Based on the following information, answer the question given below: A…
2024
Based on the following information, answer the question given below: A businessman has five articles P, Q, R, S and T. I. P weighs double that of Q. II. Q weighs four and half times of R. III. R weighs half that of T. IV. T weighs less than P but more than R. V. S is heavier only than R. Which one of the following is the lightest?
- A.
S
- B.
P
- C.
R
- D.
Q
- E.
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Correct answer: C
When several quantities are linked through a chain of ratio statements (double, half, four and a half times, etc.), express every quantity in terms of a single common variable and then compare the resulting numeric coefficients directly -- this avoids working with fractions or reciprocal relations.
Let R = x.
R weighs half that of T, so T = 2R = 2x.
Q weighs four and a half times R, so Q = 4.5R = 4.5x.
P weighs double Q, so P = 2Q = 2(4.5x) = 9x.
S is heavier only than R, so S lies strictly between R and every other article: R < S < T = 2x.
Putting every article on the same scale gives R = x, S with x < S < 2x, T = 2x, Q = 4.5x, and P = 9x, so the ascending order of weight is R < S < T < Q < P.
Checking statement IV independently: T must be less than P and more than R. With T = 2x, P = 9x, R = x, indeed x < 2x < 9x, so the relation holds. S being heavier only than R is also consistent with R < S < T. R is therefore the lightest article.