ID 777

ID 778

ID 779

ID 780

ID 784

ID 787

ID 788

ID 789

ID 790

ID 791

ID 792

ID 793

ID 811

ID 818

ID 834

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ID 845

ID 846

Find the sum of all the elements of this finite geometric sequence:

1, 2, 4, 8, 16, 32, 64, . . . , 1024.

ID 849

ID 852

ID 1037

ID 1080

Two candles are of the same height.

One burns in four hours, while the other burns in five hours.

When is one twice the height of the other?

ID 1117

In Morse code, each symbol is either a dot or a dash.

How many different sequences of 8 symbols are possible?

ID 1180

ID 1195

ID 1205

ID 1354

ID 1544

ID 1552

One apple and one banana together cost $3.

One apple and one carrot together cost $4.

One banana and one carrot together cost $5.

How much does an apple cost?

ID 1615

You have two buckets. The first bucket contains 5 liters of water and the second contains 5 liters of milk.

If you pour 1 liter of the water into the milk and then return 1 liter of the mixture to the water bucket, what are the proportions of milk to water in the first bucket?

ID 1652

ID 1960

I would like to write 1000 as n^{2} - m^{2}, where n and m are positive integers.

Which number can be a solution for the problem?

ID 3070

ID 3112

ID 3122

ID 3142

ID 3150

ID 3152

**A** is the set of all points (x,y) in the shaded region.

Find the set **B** consisting of all points (2x, -y)?

ID 3153

ID 3155

A perfect cube is an integer whose cube root is an integer.

For example, 64 and 125 are perfect cubes.

A and B are perfect cubes.

Which of the following will NOT necessarily be a perfect cube?

ID 3180

ID 3444

100% of 90 girls and 90% of 100 boys have shown up in the concert hall on time.

10 teachers came even earlier.

What percentage of the people were late?

ID 3515

Divide 77 into three parts so that one is 150 percent of each of the other two.

What is the smallest number?

ID 3660

ID 3742

Engineers at a race company make three discoveries.

The first invention saves 50% of fuel, the second 30%, and the third 20%.

If the company uses all three innovations at once, how much fuel does a car consume compared with a normal car?

ID 3865

The average age of all teachers and students in a school is 15.

The average age of the teachers is 33.

The average age of the students is 12.

What is the ratio of teachers to students in the school?

ID 3891

One pipe can empty a pool 5 times faster than a second pipe.

When both pipes are opened, they empty the pool in five hours.

How long would it take to empty the pool if only the faster pipe is used?

ID 3912

ID 3921

The sum of the ages of four sisters is 30.

The sum of their ages four years ago was 15.

How old is the youngest sister?

ID 4028

ID 4042

ID 4076

A retailer offers a 25% discount off the normal price of a wooden puzzle.

She makes a profit of 25% over the cost of the puzzle.

What is her profit if the normal price of the puzzle is $20?

ID 4079

An outlet pipe can drain a full pool in 12 hours.

An inlet pipe can fill the empty pool in 8 hours.

The performance of the pipes does not depend on the water volume in the pool.

If both valves are opened, how long will it take to fill the pool?

ID 4272

A circle of radius 3 is drawn centered at the origin.

How many squares of side length 1 and integer coordinate vertices are inside the circle or intersect it?

ID 4374

ID 4379

ID 4473

Mrs. Smith puts $10,000 into a saving account that earns 2% interest compounded annually.

Which expression can be used to find the value of her money in the account at the end of the third year?

ID 4651

James has scored an average of 10 on his first 10 tests.

What score should he get in his eleventh test, so that his average moves up to 11?

ID 4866

Gerry earns 9% commission for each camera sold.

Today, he earned $44.1 commission.

What was his sales total for today?

ID 5107

In a shop, two liters of water costs $1, two liters of natural syrup cost $21, and two liters of the beverage that includes both costs $2.

The shop does not charge a premium for mixing the beverage.

What part of this beverage is the syrup?

ID 5271

If 15 students occupy 5/6 of the seats in the classroom, how many students would occupy 2/3 of the seats in the classroom?