Two numbers in a 2:3 ratio have an L.C.M of 48. Find their sum__________?
Show answer Hide answer
Answer: C. 40
Explanation
Numbers in a 2 to 3 ratio can be expressed as 2x and 3x respectively. The least common multiple of 2x and 3x is 6x, which equals 48. Solving for x gives 8, making the numbers 16 and 24, with a sum of 40. Ratio variables represent proportional parts of an underlying common factor x. Least common multiple of proportional terms equals the product of factors and x. Sum of the two numbers equals 2x plus 3x which simplifies to 5x.
Proportional distribution problems are common in finance, chemistry, and resource sharing. Using variable multipliers simplifies the handling of unknown quantities in algebra. Ratio and proportion properties underlie scaling and mixing calculations. Choosing 28 results from an incorrect calculation of the proportional variable x. Choosing 32 underestimates the sum of the two numbers derived from the LCM. Choosing 64 overestimates the sum by miscalculating the common multiplier.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. What is the minimum number of complete years for a sum at 20% compound interest to more than double_________?
Show answer Hide answer
Answer: B. 4
At twenty percent compound interest, the investment growth multiplier each year is one point two. For three years, the multiplier is one point two cubed, equaling one point seven two eight, which is less than doubling. F...
Q2. Two numbers have an L.C.M of 495 and an H.C.F of 5. If their sum is 10, find their difference__________?
Show answer Hide answer
Answer: A. 10
The product of two numbers equals the product of their highest common factor and lowest common multiple. Multiplying five by four ninety five gives a number product of twenty four seventy five. Standard test problems of...
Q3. What is the smallest four-digit integer divisible evenly by 4, 6, 8, and 10_________?
Show answer Hide answer
Answer: A. 1080
Finding the least common multiple of four, six, eight, and ten gives a base value of one hundred twenty. Dividing the smallest four-digit number one thousand by one hundred twenty gives eight point thirty-three. Multiply...
Q4. Two numbers have an H.C.F of 8. Which of the following cannot be their L.C.M?
Show answer Hide answer
Answer: D. 60
A fundamental property of number theory states that the lowest common multiple of two numbers must always be exactly divisible by their highest common factor. Checking the given options against the HCF of eight shows tha...
Q5. What is the greatest number that leaves remainders of 6 and 5 when dividing 1657 and 2037 respectively_________?
Show answer Hide answer
Answer: B. 127
Subtracting the respective remainders from each number gives sixteen fifty one and twenty thirty two. The greatest number required must be the highest common factor of these two adjusted values. Calculating the highest c...
Q6. Find the smallest number which, when decreased by 7, is divisible by 21, 28, 36, and 45________?
Show answer Hide answer
Answer: A. 1267
Finding the least common multiple of twenty-one, twenty-eight, thirty-six, and forty-five yields twelve sixty. The problem states that when the desired number is decreased by seven, it becomes divisible by the LCM. Addin...