Mind the Remainder
A red light flashes every 8 minutes and a blue light flashes every 12 minutes. If they flash together at 1:00 PM, what is the next exact time they will flash together?
Answer: 1:24 PM (The Least Common Multiple of 8 and 12 is 24)
A shirt's price is increased from $20 to $25. What is the exact percent increase?
Answer: 25% (The price went up $5, and 5 is 25% of the original 20)
If 2a + b = 10, and b = 4, what is the value of a?
3
A square has an area of 49 square inches. What is its perimeter?
Answer: 28 inches (Each side is 7 inches)
The average of 3 numbers is 10. What is the combined sum of these 3 numbers?
Answer: 30
When a positive integer n is divided by 9, the remainder is 5. What is the remainder when the value of 2n is divided by 9?
Answer: 1 (2 x 5 = 10; 10 divided by 9 leaves a remainder of 1)
A book costs $100. It gets a 10% discount, and then a 10% sales tax is added to the sale price. What is the final price?
Answer: $99 ($90 sale price + $9 tax)
In a number pattern, each number is 4 more than the previous number. If the first number is 3, what is the 5th number?
Answer: 19 (3, 7, 11, 15, 19)
A rectangle has a length of 8 and a width of 5. If the length is doubled and the width stays the same, what is the new area?
Answer: 80 (16 x 5)
A bag contains 3 red, 2 blue, and 5 green marbles. What is the probability of randomly picking a blue marble?
Answer: 2/10 (or 1/5)
The product of three consecutive positive integers is 210. What is the sum of these three integers?
Answer: 18 (The numbers are 5, 6, and 7; 5 x 6 x 7 = 210, and 5 + 6 + 7 = 18)
A store clerk increases the price of a $50 jacket by 20%, and then discounts that brand-new price by 20% for a weekend sale. What is the final sale price?
Answer: $48 ($50 increased by 20% becomes $60; 20% off $60 is a $12 discount, leaving $48)
Solve for x: 4(x - 3) = 2x + 10
Answer: 11 (4x - 12 = 2x + 10, which simplifies to 2x = 22
The total area of a circle is 25 pi square centimeters. What is the radius of this circle?
Answer: 5 cm
The average score of 5 students on a math quiz is 82. If a 6th student joins and scores a perfect 100, what is the new group average?
Answer: 85 (The original points sum to 410; adding 100 makes it 510 total points divided by 6 students)
How many two-digit positive integers are evenly divisible by both 4 and 6?
8 (The Least Common Multiple is 12; the two-digit multiples of 12 are 12, 24, 36, 48, 60, 72, 84, and 96)
If 30% of a mystery number x is equal to 45% of 80, what is the value of x?
Answer: 120 (45% of 80 is 36; if 0.30x = 36, then x = 120)
If 3x + 5 = 20, what is the numerical value of the expression: 6x - 10?
20 (Since 3x = 15, x = 5; plugging 5 into the second expression yields 30 - 10 = 20)
A rectangular water tank measures 5 feet long, 4 feet wide, and 3 feet deep. If the tank is filled with water exactly halfway, how many cubic feet of water are inside?
Answer: 30 cubic feet (Total volume is 5 x 4 x 3 = 60 cubic feet; half of that is 30)
A desk drawer contains 4 red pens, 3 blue pens, and 5 black pens. If you reach in and pick one pen completely at random, what is the probability it is NOT blue?
9/12 (or 3/4) (There are 12 total pens, and 9 of them are either red or black)
The sum of two consecutive integers is 35. What is the value of the smaller integer?
Answer: 17 (17 + 18 = 35)
In a school of 400 students, 60% are girls. If 20% of the girls and 30% of the boys play a musical instrument, how many total students play an instrument?
Answer: 96 students (240 girls x 0.20 = 48; 160 boys x 0.30 = 48; 48 + 48 = 96)
A farm contains only chickens (2 legs) and pigs (4 legs). If there are exactly 20 heads and 56 legs total on the farm, how many pigs are there?
Answer: 8 pigs (If all 20 animals were chickens, there would be 40 legs. The 16 extra legs must belong to 8 pigs)
The total surface area of a solid cube is 96 square centimeters. What is the total volume of this cube?
Answer: 64 cubic centimeters (6 faces x area = 96, so each face area is 16. This means each edge is 4 cm; Volume = 4 x 4 x 4 = 64)
How many different 3-letter security codes can be created using the letters A, B, C, and D if no letter can be repeated within a code?
Answer: 24 codes (4 options for the first letter x 3 options for the second x 2 options for the third)