CAT 2025 Question Papers PDF FREE Download (Slot 1, 2 & 3), Memory-Based Questions With Answer Key & Solutions

CAT 2025 Question Paper PDF Download Links (Memory-Based Questions) - Slot 1, Slot 2 & Slot 3

This section gives you the memory-based CAT 2025 question paper PDFs for Slot 1, Slot 2 and Slot 3 that you can download right away. It also includes slot-wise analysis of CAT 2025 exam, recalled questions, and early percentile predictions to help you understand how you may have performed.

CAT 2025 Answer Key

This section gives you direct access to the CAT 2025 answer key for Slot 1, helping you quickly check your responses, estimate your score, and understand where you stand right after the exam.

CAT 2025 Question Paper with Solutions (All Slots)

This section includes the memory-based CAT 2025 questions collected from students across all slots, along with simple solutions to help you understand the approach. It’s a quick way to revise the type of questions asked in the exam.

Question 1: Find the minimum number of integral solutions for

$x + y < 14$

$x > y \ge 3$

Solution:

If $y = 3$, then $x$ can be from $4$ to $10$ (7 solutions)

If $y = 4$, then $x$ can be from $5$ to $9$ (5 solutions)

If $y = 5$, then $x$ can be from $6$ to $8$ (3 solutions)

If $y = 6$, then $x = 7$ (1 solution)

Total = $16$ solutions.

Question 2: The number of boys is 10 more than the number of girls. If 60% boys and 40% girls leave, the difference between remaining students is 8. Find number of boys.

Solution:

Let girls = $G$, boys = $B$.

Given:
$B = G + 10$

Remaining boys = $0.4B$
Remaining girls = $0.6G$

Difference:
$|0.4B - 0.6G| = 8$

Substitute $B = G + 10$:
$|0.4(G+10) - 0.6G| = 8$
$|4 - 0.2G| = 8$

So:
$4 - 0.2G = 8$ or $0.2G - 4 = 8$

Solve:
$G = 40$
$B = 50$

Question 3: Alven (13 days, ₹2000/day), Alen (19 days, ₹1900/day), Peter (20 days, ₹1500/day).
Find minimum cost to complete work in 10 days (fractional days allowed).

Solution:

Work rates:
Alven = $1/13$
Alen = $1/19$
Peter = $1/20$

Cost per unit work:
Alven = $2000 \times 13 = 26000$
Peter = $1500 \times 20 = 30000$
Alen = $1900 \times 19 = 36100$

Use cheapest first.

Alven works 10 days:
Work done = $10/13$
Remaining work = $3/13$

Peter works remaining time:
Time = $(3/13) \div (1/20) = 60/13$

Total cost = $20000 + 1500 \times 60/13$
Total = $20000 + 90000/13$
Total = $350000/13 \approx 26923.08$

Minimum cost ≈ ₹26,923.08

Question 4: A 200 L mixture has 30% acid. 20% mixture replaced with water, then 10% with acid. Final % acid?

Solution:

Initial acid = $0.3 \times 200 = 60$ L

After first replacement:
40 L removed → acid left = $60 \times (160/200) = 48$ L
Acid % = $48/200 = 24%$

After second replacement (20 L replaced):
Water % before = $76%$
Water after replacement = $0.76 \times 190 = 144.4$ L
So acid = $200 - 144.4 = 55.6$ L ≈ $27%$

Final answer ≈ 27% acid

Question 5: Rhombus with side 36 cm and area 396 sq cm. Find $|d_1 - d_2|$.

Solution:

$\frac{1}{2} d_1 d_2 = 396$
$d_1 d_2 = 792$

$(d_1/2)^2 + (d_2/2)^2 = 36^2 = 1296$
$d_1^2 + d_2^2 = 5184$

$(d_1 - d_2)^2 = d_1^2 + d_2^2 - 2 d_1 d_2$
$(d_1 - d_2)^2 = 5184 - 1584 = 3600$

$|d_1 - d_2| = 60$

Question 6: A invests 100000 in stocks, bonds, gold. Interest rates: 10%, 6%, 8%. Bonds = 25% of gold. Interest earned = 8200. Find interest on bonds.

Solution:

$S + B + G = 100000$
Interest:
$0.1S + 0.06B + 0.08G = 8200$
$B = 0.25G$

From total:
$S = 100000 - 1.25G$

Substitute:

$0.1(100000 - 1.25G) + 0.06(0.25G) + 0.08G = 8200$

$10000 - 0.125G + 0.015G + 0.08G = 8200$

$10000 - 0.03G = 8200$

$0.03G = 1800$
$G = 60000$
$B = 15000$

Interest on bonds = $0.06 \times 15000 = 900$

Answer: ₹900

Question 7: Sequence: $1, 3, 5, …, 57$
Find $K$ such that sum before $K$ = sum after $K$.

