CAT 2025 Slot 1 Answer Key QA: Download Question Paper with Answer Key PDF

CAT 2025 Slot 1 QA Answer Key is available here for free download. CAT 2025 Slot 1 paper was conducted on November 30 from 8.30 AM to 10.30 AM. CAT 2025 Slot 1 Answer Key QA has answers to 22 questions. CAT 2025 Slot 1 QA Answer Key will help candidates to analyze their scores.

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CAT 2025 Slot 1 QA Answer Key PDF (Memory – Based)

CAT 2025 Slot 1 QA Answer Key PDF
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Question 1:

In the sequence 1, 3, 5, 7, ..., k, ..., 57, the sum of the numbers up to k, excluding k, is equal to the sum of the numbers from k up to 57, also excluding k. What is k?

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Question 2:

A 200-litre container holds a solution that is 30% acid and the rest water. The solution undergoes the following three processes sequentially:

1. 20% of the water content is evaporated.

2. From the remaining mixture, 10% of the acid content is chemically extracted and removed.

3. Finally, 15% of the resulting solution is removed and replaced with water.

What is the volume of acid in the final solution?

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Question 3:

Find the number of real values of x satisfying the equation:
\[ \log_{2}(x^2 - 5x + 6) + \log_{1/2}(x - 2) = 3 \]

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Question 4:

Find the number of integer pairs (x, y) that satisfy the following system of inequalities:
\[ \begin{cases} x \geq y \geq 3
x + y \leq 14 \end{cases} \]

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Question 5:

Given that a, b, and c are real numbers satisfying the equations:

$2a - 5b + 11c = 0$
$11a + 10b - 2c = 5$

Find the value of the expression $ (a^2 - b^2 + c^2) $.

(A) 5/11
(B) 2/13
(C) 1
(D) CBD (Cannot be determined)

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Question 6:

A shopkeeper offers a 22% discount on the marked price of chairs. He gives 13 chairs to a customer at the discounted price of 12 chairs. If he still makes a profit of 26%, what is the marked price (MP) of a single chair, assuming its cost price (CP) is Rupees 100?

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Question 7:

Find the real value(s) of x that satisfy the equation:
\[ \log_{2}(x^2 - 5x + 6) + \log_{1/2}(x - 2) = 3 \]

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Question 8:

In a class there were more than 10 boys than a certain number of girls. After 40% of the girls and 60% of the boys left, the remaining number of girls were 8 more than the remaining boys. Find the possible number of students initially in the class.

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Question 9:

Stocks A, B and C, at 120, 90 and 80 rs respectively. A trader holds a portfolio consisting 60 shares of A, 20 of B and C together. If total value is 33000 what is the number of shares he holds.

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Question 10:

Arun, Tarun and Varun work for 24, 21 and 15 days respectively and get paid 2160, 2400 and 2160 rupees respectively. They get paid the same even if they work for a partial day. If the work has to be completed within 10 days or less, what is the minimum amount that has to be paid to complete the entire task?

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Question 11:

The number of non-negative values of n for which $\log_{1/4}(n^2 - 7n + 14) > 0$ is __.

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Question 12:

In a cafeteria, there are 5 breads. One can choose 1 bread from the available breads, either small or large sized, and can choose up to 2 sauces from 6 available sauces. What is the number of different ways one can place an order?

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Question 13:

If the length of each side of a rhombus is 36 cm, and the area of the rhombus is 396 cm$^2$, then what is the absolute value of the difference between the lengths of its diagonals?

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Question 14:

A container contains only milk. 2/3 of the mixture is removed and replaced with water. This process is done once and then repeated another 3 times. What is the final ratio of milk and water?

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CAT Questions

1.
A shopkeeper sells an item at a profit of 20%. If he had bought it at 10% less and sold it for 60 more, his profit would become 60%. What is the cost price of the item?

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2.
In the set of consecutive odd numbers $\{1, 3, 5, \ldots, 57\}$, there is a number $k$ such that the sum of all the elements less than $k$ is equal to the sum of all the elements greater than $k$. Then, $k$ equals?

