Multiple choice

Passage

Directions: Read the following information carefully and answer the question that follow: A piggy-bank contains total 18 coins of Re 1, 50 paise and 25 paise. The difference between Re 1 and 50 paise coins is same as difference between 50 paise and 25 paise coins.

If probability of selecting one 25 paise is more than 0.5, then number of Re. 1 coins can be

  1. 1

  2. 2

  3. 3

  4. Both 1 and 2

  5. 1, 2 and 3
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let coins be x, y, z for 1, 0.5, 0.25. x+y+z=18. x-y = y-z => x+z = 2y. 3y=18 => y=6. x+z=12. Probability of 25p (z) > 0.5 means z/18 > 0.5, so z > 9. Since x+z=12 and z > 9, possible values for z are 10, 11, 12. Then x = 12-z, so x can be 2, 1, 0. Since there must be coins of each type, x can be 1 or 2.

AI explanation

Let the number of Re 1, 50 paise, and 25 paise coins be x, y, and z respectively, where the arithmetic progression condition means y equals (x plus z) divided by 2. Given x plus y plus z equals 18, substituting y shows that y is 9 and x plus z is 9, where the difference condition yields 2z equals x plus 18. Testing valid values, if x is 1, then z is 16 and the probability of 25 paise is 16/18 which is greater than 0.5, and if x is 2, then z is 15 and the probability is 15/18 which is also greater than 0.5, but x cannot be 3 because it breaks the integer count for the difference. Therefore, x can be both 1 and 2.

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