Multiple choice

Passage

Directions: In the following item, quantity I and quantity II are given. Determine the relationship between the quantities and choose the appropriate option. (1) If Quantity I ≥ Quantity II (2) If Quantity I > Quantity II (3) If Quantity I < Quantity II (4) If Quantity I = Quantity II or the relationship cannot be established from the information given (5) If Quantity I ≤ Quantity II

There are 52 cards in a box and the cards are numbered from 1 to 52. Quantity I: Probability of picking a card, whose digits if interchanged, result in a number which is 45 more than the number card picked. Quantity II: Probability of picking a card, the number printed on which is a multiple of 4, but not that of 8.

  1. (1)

  2. (2)

  3. (3)

  4. (4)

  5. (5)

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: Numbers xy such that (10y+x) - (10x+y) = 45 => 9(y-x) = 45 => y-x = 5. Pairs: (1,6), (2,7), (3,8), (4,9). Total 4 cards. P(I) = 4/52 = 1/13. Quantity II: Multiples of 4 but not 8 are 4, 12, 20, 28, 36, 44, 52. Total 7 cards. P(II) = 7/52. Since 1/13 = 4/52 < 7/52, Quantity I < Quantity II.