$37$
$41$
$39$
$43$

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3.
Rahul starts on his journey at 5 pm at a constant speed so that he reaches his destination at 11 pm the same day. However, on his way, he stops for 20 minutes, and after that, increases his speed by 3 km per hour to reach on time. If he had stopped for 10 minutes more, he would have had to increase his speed by 5 km per hour to reach on time. His initial speed, in km per hour, was

$20$
$15$
$12$
$18$

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4.
Let $f(x) = \dfrac{x}{2x-1}$ and $g(x) = \dfrac{x}{x-1}$. Then, the domain of the function \[ h(x) = f(g(x)) + g(f(x)) \] is all real numbers except:

$\dfrac{1}{2},\, 1,\, \dfrac{3}{2}$
$\dfrac{1}{2},\, 1$
$-\dfrac{1}{2},\, \dfrac{1}{2},\, 1$
$-1,\, \dfrac{1}{2},\, 1$

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5.
The set of all real values of $x$ for which $(x^2 - |x+9| + x)>0$ is:

$(-\infty,-9)\cup(3,\infty)$
$(-\infty,-3)\cup(9,\infty)$
$(-\infty,-3)\cup(3,\infty)$
$(-9,-3)\cup(3,9)$

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6.
The rate of water flow through three pipes A, B and C are in the ratio 4 : 9 : 36. An empty tank can be filled up completely by pipe A in 15 hours. If all the three pipes are used simultaneously to fill up this empty tank, the time, in minutes, required to fill up the entire tank completely is nearest to

$76$
$78$
$73$
$71$

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CAT 2025 Slot 1 Answer Key QA: Download Question Paper with Answer Key PDF

CAT 2025 Slot 1 QA Answer Key PDF (Memory – Based)

How to Raise Objections Against the Answer Key

CAT Questions

1.
A shopkeeper sells an item at a profit of 20%. If he had bought it at 10% less and sold it for 60 more, his profit would become 60%. What is the cost price of the item?

2.
In the set of consecutive odd numbers $\{1, 3, 5, \ldots, 57\}$, there is a number $k$ such that the sum of all the elements less than $k$ is equal to the sum of all the elements greater than $k$. Then, $k$ equals?

4.
Let $f(x) = \dfrac{x}{2x-1}$ and $g(x) = \dfrac{x}{x-1}$. Then, the domain of the function \[ h(x) = f(g(x)) + g(f(x)) \] is all real numbers except:

5.
The set of all real values of $x$ for which $(x^2 - |x+9| + x)>0$ is:

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CAT 2025 Slot 1 QA Answer Key PDF (Memory – Based)

How to Raise Objections Against the Answer Key

CAT Questions

1.A shopkeeper sells an item at a profit of 20%. If he had bought it at 10% less and sold it for 60 more, his profit would become 60%. What is the cost price of the item?

2.In the set of consecutive odd numbers $\{1, 3, 5, \ldots, 57\}$, there is a number $k$ such that the sum of all the elements less than $k$ is equal to the sum of all the elements greater than $k$. Then, $k$ equals?

4.Let $f(x) = \dfrac{x}{2x-1}$ and $g(x) = \dfrac{x}{x-1}$. Then, the domain of the function \[ h(x) = f(g(x)) + g(f(x)) \] is all real numbers except:

5.The set of all real values of $x$ for which $(x^2 - |x+9| + x)>0$ is:

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1.
A shopkeeper sells an item at a profit of 20%. If he had bought it at 10% less and sold it for 60 more, his profit would become 60%. What is the cost price of the item?

2.
In the set of consecutive odd numbers $\{1, 3, 5, \ldots, 57\}$, there is a number $k$ such that the sum of all the elements less than $k$ is equal to the sum of all the elements greater than $k$. Then, $k$ equals?

4.
Let $f(x) = \dfrac{x}{2x-1}$ and $g(x) = \dfrac{x}{x-1}$. Then, the domain of the function \[ h(x) = f(g(x)) + g(f(x)) \] is all real numbers except:

5.
The set of all real values of $x$ for which $(x^2 - |x+9| + x)>0$ is: