Establishing inequality relationships through percentage equations
Question
When 70% of a number x is added to another number y, the sum becomes 165% of the value of y. When 60% of the number x is added to another number z, then the sum becomes 165% of the value of z. Which one of the following is correct?
Options
z < x < y
x < y < z
y < x < z
z < y < x
Explanation
Translate the percentage statements into algebraic equations:
Equation 1: 0.7x + y = 1.65y Subtract y from both sides: 0.7x = 0.65y. Solve for y in terms of x: y = 0.70/0.65x = 70/65x = 14/13x. Since 14/13 > 1, it is mathematically certain that ⟨MATH⟩y > x⟨/MATH⟩.
Equation 2: 0.6x + z = 1.65z Subtract z from both sides: 0.6x = 0.65z. Solve for z in terms of x: z = 0.60/0.65x = 60/65x = 12/13x. Since 12/13 < 1, it is mathematically certain that ⟨MATH⟩z < x⟨/MATH⟩.
Link the two inequalities together: z < x \quad and \quad x < y \implies z < x < y.
Answer: (a).
Question details
Year
2022
Paper
CSAT
Question
Q60
Section
Numerical Ability
Sub-topic
Percentages & Equations
Type
Factual single
Difficulty
Hard
Source hint
70% of x + y = 165% of y
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