Data Interpretation – A quick survey at the end of a purchase at buyagain

XAT 2021 Exam Paper – Data Interpretation – A quick survey at the end of a purchase at buyagain

A quick survey at the end of a purchase at buyagain.com asks the following three questions to each shopper:
1. Are you shopping at the website for the first time? (YES or NO)
2. Specify your gender: (MALE or FEMALE)
3. How satisfied are you? (HAPPY, NEUTRAL or UNHAPPY)
240 shoppers answer the survey, among whom 65 are first time shoppers. Furthermore:
i. The ratio of the numbers of male to female shoppers is 1 : 2 while the ratio of the numbers of unhappy, happy and neutral shoppers is 3 : 4 : 5
ii. The ratio of the numbers of happy first-time male shoppers, happy returning male shoppers, unhappy female shoppers, neutral male shoppers, neutral female shoppers and happy female shoppers is 1 : 1 : 4 : 4 : 6 : 6
iii. Among the first-time shoppers, the ratio of the numbers of happy male, neutral male, unhappy female and the remaining female shoppers is 1 : 1 : 1 : 2, while the number of happy first-time female shoppers is equal to the number of unhappy first-time male shoppers

Q1. What is the number of happy male shoppers?

Q2. Which among the following is the lowest?
1. Number of unhappy first-time female shoppers
2. Number of neutral first-time female shoppers
3. Number of neutral first-time male shoppers
4. Number of happy returning male shoppers
5. Number of unhappy first-time male shoppers

Q3. Which among the following cannot be determined uniquely?
1. The number of first-time neutral male shoppers
2. All the numbers can be determined uniquely
3. The number of first-time happy male shoppers
4. The number of returning male shoppers
5. The number of returning unhappy female shoppers

Solutions:
Male : female = 1:2
Male = 1/3 *240 = 80, female = 2/3 *240 = 160
Unhappy : happy : neutral = 3:4:5
Unhappy = 3/12 *240 = 60
Happy = 4/12 *240 = 80
Neutral = 5/12 *240 = 100
From the given information in point 1 we can make following table:

	        Male – 80		Female – 160		Total
	1st timer	Repeaters	1st timer	Repeaters
Unhappy					60
Happy					80
Neutral					100
Total

From point 2 and 3 the above table can be filled as below :

	        Male – 80		Female – 160		Total
	1st timer	Repeaters	1st timer	Repeaters
Unhappy	1.5a	0.5a	a	3a	60
Happy	a	a	1.5a	4.5a	80
Neutral	a	3a	0.5a	5.5a	100
Total	3.5a	4.5a	3a	13a

On solving ,
1.5a + 0.5a + a +3a = 60
6a = 60
Or a = 10
Thus , the final table will look like,

	        Male – 80		Female – 160		Total
	1st timer	Repeaters	1st timer	Repeaters
Unhappy	15	5	10	30	60
Happy	10	10	15	45	80
Neutral	10	30	5	55	100
Total	35	45	30	130

Now all the questions can be answered.
Q26. D
Q27. B
Q28. B

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