Multiple choice

[CAT 2002] Two boys are playing on a ground. Both the boys are less than 10 years old. Age of the younger boy is equal to the cube root of the product of the age of the two boys. If we place the digit representing the age of the younger boy to the left of the digit representing the age of the elder boy, we get the age of the father of the younger boy. Similarly, if we place the digit representing the age of the elder boy to the left of the digit representing the age of the younger boy and divide the figure by 2, we get the age of the mother of the younger boy. The mother of the younger boy is younger than his father by 3 years. Then what is the age of the younger boy?

  1. 3

  2. 4

  3. 2

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let ages be x and y (x < y < 10). x = cuberoot(xy). x^3 = xy, so x^2 = y. If x=2, y=4. Father's age = 24. Mother's age = (42/2) = 21. Difference = 24 - 21 = 3. This matches the condition.

AI explanation

Let the younger boy's age be y and the elder boy's age be e, with both ages being single digits. Since the younger boy's age equals the cube root of the product of their ages, we have y equals the cube root of y times e, which simplifies to y squared equals e. Testing the given options, if y is 2, then e is 4; placing 2 left of 4 gives the father's age as 24, and placing 4 left of 2 gives 42, which divided by 2 makes the mother's age 21. Since the mother is exactly 3 years younger than the father, the younger boy is 2 years old.

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