Using only the digits 2, 4, 6, 8 each exactly once, how much larger is the greatest 4-digit number that can be made than the least 4-digit number?

Tom is 8 years older than Kenny. Kenny is 2 years older than Mary. Mary is 7 years younger than Barbara. If Barbara is 16, how many years older than Barbara is Tom?

If 3 is subtracted from twice a number, the result is 53. What is the number?

500 dogs were surveyed about two dog foods. 220 were poodles, rest were beagles. Of 80 dogs that preferred “Tasty Treat,” 42 were poodles. How many beagles preferred “Hungry Dog”?

A seller had 360 apples. He sold 1/3 on Monday, then 1/4 of the remainder on Tuesday. How many apples are left?

A rectangular room is 15 feet long and 12 feet wide. What is the total cost to carpet the room at $3.50 per square foot?

A water tank was 3/4 full. After using 15 gallons, it was 1/2 full. What is the total capacity of the tank?

What is the next number in this pattern: 3, 7, 15, 31, ____?

The product of two consecutive even integers is 224. What is their sum?

Alice has 2 more marbles than Bob. Bob has 4 fewer marbles than Carol. Together all three have 42 marbles. How many does Carol have?

A number is increased by 25%, then the result is decreased by 20%. The final answer is 100. What was the original number?

In a class of 24 students, 1/3 are boys and 2/3 are girls. Half of the boys and 3/4 of the girls join the science fair. How many students join?

The sum of the digits of a two-digit number is 11. When the digits are reversed, the new number is 27 more than the original. What is the original number?

A train travels from City A to City B at 60 mph and returns at 40 mph. What is the average speed for the entire round trip?

What is the sum of all two-digit multiples of 7?

Alex finished 15 seconds before Ben. Chris finished 8 seconds after Alex. Ben finished in 4 minutes 12 seconds. In what time did Chris finish?

A store has a “buy 3, get 4th free” sale. Juan buys 8 items at $12 each. How much does he pay?

A square has the same perimeter as a rectangle with length 12 cm and width 8 cm. What is the area of the square?

In a survey of 50 people, everyone eats breakfast, lunch, or both. 35 eat breakfast and 30 eat lunch. How many eat both?

A number is divided by 4, then 7 is added, then the result is multiplied by 3. The final answer is 45. What was the original number?

5 × (8 − 3) + 4 × (7 − 2) = ____

B is the midpoint of segment AC. A is at position 3 and C is at position 15 on a number line. What is the value of B?

Jake is 4 times his sister’s age. In 6 years, Jake will be twice his sister’s age. How old is Jake’s sister now?

When a number is multiplied by 7 and then 11 is subtracted, the result is 38. What is the number?

How many integers from 1 to 40 are divisible by either 2 or 5?

Using digits 1, 3, 5, 7 each exactly once, how much larger is the greatest 4-digit number than the least 4-digit number that can be formed?

What perfect square is missing from this sequence: 1, 4, 9, 16, ___, 36?

Three-fourths of a number N equals 18. What is two-thirds of N?

A shopkeeper buys items at $0.50 each and sells at $0.80 each. If 400 items are sold, what is the total profit?

In how many different ways can 3 different books be arranged on a shelf?

In a school of 400 students, 35% prefer science as their favorite subject. How many students prefer science?

A rectangle has an area of 91 sq cm and a length of 13 cm. What is the perimeter?

A 150-meter-long train travels at 54 km/h. How many seconds does it take to pass a stationary pole?

A student scored 72, 78, 84, 90, and 96 on five tests. After removing the two lowest scores, what is the average of the remaining scores?

What is the sum of all distinct prime factors of 60?

A right triangle has legs of 9 cm and 12 cm. What is the perimeter of the triangle?

How many perfect square numbers are there between 50 and 150?

If today is Wednesday, what day of the week will it be 100 days from now?

What is the sum of all factors of 28?

Five consecutive odd integers have a sum of 85. What is the smallest of these integers?

