XAT 2024 Question Paper
Read the following scenario and answer the THREE questions that follow.
The upper hinge of a dataset is the median of all the values to the right of the median of the dataset in an ascending arrangement, while the lower hinge of the dataset is the median of all the values to the left of the median of the dataset in the same arrangement.
For example, consider the dataset 4, 3, 2, 6, 4, 2, 7. When arranged in the ascending order, it becomes 2, 2, 3, 4, 4, 6, 7. The median is 4 (the bold value), and hence the upper hinge is the median of 4, 6, 7, i.e., 6. Similarly, the lower hinge is 2.
A student has surveyed thirteen of her teachers, and recorded their work experience (in integer years). Two of the values recorded by the student got smudged, and she cannot recall those values. All she remembers is that those two values were unequal, so let us write them as A and B, where A < B. The remaining eleven values, as recorded, are: 5, 6, 7, 8, 12, 16, 19, 21, 21, 27, 29. Moreover, the student also remembers the following summary measures, calculated based on all the thirteen values:
Minimum: 2
Lower Hinge: 6.5
Median: 12
Upper Hinge: 21
Maximum: 29
Based on the information recorded, which of the following can be the average work experience of the thirteen teachers?
While rechecking her original notes to re-enter the smudged values of A and B in the records, the student found that one of the eleven recorded work experience values that did not get smudged was recorded wrongly as half of its correct value. After re-entering the values of A and B, and correcting the wrongly recorded value, she recalculated all the summary measures. The recalculated average value was 15. What is the value of B?
Read the following scenario and answer the THREE questions that follow.
A T20 cricket match consists of two teams playing twenty overs each, numbered 1 to 20. The runs scored in any over is a non-negative integer. The run rate at the end of any over is the average runs scored up to and including that over, i.e., the run rate at the end of the k-th over is the average number of runs scored in overs numbered 1, 2, …, k, where 1 ≤ k ≤ 20, k a positive integer.
The following table indicates the run rate of a team at the end of some of the overs during a T20 cricket match (correct up to 2 decimal places), where 1 ≤ N - 2 < N + 6 ≤ 20, N a positive integer. It is also known that the team did not score less than 6 runs and more than 15 runs in any over.
In which of the following over numbers, the team MUST have scored the least number of runs?
Read the following scenario and answer the THREE questions that follow.
A store offers a choice of five different discount coupons to its customers, described as follows:
Coupon A: A flat discount of Rs. 250 on a minimum spend of Rs. 1200 in one transaction.
Coupon B: A 15% discount on a minimum spend of Rs. 500 in one transaction, up to a maximum discount of Rs. 300.
Coupon C: A flat discount of Rs. 100 on a minimum spend of Rs. 600 in one transaction.
Coupon D: A 10% discount on a minimum spend of Rs. 250 in one transaction, up to a maximum discount of Rs. 100.
Coupon E: A flat discount of Rs. 50 on a minimum spend of Rs. 200 in one transaction.
The customers are allowed to use at most one coupon in one transaction, i.e., two or more coupons cannot be combined for the same transaction.
Four customers used four different discount coupons for their respective transactions in such a way that they obtained a total discount of Rs. 710. Which discount coupon was not used?
Four customers used four different discount coupons for their respective transactions in such a way that nobody used any discount coupon sub-optimally. (A discount coupon is used sub-optimally if using another discount coupon could have resulted in a higher discount for the same transaction.) What was the minimum combined spend (before application of any discount)?
A family wanted to purchase four products worth Rs. 1000 each, and another product worth Rs. 300. They were told that they could:
I) pay for the five products through one or more transactions in any way they wanted, as long as the purchase amount of any one product would not get split into different transactions, and
II) use the same discount coupon repeatedly for separate transactions, if they opt for more than one transaction.
What was the maximum discount that they could obtain for their purchase?
Read the following scenario and answer the THREE questions that follow.
Mr. Singh lived in a sprawling housing society. He employed two part-time domestic helps, Vimla and Sharda. Vimla was responsible for cleaning and dusting, while Sharda took care of cooking.
Once Sharda fell ill and consequently took leave for three days. When Sharda returned to work, she learned that Mr. Singh’s gold ring, a gift from his mother, was missing. Suspecting theft, Mr. Singh had terminated Vimla. Mr. Singh asked Sharda to take additional responsibility of cleaning the house, along with an offer to double her salary. Sharda accepted the offer as her previous two jobs were lost due to frequent health-related absences. She was struggling to make ends meet; this offer would go a long way to help her.
Next day, while cleaning under the dressing table, Sharda found the gold ring. Overjoyed, Mr. Singh expressed his gratitude by presenting Sharda a reward of one thousand rupees! However, he made no mention of reinstating Vimla.
Sharda was contemplating whether she should inform Vimla that she found Mr. Singh’s ring.
Which of the following considerations will BEST dissuade Sharda in sharing the information about the ring with Vimla?
Two months passed, and owing to Sharda’s improved health and dedication, Sharda started working in three more houses. However, Vimla was dismissed from her jobs in two more houses primarily due to the ring incident. News of the discovery of the lost ring had not become public, and Sharda wanted to help Vimla. Sharda is contemplating over possible actions.
Which of the following actions, by Sharda, will BEST help Vimla?
