Easy Questions

1. The difference of two number is 25. If the larger number is 1 less than 3 times the smaller, find the numbers.

1. The difference of two number is 25. If the larger number is 1 less than 3 times the smaller, find the numbers.

X=38, Y=13

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2. The sum of a number and it reciprocal is 5/2. Find the number.

2. The sum of a number and it reciprocal is 5/2. Find the number.

ANSWER

X=2

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3. A certain number is added to both the numerator and denominator of 5/7. If the resulting fraction is 4/5, find the number added.

3. A certain number is added to both the numerator and denominator of 5/7. If the resulting fraction is 4/5, find the number added.

ANSWER

X=3

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4. Diane can do a job in 9 hours while Lani can do the same job in 7 hours. How long would it take them working together?

4. Diane can do a job in 9 hours while Lani can do the same job in 7 hours. How long would it take them working together?

ANSWER

3 15/16 hours

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5. Machine A can do a job in 17 hours and machine B takes 12 hours to do the

same job . How long will the job take the two machines

working together?

5. Machine A can do a job in 17 hours and machine B takes 12 hours to do the

same job . How long will the job take the two machines

working together?

ANSWER

4 8/19 hours

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6. Find the equation of the line with slope 2 passing through (4, 6).

6. Find the equation of the line with slope 2 passing through (4, 6).

ANSWER

2x-y=14

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7. Find the equation of the line passing through (-3, 5) and (1, 1).

7. Find the equation of the line passing through (-3, 5) and (1, 1).

ANSWER

x+y=2

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8. Find the equation of the line with slope -3

and y-intercept 5.

8. Find the equation of the line with slope -3

and y-intercept 5.

ANSWER

3x+y=5

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9. Find the equation of the line with x-intercept 2 and y-intercept -1.

9. Find the equation of the line with x-intercept 2 and y-intercept -1.

ANSWER

x-2y=2

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10. Find the equation of the line (6, -2) and parallel to the line x-9y=6.

10. Find the equation of the line (6, -2) and parallel to the line x-9y=6.

ANSWER

x-9y=24

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Average Questions

1. Louie drives his civic 270 kilometers in the same time that Derek drives his Lancer 250 kilometer. If Louie averages 4 kilometers faster than Derek, find their rates.

1. Louie drives his civic 270 kilometers in the same time that Derek drives his Lancer 250 kilometer. If Louie averages 4 kilometers faster than Derek, find their rates.

ANSWER

Derek=50kphLouie=54kph

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2. The sum of two numbers is 100. If the sum of their

square roots is 14, what are the numbers?

2. The sum of two numbers is 100. If the sum of their

square roots is 14, what are the numbers?

ANSWER

x=36 or x=64

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3. A motorboat can travel 18 km downstream in the same

time it can travel 12 km upstream. If the rate of the

current is 5 km per hour, what is the speed of he boat in still

water?

3. A motorboat can travel 18 km downstream in the same

time it can travel 12 km upstream. If the rate of the

current is 5 km per hour, what is the speed of he boat in still

water?

ANSWER

25 kilometer per hour

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4. In a chemistry class, 6 liters of a 12% alcohol solution must be mixed with a 20% solution

to get a 14% solution. How many liters of the 20%solution

are needed?

4. In a chemistry class, 6 liters of a 12% alcohol solution must be mixed with a 20% solution

to get a 14% solution. How many liters of the 20%solution

are needed?

ANSWER

2 liters of the 20% solution

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5. Two train leave the same terminalat the same time and travel in opposite directions, with the first train traveling at a speed of 20 kilometers per hour faster than the other. After 5 hours , they are 700 kilometers apart. Find the speed of each.

5. Two train leave the same terminalat the same time and travel in opposite directions, with the first train traveling at a speed of 20 kilometers per hour faster than the other. After 5 hours , they are 700 kilometers apart. Find the speed of each.

ANSWER

60 kph and 80 kph

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6. Tony has 11 more nickels than quarters. How many coins does he have if the total value of his coins is $2.65?

6. Tony has 11 more nickels than quarters. How many coins does he have if the total value of his coins is $2.65?

ANSWER

7 coins

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7. Train A, traveling 70 miles per hour (mph), leaves Westford heading toward Eastford, 260 miles away. At the same time Train B, traveling 60 mph, leaves Eastford heading toward Westford. When do the two trains meet?

7. Train A, traveling 70 miles per hour (mph), leaves Westford heading toward Eastford, 260 miles away. At the same time Train B, traveling 60 mph, leaves Eastford heading toward Westford. When do the two trains meet?

ANSWER

The trains meet two hours after leaving their respective cities.

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8. Let P be a point inside a square S so that the distances from P to the four vertices, in order, are 7, 35, 49, and x. What is x?

8. Let P be a point inside a square S so that the distances from P to the four vertices, in order, are 7, 35, 49, and x. What is x?