What is the value of 1000 − 999 + 998 − 997 + … + 2 − 1?

How many times does the digit 4 appear when writing all integers from 1 to 50?

Alice can paint a fence in 4 hours. Bob can paint it in 6 hours. Working together, how long will it take?

A jacket costs $80. It goes on sale at 25% off, then another 10% off the sale price. What is the final price?

In a 3×3 magic square using the digits 1 through 9 (each once), every row, column, and diagonal sums to the same number. What is that sum?

What is the least common multiple (LCM) of 12, 18, and 24?

The ratio of red marbles to blue marbles in a bag is 3:7. There are 100 marbles total. How many are blue?

x/3 + x/4 = 7. What is the value of x?

A car travels 90 km at a constant speed of 60 km/h. How many minutes does the trip take?

A farmer has chickens and cows. There are 20 heads and 56 legs in total. How many cows are there?

How many two-digit numbers have a digit sum equal to 10?

Find the next term in the sequence: 2, 5, 14, 41, ____

A rectangular pool is 10 m × 8 m. A 3-meter-wide path surrounds it. What is the area of the path only?

An operation “★” is defined as: a★b = a² − b. Find 5★(3★2).

A bag has 4 red, 6 blue, and 2 green balls. Red balls are added until red:total = 1:2. How many red balls are added?

Candle A is 12 cm tall and burns at 3 cm/hour. Candle B is 10 cm tall and burns at 2 cm/hour. After how many hours will they be the same height?

A bag contains 3 red, 4 blue, and 3 green balls. What is the probability of NOT drawing a red ball?

What is the next number in the Fibonacci-like sequence: 2, 3, 5, 8, 13, 21, ____?

What is the greatest common factor (GCF) of 84 and 126?

Sarah’s age is 1/4 of her mother’s age. In 10 years, Sarah will be 1/2 of her mother’s age. How old is Sarah now?

M is the midpoint of segment AB on a number line. If A = −8 and B = 4, what is the value of M?

The first three classes in a school average 26 students. The fourth class has 38 students. What is the average number of students for all four classes?

A student reads at 40 pages per hour. How many hours will it take to read 300 pages?

The sum of two prime numbers is 40. One of them is 17. What is the other prime number?

A store has 4 different shirts, 3 different pants, and 2 different belts. How many different complete outfits (one of each) are possible?

A clock gains 4 minutes every hour. Set correctly at 8:00 AM, what time does it show when the actual time is 6:00 PM?

2n − 9 = n + 15. What is the value of n?

A regular hexagon has a perimeter of 48 cm. What is the length of each side?

A 900 ml solution is 8% salt. How many milliliters of salt does the solution contain?

A library has 3 shelves with 60, 75, and 90 books respectively. If 1/5 of all books are checked out, how many remain?

A snail is at the bottom of a 10-foot well. Each day it climbs 3 feet, but each night it slips back 1 foot. How many days until it reaches the top?

What is the sum of the digits of 17 × 18?

A square with side 6 cm and a rectangle with length 9 cm have the same area. What is the perimeter of the rectangle?

If 5^x = 625, what is the value of 2^x?

An auditorium has 15 rows. The first row has 12 seats and each subsequent row has 3 more seats than the previous. How many total seats are there?

In triangle ABC, angle A = 55° and angle B = 60°. What is the measure of angle C?

An isosceles triangle has a perimeter of 28 cm. If the two equal sides are each 10 cm, what is the length of the base?

In a class of 120 students, the ratio of boys to girls is 2:3. How many more girls are there than boys?

A recipe for 8 people requires 3 cups of flour. How many cups are needed for 10 people?

A person can climb a staircase taking 1 or 2 steps at a time. How many different ways can they climb exactly 4 steps?

What is the units digit of 7^100?

How many integers from 1 to 50 are divisible by 6 but NOT by 9?

9 pizzas are each cut into 8 slices. If each student eats exactly 6 slices, how many students can be served?

A right triangle has legs in ratio 3:4 and a hypotenuse of 10 cm. What is the length of the shorter leg?

