Multiple choice

Passage

A, B, C, D, E, F and G are cousins. D is thrice as old as A. Further, C is as many years younger to B, as G to E and E to D. The average age of D and G is 16 years; the average age of A and E is 11 years; the average age of B and C is also 11 years. B and C have equal weight. A's weight is 10 kg less than that of B; D is 4 kg heavier than E; E is 4 kg heavier than F; F is 4 kg heavier than G. Further, D has age-weight ratio of 9 : 20, where age is in years and weight in kg; A has age-weight ratio of 2 : 5. Moreover, none of them is more than 40 kg.

Consider the following statements: 1. The age of F cannot be determined due to insufficient data. 2. The average weight of D and F is equal to weight of E. 3. The weight difference is maximum for D and A. Which of the statements given above are correct?

  1. 1 and 2 only

  2. 2 and 3 only

  3. 1 and 3 only

  4. 1, 2 and 3
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

By solving the age equations, we find A = 6, D = 18, E = 16, G = 14, B = 12, and C = 10, but there is no information to determine F's age, making Statement 1 correct. For weights, using the ratios and differences, we find W_D = 40, W_E = 36, W_F = 32, W_G = 28, W_A = 15, and W_B = W_C = 25. Thus, the average of W_D and W_F is 36 (equal to W_E), and the maximum weight difference is indeed between D (40) and A (15), making Statements 2 and 3 correct as well.

AI explanation

Using the provided ratios, the ages and weights are calculated as A is 8 years and 20 kg, D is 24 years and about 53.33 kg, E is 14 years and 49.33 kg, F is 45.33 kg, G is 8 years and 41.33 kg, and B and C are 46.33 kg each. Because F's age is never mentioned in any ratio or relation, statement 1 is correct. The average weight of D and F is 49.33 kg, which equals E's weight, making statement 2 correct. Finally, the weight difference between D and A is 33.33 kg, which is the maximum among all the cousins, making statement 3 correct. Therefore, statements 1, 2 and 3 are all correct.

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