ANSWER

35

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9. A father in his will left all his money to his children in the following manner:$1000 to the first born and 1/10 of what then remains, then$2000 to the second born and 1/10 of what then remains, then$3000 to the third born and 1/10 of what then remains, and so on.When this was done each child had the same amount. How many children were there?

ANSWER

9 children

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10. Sally is thinking of a 6-digit number. The sum of the digits is 43. And only two of the following three statements about the number are true: (1) it's a square number. (2) it's a cube number, and (3) the number is under 500000. What number was Sally thinking of?

10. Sally is thinking of a 6-digit number. The sum of the digits is 43. And only two of the following three statements about the number are true: (1) it's a square number. (2) it's a cube number, and (3) the number is under 500000. What number was Sally thinking of?

ANSWER

499,849

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Difficult

Questions

1. There are 1000 lockers in a high school with 1000 students. The problem begins with the first student opening all 1000 lockers; next the second student closes lockers 2,4,6,8,10 and so on to locker 1000; the third student changes the state (opens lockers closed, closes lockers open) on lockers 3,6,9,12,15 and so on; the fourth student changes the state of lockers 4,8,12,16 and so on. This goes on until every student has had a turn. How many lockers are opened?

ANSWER

31 of the 1000 lockers are still open

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2. Two trains 150 miles apart are traveling toward each other along the same track. The first train goes 60 miles per hour; the second train rushes along at 90 miles per hour. A fly is hovering just above the nose of the first train. It buzzes from the first train to the second train, turns around immediately, flies back to the first train, and turns around again. It goes on flying back and forth between the two trains until they collide. If the fly's speed is 120 miles per hour, how far will it travel?

2. Two trains 150 miles apart are traveling toward each other along the same track. The first train goes 60 miles per hour; the second train rushes along at 90 miles per hour. A fly is hovering just above the nose of the first train. It buzzes from the first train to the second train, turns around immediately, flies back to the first train, and turns around again. It goes on flying back and forth between the two trains until they collide. If the fly's speed is 120 miles per hour, how far will it travel?

ANSWER

The fly spends the same amount of time traveling as the trains. It goes 120 miles/ hour, so in the one hour the trains take to collide, the fly will go 120 miles.

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Answer

3. Every month, a girl gets allowance. Assume last year she had no money, and kept it up to now. Then she spends 1/2 of her money on clothes, then 1/3 of the remaining money on games, and then 1/4 of the remaining money on toys. After she bought all of that, she had $7777 left. Assuming she only gets money by allowance, how much money does she earn every month?

3. Every month, a girl gets allowance. Assume last year she had no money, and kept it up to now. Then she spends 1/2 of her money on clothes, then 1/3 of the remaining money on games, and then 1/4 of the remaining money on toys. After she bought all of that, she had $7777 left. Assuming she only gets money by allowance, how much money does she earn every month?

$2222

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Answer

4. An absentminded bank teller switches the dollars and cents when he cashed a check for Mr. Spencer, giving him dollars instead of cents, and cents instead of dollars. After buying a five cent newspaper, Mr. Spencer discovered he had left exactly twice as much as his original check. What was the amount of the check?

4. An absentminded bank teller switches the dollars and cents when he cashed a check for Mr. Spencer, giving him dollars instead of cents, and cents instead of dollars. After buying a five cent newspaper, Mr. Spencer discovered he had left exactly twice as much as his original check. What was the amount of the check?

$31.63

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Answer

5. Suppose a circular hole was drilled through the center of a sphere. When the length of the hole was measured along its wall, it was found to be six inches long.  What is the volume of the part of the sphere that remains after the material is removed from the hole?  Express your answer as an exact real number of cubic inches.

(4/3)π(3³) = 36π

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6.Two people stand back to back next to the rails in a small railway station. As the head of the express train that passes the station reaches them, they start to walk parallel to the rails. As the tail of the train reaches each of them, they stop, having walked 30m and 40m respectively. If they both walked with identical, constant speed and the train kept its speed as well, can you tell how long the train was?

240m

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5

Answer

7. Two boats on the opposite shores of a river start moving towards each other. When they pass each other they are 750 yards from one shoreline. They each continue to the opposite shore, immediately turn around and start back. When they meet again they are 250 yards from the other shoreline. Each boat maintains a constant speed throughout. How wide is the river?

2000 yards

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6

Answer

8. A man had a 10-gallon keg of wine and a jug.  One day, he drew off a jugful of wine and filled up the keg with water.  Later on, when the wine and water had got thoroughly mixed, he drew off another jugful and again filled up the keg with water.  The keg then contained equal quantities of wine and water.  What was the capacity of the jug?

2.928932188 gallons

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9. Let P be a point inside a square S so that the distances from P to the four vertices, in order, are 7, 35, 49, and x. What is x?

x = 35

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10. The number of divisors of 55n3 are 55 (Including 1 and the number itself). How many divisors does 7n7 have?

352

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