A boy has 15 coins (dimes and quarters) totaling $2.85. How many quarters does he have?

What is the sum of all the individual digits used to write the integers from 1 to 20?

(N/4 − 3)² = 16. What is the positive value of N?

What is the sum of 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256?

Carol has $80. Ben has $15 less than Carol. Anna has $10 more than Ben. How much does Anna have?

Five friends share $150 equally. Then Alex gives $10 to Beth. How much money does Beth have?

What is the 11th term of the Fibonacci sequence (starting 1, 1, 2, 3, 5, 8, …)?

Three consecutive multiples of 4 have a sum of 60. What is the largest of the three?

A bus starts with 55 passengers. Stop 1: 8 off, 3 on. Stop 2: 5 off, 2 on. Stop 3: 12 off, 6 on. Stop 4: 4 off, 10 on. Stop 5: 7 off, 1 on. How many passengers are on the bus after stop 5?

What is the sum of all prime numbers strictly between 20 and 40?

What is the value of 2³ + 3² + 4¹?

Paul made a mistake: he subtracted 9 from a number instead of dividing by 9. His wrong answer was 27. What is the correct answer?

There are two numbers, each of which is twice as far from 6 as it is from 9 on the number line. What is the sum of these two numbers?

Sam was on the middle rung of a ladder. He climbed up 4 rungs, then down 7 rungs, then up 2 rungs. He is now 9 rungs from the top rung. How many rungs does the ladder have?

A school team has 11 players but only 6 can play at a time. The season has 22 games. The coach decides each player plays in the same number of complete games. How many games does each player play?

The operation a△b is defined as (a × b) − (a + b). For example, 4△2 = (4×2)−(4+2) = 8−6 = 2. Find the value of 5△3.

A hose fills a 48-gallon tank at the rate of 1/2 gallon every 5 seconds. How many minutes will it take to completely fill the tank?

Lisa earns 3 times as much per hour as Jane. Kate earns 5 times as much as Jane. If Lisa earns $18 per hour, how much does Kate earn per hour?

The digits 4, 3, 2, 1, 4, 3, 2, 1, … are written over and over in that pattern. What will be the 103rd digit?

In a toy store there are 5 times as many bicycles as tricycles. The total number of wheels is 52. How many bicycles are in the store?

Mr. Lee fell asleep halfway through a train journey. He slept until he had half as far to go as the distance he had traveled while sleeping. What fraction of the whole trip did Mr. Lee spend sleeping?

Tom bought 25 DVDs for $300 total. Five were special editions, each costing 4 times as much as a regular DVD. How much did Tom spend on the 5 special editions?

The average of 7 consecutive integers is 15. Take the sum of the smallest and largest of the 7, then divide by the middle integer. What is the result?

On a balance scale, 4 apples balance 1 apple and a 1½-pound weight. How much does one apple weigh?

A 2-digit number has its digits reversed to form a new number. The larger number is 54 more than the smaller. The original number plus the reversed number equals 110. What is the sum of the digits?

A 3-digit palindrome (reads the same forwards and backwards, like 343) has a digit sum of 8 and a digit product of 16. What is the palindrome?

In the addition problem A + A + A = BA, each letter represents a different digit and BA is a 2-digit number. Find the value of A.

A farmer has 360 acres. Corn is planted on 120 acres and 15 acres are reserved for buildings. The remaining acres are divided equally among 5 crops. How many acres does each crop get?

An L-shaped figure is made of 4 small squares (3 in a row with 1 square below the right end). If each small square has area 9 sq cm, what is the perimeter of the L-shaped figure?

Horace has 3 quarters, 4 dimes, and 3 pennies. Irwin has 1 more quarter than Horace, half the dimes, and twice the pennies. If Irwin gives Horace __¢, they will have the same amount. How many cents does Irwin give?

Mr. Monroe spent $830 on two suits. One suit cost $70 more than the other. How much did the less expensive suit cost?

Anna can knit 2 sweaters in 5 days. Maria can knit 3 sweaters in 10 days. They both work for the entire month of June (30 days). How many sweaters do they produce in total?

In a competition, the US team scored 3 more points than Canada. Canada scored 5 more points than Norway. Altogether the three teams scored 175 points. How many points did Canada score?

The operation a♦b is defined as a² + b². For example, 3♦2 = 9+4 = 13. Find the value of (2♦1)♦(1♦1).

A box has 15 red, 17 yellow, 12 green, and 21 blue marbles. Without looking, what is the fewest number of marbles you must take to be certain you have at least one of each color?

In a 3-digit number, the hundreds digit is 2 more than the tens digit, and the tens digit is 2 more than the units digit. The number is also divisible by 9. What is the smallest such number?

The operation a◆b is defined as a×b − b. For example, 2◆3 = 6−3 = 3. Find the value of (3◆4)◆2.

The operation p▲q is defined as (p−q)×p. Find the value of (4▲1)+(5▲2).

Sue is 5 years older than Ted. Ted is 3 times as old as Uma. Uma is 4 years old. How old is Sue?

The operation m⊕n is defined as 2m+n. For example, 2⊕1 = 5. Find the value of (3⊕2)⊕(1⊕4).

Ben is 6 years older than Cal. Cal is half as old as Dee. Dee is 4 years younger than Eve. Eve is 18. How old is Ben?

How many rectangles (including squares) are there in a 2×3 grid of unit squares (2 rows, 3 columns)?

80 marbles flow into junction A. At A, half go to B and half go to C. At B, half go to D and half go to E. At C, half go to E and half go to F. How many marbles reach E?

How many squares of ALL sizes (1×1, 2×2, and 3×3) are in a 3×3 grid of unit squares?

120 marbles enter junction P. At P, ⅓ go to Q and ⅔ go to R. At junction R, half go to S and half go to T. How many marbles reach T?

How many rectangles (including unit squares) are there in a 1×5 strip of unit squares (1 row, 5 columns)?

Points A, B, C, D lie on a straight line in that order. AB = 6 inches. BC is twice AB. CD is half of BC. What is the distance from A to D?

Pencils cost $3 each and erasers cost $2 each. Emma spent exactly $25, buying as many pencils as possible. Jake spent exactly $25, buying as many erasers as possible. How many more items does Jake have than Emma?

Points P, Q, R, S lie on a line in that order, equally spaced. The total distance from P to S is 18 inches. How far is Q from P?

Markers cost $5 each and crayons cost $3 each. Nina spent exactly $29, buying as many markers as possible. How many crayons did she buy?

A, B, C, D, E are equally spaced on a line with A at one end and E at the other, AE = 24 inches. A frog starts at C and makes these jumps: +2 spaces, −3 spaces, +1 space. How far from A is the frog?

Rita is 8 years older than Sam. Sam is 5 years younger than Tina. Tina is twice as old as Ulma. Ulma is 7 years old. How old is Rita?

How many squares of ALL sizes (1×1, 2×2, 3×3, and 4×4) are there in a 4×4 grid of unit squares?

“Zaps” cost $8 each and “zoops” cost $5 each. Mike spent exactly $53, buying as many zaps as possible. How many zoops did Mike buy?

The operation a♥b is defined as (a×b)+(a−b). Find the value of (4♥2)+(3♥1).

A basketball team scored exactly 50 points. Each basket scores 3 points and each free throw scores 1 point. The team made exactly 6 more baskets than free throws. How many baskets did they make?

How many rectangles (including squares) are in a 2×4 grid of unit squares (2 rows, 4 columns)?

Pat is 9 years older than Quinn. Quinn is ⅓ as old as Roz. Roz is 5 years younger than Stan. Stan is 26. How old is Pat?

The operation a⊗b is defined as 2a+3b. Find the value of (2⊗1)+(1⊗3).

