cat 2018 solutions slot 1

The Common Admission Test (CAT) is one of the most competitive exams in India, serving as a gateway to prestigious management programs. The 2018 edition of CAT was particularly challenging, with a diverse set of questions across various sections. This article provides detailed solutions for the questions in Slot 1 of the CAT 2018 exam. Quantitative Ability Question 1: Arithmetic Progression Problem: Find the sum of the first 20 terms of the arithmetic progression where the first term is 3 and the common difference is 4.

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cat 2018 solutions slot 1

The Common Admission Test (CAT) is one of the most competitive exams in India, serving as a gateway to prestigious management programs. The 2018 edition of CAT was particularly challenging, with a diverse set of questions across various sections. This article provides detailed solutions for the questions in Slot 1 of the CAT 2018 exam.

Quantitative Ability

Question 1: Arithmetic Progression

Problem: Find the sum of the first 20 terms of the arithmetic progression where the first term is 3 and the common difference is 4.

Solution:

1. The formula for the sum of the first ( n ) terms of an arithmetic progression is: [ S_n = \frac{n}{2} \times (2a + (n-1)d) ]
2. Here, ( a = 3 ), ( d = 4 ), and ( n = 20 ).
3. Substitute the values into the formula: [ S_{20} = \frac{20}{2} \times (2 \times 3 + (20-1) \times 4) ]
4. Simplify the expression: [ S_{20} = 10 \times (6 + 76) = 10 \times 82 = 820 ]

Answer: 820

Question 2: Geometry

Problem: A circle with center ( O ) has two chords ( AB ) and ( CD ) intersecting at ( E ). If ( AE = 6 ), ( EB = 4 ), and ( CE = 3 ), find ( ED ).

Solution:

1. Using the property of intersecting chords in a circle: [ AE \times EB = CE \times ED ]
2. Substitute the given values: [ 6 \times 4 = 3 \times ED ]
3. Solve for ( ED ): [ ED = \frac{24}{3} = 8 ]

Answer: 8

Data Interpretation and Logical Reasoning

Question 1: Data Interpretation

Problem: A company’s annual report shows the following data for the last five years:

Year	Revenue (in millions)	Profit (in millions)
2014	100	10
2015	120	15
2016	150	20
2017	180	25
2018	200	30

Calculate the average annual growth rate of profit over the five years.

Solution:

1. The formula for the compound annual growth rate (CAGR) is: [ CAGR = \left( \frac{P{\text{end}}}{P{\text{start}}} \right)^{\frac{1}{n}} - 1 ]
2. Here, ( P{\text{end}} = 30 ), ( P{\text{start}} = 10 ), and ( n = 5 ).
3. Substitute the values into the formula: [ CAGR = \left( \frac{30}{10} \right)^{\frac{1}{5}} - 1 = 3^{0.2} - 1 ]
4. Calculate ( 3^{0.2} ): [ 3^{0.2} \approx 1.2457 ]
5. Subtract 1 to find the CAGR: [ CAGR \approx 1.2457 - 1 = 0.2457 \approx 24.57\% ]

Answer: 24.57%

Question 2: Logical Reasoning

Problem: Five friends - A, B, C, D, and E - are sitting in a row. A and B are not sitting next to each other. C is sitting to the immediate right of D. Who is sitting at the extreme right end?

Solution:

1. Given that C is sitting to the immediate right of D, possible arrangements are:
   • D, C, _, _, _
   • _, D, C, _, _
   • _, _, D, C, _
   • _, _, _, D, C
2. Since A and B are not sitting next to each other, the only valid arrangement is:
   • _, D, C, _, _
3. Now, we need to place A and B such that they are not next to each other:
   • A, D, C, B, E

Answer: E is sitting at the extreme right end.

Verbal Ability

Question 1: Reading Comprehension

Problem: Read the following passage and answer the question:

“The rapid advancement of technology has led to significant changes in the way we communicate. Social media platforms have become the primary means of interaction for many people, leading to a decline in face-to-face communication.”

Question: What is the primary reason for the decline in face-to-face communication?

Solution: The primary reason for the decline in face-to-face communication is the rapid advancement of technology, which has made social media platforms the primary means of interaction for many people.

Answer: Rapid advancement of technology

Question 2: Sentence Correction

Problem: Correct the following sentence: “The students was excited for the trip.”

Solution: The sentence should be corrected to: “The student was excited for the trip.”

Answer: The student was excited for the trip.

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These solutions should help candidates understand the approach to solving the questions from CAT 2018 Slot 1. Practicing with such detailed solutions can significantly improve problem-solving skills and boost confidence for future exams.

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