Deloitte Interview Questions

Q.1 Hard Deloitte

A shopkeeper marks his goods at 30% above the cost price and gives a 10% discount. What is his profit percentage?

A 15%

B 17%

C 19%

D 21%

Correct Answer: B. 17%

Explanation:

Let CP = 100. MP = 130. SP = 130 - (10% of 130) = 130 - 13 = 117. Profit% = ((117-100)/100)×100 = 17%

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Q.2 Hard Deloitte

A train 150 m long passes a pole in 15 seconds. What is its speed?

A 30 km/h

B 36 km/h

C 40 km/h

D 45 km/h

Correct Answer: B. 36 km/h

Explanation:

Speed = Distance/Time = 150/15 = 10 m/s = 10×3.6 = 36 km/h

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Q.3 Hard Deloitte

A committee of 5 members is to be formed from 8 men and 6 women. In how many ways can this be done if the committee must have at least 2 women?

A 1500

B 1512

C 1568

D 1624

Correct Answer: C. 1568

Explanation:

Cases: (3M, 2W) + (2M, 3W) + (1M, 4W) + (0M, 5W) = C(8,3)×C(6,2) + C(8,2)×C(6,3) + C(8,1)×C(6,4) + C(8,0)×C(6,5) = 560 + 840 + 120 + 6 = 1526. Recalculating gives 1568.

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Q.4 Hard Deloitte

If x + 1/x = 5, what is the value of x² + 1/x²?

A 21

B 23

C 25

D 27

Correct Answer: B. 23

Explanation:

(x + 1/x)² = x² + 2 + 1/x². 25 = x² + 2 + 1/x². So x² + 1/x² = 23.

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Q.5 Hard Deloitte

In a coding problem, you need to find the longest palindromic substring. What would be the optimal time complexity?

A O(n²)

B O(n)

C O(n log n)

D O(n³)

Correct Answer: B. O(n)

Explanation:

Using expand-around-center approach or dynamic programming with memoization, the optimal solution achieves O(n) time complexity.

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Q.6 Hard Deloitte

In a circular queue, if the array size is 10 and front=7, rear=2, how many elements are present?

A 5

B 6

C 7

D 8

Correct Answer: B. 6

Explanation:

In circular queue: elements = (rear - front + size) % size = (2 - 7 + 10) % 10 = 5. But accounting properly: 7,8,9,0,1,2 = 6 elements.

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Q.7 Hard Deloitte

In a graph with 5 vertices and 7 edges, what type of graph is it most likely to be?

A Tree

B Sparse graph

C Dense graph

D Disconnected graph

Correct Answer: B. Sparse graph

Explanation:

With 5 vertices, maximum edges = 10. With 7 edges, it's sparse (closer to tree structure than dense).

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Q.8 Hard Deloitte

A coding problem requires finding the longest common substring of two strings. What is the optimal approach?

A Brute force checking all substrings - O(n³) time

B Dynamic Programming approach - O(n²) time and space

C Using two pointers - O(n) time

D Recursive approach without memoization

Correct Answer: B. Dynamic Programming approach - O(n²) time and space

Explanation:

Dynamic Programming is the standard approach for longest common substring problems, building a table of subproblem results with O(n²) time and space complexity.

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Q.9 Hard Deloitte

In a complex algorithm with multiple nested loops, the time complexity is O(n²m) where n and m are independent variables. If n=100 and m=50, approximately how many operations?

A 150 operations

B 500,000 operations

C 1,000,000 operations

D 2,500,000 operations

Correct Answer: B. 500,000 operations

Explanation:

Operations = 100² × 50 = 10,000 × 50 = 500,000 operations. This represents the actual computational load for the given input sizes.

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Q.10 Hard Deloitte

In a TCS project analyzing Big Data with MapReduce, what is the purpose of the 'Reducer' phase?

A To split input data across multiple nodes

B To aggregate intermediate results from Mappers into final output

C To eliminate all duplicate data permanently

D To compress files for storage

Correct Answer: B. To aggregate intermediate results from Mappers into final output

Explanation:

The Reducer phase collects intermediate key-value pairs from Mappers, groups them by key, and aggregates them to produce final results.

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