“Snaps” cost $7 each and “crackles” cost $4 each. Maria spent exactly $42, buying the most snaps possible. Sam spent exactly $42, buying the most crackles possible. How many more items does Sam have than Maria?

144 marbles flow into a network. At the first split, ¾ go right and ¼ go left. At the second split (on the right path), ⅓ go up and ⅔ go down. How many marbles go up at the second split?

The operation a☀b is defined as 2a+b. Find the value of (3☀2)☀(1☀4).

Alex is 4 times as old as Beth. In 6 years, Alex will be twice as old as Beth will be. How old is Alex now?

Hot dogs cost $4 each and drinks cost $3 each. Mrs. Reed spent exactly $33, buying 3 more hot dogs than drinks. How many drinks did she buy?

The operation p◎q is defined as (p+q)² − (p−q)². For example, 3◎2 = (5)²−(1)² = 25−1 = 24. Find the value of 5◎3.

How many rectangles (including squares) of all sizes are in a 4×4 grid of unit squares?

The operation a♥b is defined as 3a − 2b. Find the value of (5♥2)♥(4♥1).

A store sells small boxes for $3 and large boxes for $8. A customer bought exactly 10 boxes and spent exactly $55. How many large boxes did the customer buy?

How many squares of ALL sizes (1×1 and 2×2) are in a 2×5 grid of unit squares (2 rows, 5 columns)?

Jenny is 3 times as old as Mark. In 4 years, Jenny will be exactly twice as old as Mark will be. How old is Jenny now?

“Widgets” cost $9 each and “gidgets” cost $6 each. Sofia spent exactly $54 buying as many widgets as possible. Theo spent exactly $54 buying as many gidgets as possible. How many more items does Theo have than Sofia?

240 marbles flow into junction A. At A, half go to B and half go to C. At B, ⅔ go to D and ⅓ go to E. At C, ¼ go to E and ¾ go to F. How many marbles reach E in total?

An L-shaped figure is made of 3 squares stacked vertically with 2 additional squares extending to the right from the bottom square (5 squares total). Each small square has side length 4 cm. What is the perimeter of the L-shaped figure?

Two runners start at opposite ends of a 400-meter track and run toward each other. Runner A goes 5 meters per second and Runner B goes 3 meters per second. After how many seconds will they meet?

The operation a▢b is defined as (a+b)÷2 × a (where a+b is always even). For example, 3▢1 = (3+1)÷2 × 3 = 6. Find 4▢2.

How many rectangles (including squares) of all sizes are in a 3×3 grid of unit squares?

Kim is 5 times as old as Lee. In 10 years, Kim will be exactly 3 times as old as Lee will be. How old is Kim now?

“Clips” cost $6 each and “pins” cost $4 each. Tony spent exactly $60 buying as many clips as possible. Mia spent exactly $60 buying as many pins as possible. How many more items does Mia have than Tony?

How many rectangles (including squares) of all sizes are in a 3×5 grid of unit squares (3 rows, 5 columns)?

The operation x▼y is defined as x×y − x − y + 1. For example, 4▼2 = 8−4−2+1 = 3. Find the value of 5▼3.

A bookshelf has 3 shelves. The bottom shelf has 5 more books than the middle shelf. The top shelf has half as many books as the middle shelf. There are 45 books in total. How many books are on the top shelf?

The operation a♠b is defined as a² + a×b − b. Find the value of (2♠3)+(3♠2).

Alex is 6 years more than twice Beth’s age. Beth is 4 years younger than Carl. Carl is 3 times as old as Daisy. Daisy is 5. How old is Alex?

360 marbles enter junction A. At A, ⅓ go to B and ⅔ go to C. At B, half go to D and half go to E. At C, ¼ go to E and ¾ go to F. How many marbles reach E in total?

How many rectangles (including squares) of all sizes are in a 2×6 grid of unit squares (2 rows, 6 columns)?

“Item A” costs $11 and “Item B” costs $7. Raj buys some of each type and spends exactly $100 in total. What is the maximum total number of items Raj can buy?