Difficulty: Medium
Correct Answer: 23
Explanation:
Introduction:
This is a two-variable linear equation problem describing a relationship between a greater and a smaller number. Each sentence gives a different linear connection between the two numbers. The task is to convert both statements into equations and solve them together. This type of question is common in aptitude tests to check your ability to translate verbal relationships into algebra.
Given Data / Assumptions:
Concept / Approach:
Convert each statement into an equation. “G is 2 more than three times S” becomes G = 3S + 2. “4 times the smaller is 5 more than the greater” becomes 4S = G + 5. Solving these two linear equations simultaneously will give unique values for S and G, after which we report the greater number G.
Step-by-Step Solution:
Let G = 3S + 2 … (1).Also, 4S = G + 5 … (2).Substitute G from (1) into (2): 4S = (3S + 2) + 5.4S = 3S + 7.4S - 3S = 7 => S = 7.Now use S in (1): G = 3*7 + 2 = 21 + 2 = 23.Thus the greater number is 23.
Verification / Alternative check:
Check the first condition: Three times the smaller is 3 * 7 = 21; G should be 2 more, so 23, correct. Check the second condition: 4 times the smaller is 4 * 7 = 28; G + 5 = 23 + 5 = 28, which also matches. Both conditions are satisfied by S = 7 and G = 23.
Why Other Options Are Wrong:
7 and 9: These are small numbers that do not satisfy both algebraic relations simultaneously.21: This is close to 3 * 7 but misses the extra 2 required by the first condition.25: If G were 25, there would be no integer S that satisfies both equations exactly.
Common Pitfalls:
Mixing up which number is greater and which is smaller when forming the equations.Interpreting “2 more than three times the second number” as 3S = G + 2 instead of G = 3S + 2.Solving only one equation and forgetting that both conditions must be satisfied at the same time.
Final Answer:
23
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