XAT 2022 — QA & DI Question 27
Read the following scenario and answer the THREE questions that follow.
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The given candlestick chart depicts the prices of a particular stock over 10 consecutive days. A candlestick comprises of a rectangular box pieced by a line. The top and bottom ends of the line respectively indicate the maximum and minimum prices of the stock on that day, while the horizontal edges of the rectangle correspond to the stock's opening and closing prices. If the rectangle is white, the opening price is lower than the closing price, but if the rectangle is black, then it is the other way around.
Using the above information, answer the questions that follow:
The Madhura Fruits Company is packing four types of fruits into boxes. There are 126 oranges, 162 apples, 198 guavas and 306 pears. The fruits must be packed in such a way that a given box must have only one type of fruit and must contain thesame number of fruit units as any other box.
What is the minimum number of boxes that must be used?
Answer & solution
- A
21
- B
18
44
- D
42
- E
36
The number of oranges, apples, guavas, and pears = 126, 162, 198, and 306.
Each box must contain an equal number of fruits with only one type of fruit. The additional condition provided is that there should be a minimum number of boxes in total.
The distribution is possible in multiple ways in such a way that distribution in each box is placed in such that each box contains a certain number of fruits n which is a factor for all the four given number of fruits :
Arrangement of 1 fruit of one kind in a basket.
2 is a factor of 126, 162, 198, and 306. So we can place 2 fruits of a particular kind in a basket.
Since we were asked for the minimum number of boxes this is possible when a maximum number of fruits of a kind are placed in a box.
Hence each box must contain the Highest common factor for the four numbers :
The prime factorization for the four numbers:
126 : 2 â 7 â 9, 162 : 2 â 9 â 9, 198 : 2 â 9 â 11, 306 = 2 â 9 â 17
The HCF is 18.
The number of boxes required for each :
, , ,
7 + 9 + 11 + 17 = 44.