# CAT 2023 QA - Slot 1

Get the complete CAT 2023 paper with answers and explanations

## CAT 2023 Question Paper With Answers & Explanation

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#### Q. 8 The minor angle between the hours hand and minutes hand of a clock was observed at 8:48 am. The minimum duration, in minutes, after 8:48 am when this angle increases by 50% is

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###### Explanation

The angle moved by hour hand in 8 hours = 30°× 8 = 240°
Angle difference in 1 minute between hour hand and minute hand = (11/2)°
Angle difference in 48 minutes between hour hand and minute hand 48 × (11/2)° = 264°
So minor angle between them = 264° – 240° = 24° 50% of 24° = 12°
Hence, 12° will increase in 12/(11/2) = 24/11 minutes.

#### Q. 9 The salaries of three friends Sita, Gita and Mita are initially in the ratio 5 : 6 : 7, respectively. In the first year, they get salary hikes of 20%, 25% and 20%, respectively. In the second year, Sita and Mita get salary hikes of 40% and 25%, respectively, and the salary of Gita becomes equal to the mean salary of the three friends. The salary hike of Gita in the second year is

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###### Explanation

Let the initial salaries of Sita, Gita and Mita be 5x, 6x and 7x respectively.
Then, in first year their salaries will be 5x × 1.2, 6x × 1.25 and 7x × 1.2 i.e., 6x, 7.5x and 8.4x respectively.
In second year salaries of Sita and Mita will be 6x × 1.4 and 8.4x × 1.25 i.e., 8.4x and 10.5x respectively.
In second year, salary of Gita = (8.4x + 10.5x)/2 = 9.45x
Hence, in second year the percentage increase in salary of Gita = (9.45x – 7.5x)/7.5x × 100 = 26%.

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#### Q. 11 Brishti went on an 8-hour trip in a car. Before the trip, the car had travelled a total of x km till then, where x is a whole number and is palindromic, i.e., x remains unchanged when its digits are reversed. At the end of the trip, the car had travelled a total of 26862 km till then, this number again being palindromic. If Brishti never drove at more than 110 km/h, then the greatest possible average speed at which she drove during the trip, in km/h, was

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###### Explanation

From options:
Option (1): 26862 – 8 × 110 = 25982 (Not possible)
Option (2): 26862 – 8 × 100 = 26062 (Possible)
Since we have to find greatest possible average speed, so we can leave option (3) and option (4).
Hence, the required greatest possible average speed is 100 km/h.

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#### Q. 14 The amount of job that Amal, Sunil and Kamal can individually do in a day, are in harmonic progression. Kamal takes twice as much time as Amal to do the same amount of job. If Amal and Sunil work for 4 days and 9 days, respectively, Kamal needs to work for 16 days to finish the remaining job. Then the number of days Sunil will take to finish the job working alone, is

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###### Explanation

Work done by Amal, Sunil and Kamal is in HP.
So time taken by Amal, Sunil and Kamal will be in AP.
Let Amal complete the work in n days.
Then, Kamal will complete the work in 2n days and Sunil will complete the work in (n + 2n)/2 = 1.5n days.
Ratio of time taken = n : 1.5n : 2n = 2 : 3 : 4
Ratio of work done = 1/2 : 1/3 : 1/4 = 6 : 4 : 3
Total units of work = 6 × 4 + 4 × 9 + 3 × 16 = 108
Hence, time taken by Sunil alone to complete the work is 108/4 = 27 days.

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#### Q. 20 The number of all natural numbers up to 1000 with non-repeating digits is

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###### Explanation

Number of non-repeating one digit numbers
= 1 × 9 = 9
Number of non-repeating two digit numbers
= 9 × 9 = 81
Number of non-repeating three digit numbers
= 9 × 9 × 8 = 648
Hence, total numbers = 9 + 81 + 648 = 738.

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