Read the following information carefully and answer the questions below it.…
2022
Read the following information carefully and answer the questions below it.
Rashmi is very fond of collecting greeting cards. Her collection of 211 cards has a good mix of Birthday cards, New Year cards, Deepawali cards, Christmas cards and even a Marriage anniversary card. The number of Birthday cards is equal to the sum of the others except the Marriage anniversary cards. The number of New Year card is double of Deepawali cards which in turn is double of Christmas cards.
Ques: The number of Christmas card is
- A.
10
- B.
15
- C.
20
- D.
25
Attempted by 4 students.
Show answer & explanation
Correct answer: B
Concept: When a word problem states every quantity only through its relationship to the others and gives one combined total, express each quantity as a multiple of a single reference quantity, write one equation for the total, and solve for that reference quantity.
Let the number of Christmas cards be x.
New Year cards are double of Deepawali cards, and Deepawali cards are double of Christmas cards, so Deepawali cards = 2x and New Year cards = 2 × 2x = 4x.
Birthday cards equal the sum of the other categories except the Marriage anniversary card: Birthday cards = New Year + Deepawali + Christmas = 4x + 2x + x = 7x.
The passage mentions "a Marriage anniversary card" (singular), so this category contributes exactly 1 card.
The total collection is the sum of all five categories: 7x + 4x + 2x + x + 1 = 211, i.e. 14x + 1 = 211.
Solving: 14x = 210, so x = 15.
Check: Substituting x = 15 back gives Birthday = 105, New Year = 60, Deepawali = 30, Christmas = 15 and Marriage anniversary = 1; their sum is 105 + 60 + 30 + 15 + 1 = 211, which matches the given total and confirms the value.
Answer: The number of Christmas cards is 15.