CAT 2021 · Slot 2
A full-length paper in the 2021 pattern. Sit it under exam conditions with solutions locked until you submit, or open it in learn mode and check each answer as you go.
66questions
120 min40 min per section
20TITA, no negative marks
18/34/14easy / medium / hard
Section-wise pattern and topics
Sections run in this order with their own timer, as in CAT 2021.
Verbal Ability & Reading Comprehension · 24 questions · 40 min
- Reading Comprehension20
- Verbal Ability4
Data Interpretation & Logical Reasoning · 20 questions · 40 min
- Games & Tournaments5
- tables5
- Allocation & Matching5
- Grids & Arrangements5
Quantitative Ability · 22 questions · 40 min
- Profit & Loss2
- trains1
- Time & Work1
- replacement1
- Simple & Compound Interest1
- Ratio & Proportion1
- Averages1
- boats & streams1
- Quadratic Equations1
- Inequalities & Modulus1
- Logarithms1
- AP1
- functional equations1
- exponential equations1
- triangles (incircle & circumcircle)1
- circles & tangents1
- Coordinate Geometry1
- cones & frustums1
- quadrilaterals & areas1
- distribution1
- Probability1
Sample question from this paper
Time & Work · medium
A is thrice as efficient as B, and working together they can complete a job in 12 days. B starts the job alone and works for 8 days, after which A joins him and they finish the remaining work together. In how many days, from the start, is the job completed?
- A. 16
- B. 18
- C. 20
- D. 22
Show answer and solution
Answer: B
Let B's rate = r, so A's rate = 3r. Together: 4r = 1/12 ⇒ r = 1/48.
So B alone would take 48 days, and A alone would take 16 days.
In the first 8 days, B alone does 8 × (1/48) = 1/6 of the job, leaving 5/6.
Once A joins, their combined rate is again 4r = 1/12 per day, so the remaining 5/6 takes (5/6) ÷ (1/12) = 10 days.
Total time = 8 + 10 = 18 days.
Tip: the combined rate after A joins is the same 'together' rate given at the start — no need to recompute it.
Let B's rate = r, so A's rate = 3r. Together: 4r = 1/12 ⇒ r = 1/48.
So B alone would take 48 days, and A alone would take 16 days.
In the first 8 days, B alone does 8 × (1/48) = 1/6 of the job, leaving 5/6.
Once A joins, their combined rate is again 4r = 1/12 per day, so the remaining 5/6 takes (5/6) ÷ (1/12) = 10 days.
Total time = 8 + 10 = 18 days.
Tip: the combined rate after A joins is the same 'together' rate given at the start — no need to recompute it.