p exceeds q by 50%. Express the ratio of p to q.
Show answer Hide answer
Answer: A. 3:2
Explanation
An increase of fifty percent means the larger quantity equals one hundred fifty percent of the smaller baseline quantity. Expressing this relationship mathematically gives the equation p equals one point five times q, simplifying to three halves of q. Dividing both sides by q establishes the final ratio of p to q as three is to two. Percentages represent proportions scaled out of a total value of one hundred for easy comparison across different magnitudes. A mathematical ratio compares two quantities by showing division, indicating how many times one value contains another. Scaling factors allow complex proportional relationships to be simplified into irreducible integer ratios.
Option B represents a reciprocal relationship where q exceeds p rather than the other way around. Option C drastically underestimates the proportional difference by treating the increase as a minor fraction. Option D suggests a one hundred percent increase rather than the specified fifty percent growth.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. Solve equations I. x2 + 5x + 6 = 0 and II. y2 + 9y + 14 = 0 to determine x and y?
Show answer Hide answer
Answer: D. If x = y or the relationship between x and y cannot be established.
Equation one factors into roots of negative two and negative three through standard factoring techniques. Equation two factors into roots of negative two and negative seven using similar factorization methods. Because ne...
Q2. Solve equations I. x2 + 11x + 30 = 0 and II. y2 + 15y + 56 = 0 to determine x and y?
Show answer Hide answer
Answer: B. If x > y
Solving equation one yields roots of negative five and negative six through standard factoring methods. Solving equation two yields roots of negative seven and negative eight by factoring the quadratic expression. Compar...
Q3. P finishes a job in 18 days and Q in 15 days. After Q worked for 10 days and left, how many days does P need to finish the remainder?
Show answer Hide answer
Answer: B. 6
Worker Q completes two thirds of the total job within the first ten days. The remaining one third of the task must be finished by worker P alone. Worker P requires six days to finish the remaining fraction at standard sp...
Q4. In a 1000 m event, A defeats B by 100 m, whereas in an 800 m event, B defeats C by 100 m. By what margin will A defeat C in a 600 m event?
Show answer Hide answer
Answer: B. 127.5 m
A defeats B by one hundred meters in a one thousand meter race, establishing a speed ratio. B defeats C by one hundred meters in an eight hundred meter race, establishing another speed ratio. Combining these proportional...
Q5. Solve equations I. x2 + 9x + 20 = 0 and II. y2 + 5y + 6 = 0 to determine x and y?
Show answer Hide answer
Answer: A. If x < y
Solving equation one yields roots of negative four and negative five via standard quadratic factoring. Solving equation two yields roots of negative two and negative three through binomial factorization. Comparing all re...
Q6. Solve equations I. x2 + 3x – 18 = 0 and II. y2 + y – 30 = 0 to determine x and y?
Show answer Hide answer
Answer: E. If x = y or the relationship between x and y cannot be established.
Quadratic equation roots can overlap across different intervals on the number line. Solving the first equation gives specific roots that intersect the roots of the second. An overlapping range prevents establishing a def...