CAT Number System Questions with Solutions PDF

Number Systems questions account for nearly 10-15% of direct questions in the entire CAT question paper. A good hold on CAT Number Systems can help candidates obtain a good score in Quant. In each session of the CAT exam, candidates can expect around 3-4 direct questions.

In the CAT exam, apart from the direct Number Systems questions, candidates will find Number System concepts of use while solving DI sets. Candidates find CAT Number Systems questions on Divisibility Rules, HCF/LCM, and Remainder Theorems. A good hold on Number Systems also helps in different types of CAT Number System questions like basic properties of integers to advanced theorems, with questions evaluating logical deduction and pattern recognition. This article hosts some CAT Number Systems questions with solutions PDFs. Candidates can practice these CAT Number Systems questions tier-wise difficulty levels for holistic preparation for the CAT 2026 exam.

Sample CAT Number Systems Questions with Solutions

Question 1: A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio 1 : 3, then the ratio of lemon juice and sugar syrup in the new mixture is:

1. 1 : 4

2. 1 : 5

3. 1 : 6

4. 1 : 7

Difficulty Level: Easy

Question 2: 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:

*(Note: This is a Non-MCQ / Type-In-The-Answer question)*

Difficulty Level: Medium

Question 3: A shop owner bought a total of 64 shirts from a wholesale market that came in two sizes, small and large. The price of a small shirt was INR 50 less than that of a large shirt. She paid a total of INR 5000 for the large shirts, and a total of INR 1800 for the small shirts. Then, the price of a large shirt and a small shirt together, in INR, is:

1. 225

2. 150

3. 200

4. 175

Difficulty Level: Medium

Question 4: Amal and Vimal together can complete a task in 150 days, while Vimal and Sunil together can complete the same task in 100 days. Amal starts working on the task and works for 75 days, then Vimal takes over and works for 135 days. Finally, Sunil takes over and completes the remaining task in 45 days. If Amal had started the task alone and worked on all days, Vimal had worked on every second day, and Sunil had worked on every third day, then the number of days required to complete the task would have been:

*(Note: This is a Non-MCQ / Type-In-The-Answer question)*

Difficulty Level: Difficult

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