Solution:

Total terms = 29
Sum = $29^2 = 841$

Let $K$ be the $k$-th term.
Value of term = $2k - 1$
Sum before = $(k - 1)^2$

Condition:
$2(k-1)^2 + (2k - 1) = 841$

Solve:
$k^2 - k - 420 = 0$
$k = 21$

So $K = 2(21) - 1 = 41$

Answer: 41

Question 8: N is the smallest 3-digit number with:
– no perfect square digits
– exactly one prime digit
– all digits distinct
Find factors of this number.

Solution:

Smallest possible = 268

$268 = 2^2 \times 67$

Number of factors = $(2+1)(1+1) = 6$

Question 9: $x^2 - 5x + k = 0$ has integer roots. Find non-negative integer $k$.

Solution:

Sum of roots = 5.

Possible pairs:
(1,4), (0,5), (2,3)

Corresponding $k$ = product:

$1 \cdot 4 = 4$
$0 \cdot 5 = 0$
$2 \cdot 3 = 6$

Values of $k$: 0, 4, 6

Question 10: $\log_{1/4}(x^2 - 7x + 11) > 0$.
Find number of natural number solutions.

Solution:

Base $1/4 < 1$, so:

$x^2 - 7x + 11 < 1$

$x^2 - 7x + 10 < 0$

$(x - 5)(x - 2) < 0$

So $2 < x < 5$ → possible $x = 3, 4$

Check both:

$x=3$: $9 - 21 + 11 = -1$ (invalid)
$x=4$: $16 - 28 + 11 = -1$ (invalid)

No valid $x$.

Answer: 0

Question 11: Shopkeeper gives 22% discount, 13 chairs for price of 12, profit 26%. CP = 100. Find MP.

Solution:

SP of 13 chairs = $126 \times 13 = 1638$

Let MP = $100x$
Discounted price = $78x$

Price of 12 chairs: $12 \times 78x = 936x$

$936x = 1638$
$x = 1.75$

MP = ₹175

Question 12: Amount becomes 13920 in 3 years, and 18960 in 6.5 years at SI.
Find interest in 2 years CI (half-yearly).

Solution:

Using SI:

$P(1 + 3r) = 13920$
$P(1 + 6.5r) = 18960$

Divide:

$\frac{1 + 6.5r}{1 + 3r} = \frac{18960}{13920} = 1.36207$

Solve:
$r = 0.15$

Now:

$P \times 1.45 = 13920$
$P = 9600$

CI (half-yearly):

Rate = $0.075$
Periods = 4

Amount = $9600 \times (1.075)^4 = 12820.5$

Interest = 3220.5

Question 13: $a, b, c$ distinct natural numbers, satisfying $3ac = 8(a + b)$.
Minimize $3a + 2b + c$.

Solution:

$b = ak$
$3ac = 8a(1 + k)$
$c = \frac{8(1+k)}{3}$

For $c$ natural → $1+k \equiv 0 \pmod{3}$ → $k = 2, 5, 8...$

To minimize, take $a = 1$, $k=2$:

$b = 2$
$c = 8$

Value:

$3a + 2b + c = 3 + 4 + 8 = 15$

Answer: 15

CAT 2025 CAT 2025 Analysis - Slot 1, 2 and 3

This section shares the detailed exam analysis for all three slots, along with the YouTube video by our CAT expert, Mr. Ark Srinivas. It helps you understand the difficulty level, question trends, and overall student experience.

CAT 2025 Official Question Paper PDF Download - Slot 1, Slot 2 & Slot 3

The CAT 2025 question paper PDFs for Slot 1, Slot 2 and Slot 3 will be available for download once the official papers are released. This section gives you the direct download details, along with what each slot-wise paper will include.

CAT 2025 Exam Overview: Slots, Pattern

This section gives you a quick look at how the CAT 2025 exam was held across all three slots, along with the overall paper pattern. It helps you understand the structure, number of questions, and what pattern students experienced in each slot.

How to Download the CAT 2025 Question Paper?

IIMs do not release a separate official question paper PDF, but you can view all the questions from your slot through the response sheet. Once the response sheets are live, students can also access questions from all three slots online. Here’s the easy process:

1. Visit the official CAT website: iimcat.ac.in.

2. Click on the Login button on the homepage.

3. Enter your CAT registration number and password.

4. After logging in, open the Response Sheet and Answer Key section.

5. Download your response sheet - it contains every question that appeared in your slot.

6. Save the PDF to your device for later review or analysis.

CAT 2025 Expected Score vs Percentile: First Cut – All Slots

This section gives the first rough estimate of score vs percentile for all three slots. It includes a clear table showing the predicted percentiles based on expected scores to help you understand where you might stand.

CAT 2025 Score vs Percentile - Slot 1, 2 and 3

This part explains the expected score vs percentile for each slot, supported by insights from the YouTube analysis by Mr. Ark Srinivas. It gives you a simple idea of how your raw score may convert into a percentile.