Explore basic concepts of averages and mixtures with this easy multiple-choice quiz, designed to strengthen foundational skills in calculating means, solving mixture problems, and interpreting simple scenarios involving averages. Tackle practical and theoretical challenges ideal for learners seeking to master common quantitative reasoning involving averages and blending solutions.
What is the average of the numbers 6, 8, and 10?
Explanation: To find the average, add all the numbers and divide by their total count: (6 + 8 + 10) / 3 = 24 / 3 = 8. Option B, 9, and Option C, 7, are common errors from incorrect addition or division, while Option D, 6, simply repeats one input number and is not the mean. The correct process yields 8 as the average.
Sarah scored 80 in Test 1 and 90 in Test 2, where Test 1 counts for 40% and Test 2 counts for 60%. What is her weighted average score?
Explanation: Multiply each score by its weight and add: (80×0.4) + (90×0.6) = 32 + 54 = 86. Option B, 84, might be chosen if the weights are mixed up, while Option C, 88, and Option D, 82, are results of using equal weights or miscalculating. Only 86 uses the correct method with the right percentages.
The average of 12, 15, and a third number is 18. What is the third number?
Explanation: Let the third number be x. So, (12 + 15 + x) / 3 = 18; thus 27 + x = 54, so x = 27. Options B and C are miscalculations from not multiplying the average by the total number of items. Option D, 18, simply repeats the average and ignores the calculation. Only 27 correctly satisfies the equation.
If all five numbers in a set are 7, what is their average?
Explanation: The sum is 7×5=35, divided by 5 equals 7. Option B, 35, is the total, not the average. Option C, 5, incorrectly divides the sum or uses the count. Option D, 14, comes from doubling a number, not from averaging. When all numbers are identical, the average equals that number.
You mix 2 liters of juice with a 10% sugar content and 3 liters with a 20% sugar content. What is the average sugar content of the mixture?
Explanation: Total sugar is (2×10) + (3×20) = 20 + 60 = 80 grams in 5 liters. 80/5 = 16 grams per liter, or 16%. Options B and C result from mixing or averaging percentage values directly, which is incorrect. Option D comes from only using the higher concentration. The correct way averages the mass, not just the percentages.
If the average of four numbers is 12, what will the new average be if a fifth number, also 12, is added?
Explanation: The sum becomes 12×4 + 12 = 60, and dividing by 5 yields an average of 12. Option B, 13, and D, 14, assume the average increases by 1 or 2. Option C, 11, might result from subtracting. When the same value as the average is added, the average remains unchanged.
The average age of 5 players is 20 years. If the youngest player, aged 16, leaves, what is the new average age?
Explanation: Total age is 5×20=100. After removing 16, total is 84; divide by 4 gives 21. Option B, 20, wrongly keeps the average. Option C, 19, could result from not adjusting the count. Option D, 22, is too high. Proper calculation is essential when removing members.
A group of 4 boys has an average age of 10, while a group of 6 girls averages 12. What is the combined average age?
Explanation: Boys' total: 4×10=40, girls' total: 6×12=72, combined: 112. Divide by 10, the total count, gives 11.2. Option B ignores the total sum; Option C, 10.8, is the result of a simple average of 10 and 12, not weighted. Option D is an incorrect estimate. Always weight by group size.
The average of three numbers is 9. If a fourth number, 21, is added, what is the new average?
Explanation: Sum of three numbers is 3×9=27. Adding 21 makes 48, divided by 4, yields 12. Option B, 10.5, is from incorrect calculations. Option C, 15, may be from misapplied operations. Option D, 9, doesn't change the original average. Adding a larger number than the average increases the mean.
What is the average of the numbers 0, 4, and 8?
Explanation: Sum is 0+4+8=12; divide by 3 for an average of 4. Option B, 0, ignores the nonzero values. Option C, 6, could stem from misunderstanding how zero affects the result. Option D, 3, is underestimating by dividing the sum wrongly. Zero does not cancel out other values; it's simply included in the total.