was removed is 4/5
A jar has 5 marbles, 1 of each of the colors red, white, blue, green, and yellow. If 4 marbles are removed from the jar, what is the probability that the yellow marble was removed?
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100 times
Least common multiple of 4 and 9 is 36, so they will beep together every 36 seconds. In one hour there are 60 minutes, so 3600 seconds. Divide 3600 by 36, that's 100 instances of simultaneous beeping.
Maria has two electronic beepers. One of them beeps every 4 seconds; the other beeps every 9 seconds. If they are turned on at exactly the same time, how many times during the next hour will both beepers beep at the same time?
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.183
a= 3/7 and b=7/3. To divide these fractions, multiply by the reciprocal - so 3/7 x 3/7 = 9/49 or .183
If 7a = 3 and 3b = 7, what is the value of a/b?
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26
Add all the percentages together to get 98.7% are one of these three colors, meaning 1.3% are not these colors. .013 x 2000 is 26.
A jar contains 2000 marbles. If 61.5% of them are red, 27.2% of them are white, and 10% of them are blue, how many are neither red, white, or blue?
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2π
π = C/d, so π = C/2r, so 2π = C/r
What is the ratio of the circumference of a circle to its radius?
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312 minutes
First find the printing time without the rests, so 1 page every 5 seconds is 12 pages a minute. Divide the pages 3600 by the pages/minute - giving you 300 minutes. However, every hour there is 3 minutes of cooling time. 300 minutes is 5 hours, so you'll need 4 cooling off periods of 3 minutes each - adding 12 minutes to your total time for 312 minutes.
A printer that can print 1 page in 5 seconds shuts down for 3 minutes to cool off after every hour of operation. How many minutes will the printer take to print 3600 pages?
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19
To make y-x as large as possible, let y be as large as possible (so 12) and x as small as possible (-7) so 12--7 is 19
If -7≤ x ≤ 7 and 0 ≤ y ≤ 12, what is the greatest possible value of y-x?
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Multiply it by 1,000,000
Multiplying by 1,000 undoes the final erroneous division, but he still needs to multiply by 1,000 (the step he missed). So multiply by 1,000 x 1,000, or 1 million.
For the final step in a calculation, Paul accidentally divided by 1000 instead of multiplying by 1000. What should he do to his answer to correct it?
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1%
400% of a = 4a, which is 1% of 400a.
If a is a positive number, 400% of a is what percent of 400a?
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1200
Shares are 2x, 5x and 8x and the sum is 3000. 15x = 3000, x therefore is 200, so 1600 - 400 is 1200 for the difference.
Three associates agreed to split the profit of an investment in the ratio of 2:5:8. If the profit was $3000, what is the difference between the largest share and the smallest?
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1440
Think about the vowels first, there are 4 vowels in the word. So using the counting principle there are 4x3 = 12 ways to rearrange the first and last vowel-letters. The five other letters in the middle have no restrictions and could be vowels or consonants, leaving us with 5x4x3x2x1 options for rearranging these (120) 120x12=1440.
How many different ways are there to rearrange the letters in the word ELATION, if the first and last letter must each be a vowel?
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