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This essential trains for: SAT-I, GMAT, AMC-8, Math Kangaroo 7-8, Math Kangaroo 5-6.
For age problems, observe the following 2 rules:
|Time flows for everyone.||Jed is three times the age of Ned. Five years from now, Jed will be twice older than Ned. How old is Ned now?||
J is the age of Jed now and N is the age of Ned now.
Note how the 5 years were added to both J and N.
|An age difference does not change in time.||Ted is 45 and Zed is 17. How many years ago was Ted 5 times older than Zed?||
T denotes the age of Ted now. Z denotes the age of Zed now.
Some years ago Zed's age was X and Ted's age was 5X, but the difference was the same: 28 years.
At the time, Zed was 7 - it happened 10 years ago.
For coin problems, remember that the number of coins is different from the monetary value of the coins.
Example of coin problem:
In a piggy bank there are q quarters, d dimes and n nickels. There are twice as many nickels as quarters and half as many quarters as dimes. How many quarters are there if the total amount in the piggy bank is $6.50?
The most important thing is to keep in mind that q, d, and n are numbers of coins, whereas their monetary values are 0.25, 0.1, and 0.05, respectively.
Now compute the monetary value of the coins (in cents):
and set it to equal 650 cents:
There are 10 quarters in the piggy bank.
Examples of time problems:
There are 480 min in 8 hours.
9 periods of 53 minutes total 477 minutes.
There are 9 3-minute breaks totaling 27 minutes of break time.
|1 min = 60 s||
The maximum duration of a solar eclipse has been calculated to be of 7 minutes and 30 seconds.
How much percent of the longest possible duration was the duration of the 2009 eclipse?
|Convert the time to seconds in both cases.
The longest possible eclipse lasts 450 seconds. The 2009 eclipse lasted 396 seconds.
Denote the unknown percentage with x.
Solve for x to get 88%.
|1hr = 3600 s||Hearsay has it that Bill Gates' fortune increases by $150 every second. How much money does he make by sitting around doing nothing for 8 hours a day?||There is nothing to explain, really.|