In this article, we will be discussing solved TNQT Digital/TCS Digital aptitude questions. But before we look at the questions, make sure you are completely aware of the latest TNQT Digital Pattern & Syllabus.

**TCS Digital Aptitude Questions Pattern**

In TCS/TNQT Digital exam, the aptitude section consists of **12 questions** in total. You will be given 30 minutes to solve these 12 questions. This means you roughly have around 2-2:30 minutes to solve one question. **The below table will give you an idea of TCS Digital aptitude questions syllabus**.

- Permutations and Combinations
- Probability
- Divisibility
- Elementary modulo arithmetic
- Elementary algebra
- Expansions using Binomial theorem
- Roots of polynomials
- Relations between roots and coefficients
- Averages, Mean, median and mode
- Time, speed and distance
- Elementary Geometry
- Elementary trigonometry
- Basic algorithmic thinking.

**TCS Digital Aptitude Questions with Answers**

Here are some of the TCS Digital aptitude questions you can refer for practice. Some of these are TCS digital sample questions. So practice with care.

**1) Of 60 students in a class, anyone who has chosen to study Maths elects to study Physics as well. But no student studies Maths and Chemistry, and 16 study Physics and Chemistry. Each of the students elects for at least one of the three subjects and the number of people who study exactly one of the three is more than the number who do more than one of the three. What are the maximum and the minimum number of students who could have studied only Chemistry?**

a) 44, 0

b) 38, 2

c) 28, 0

d) 40, 0

**Answer:** Option a

Let us outline the diagram. Anyone who does Maths does Physics also.

Maths is a subset of Physics. Now, let us build on this. No one does maths and chemistry, 16 do physics and chemistry.

Number outside is 0 as all the students do at least one of the three subjects. a + b + c +16 = 60, or a + b + c = 44

The number of people who do exactly one of the three is more than the number who do more than

one of the three. => a + b > c + 16. So, we have a + b + c = 44 and a + b > c + 16. We need to find the

maximum and minimum possible values of b.

Let us start with the minimum. Let b = 0, a + c = 44. a > c + 16. We could have

a = 40, c = 4. So, b can be 0.

Now, thinking about the maximum value. b = 44, a = c = 0 also works.

So, minimum value = 0, maximum value = 44

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**2) ****The average score in an examination of 10 students in a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores and each of their scores are greater than any of the remaining scores, the maximum possible score of the topper is**

a) 95

b) 100

c) 87

d) 99

**Answer:** Option d**Explanation:**

10 students have scored 600 marks amongst them, and no one is allowed to score lesser than 40

or higher than 100. The idea now is to maximize what the highest scorer gets.

The 5 least scores have an average of 55, which means that they have scored 55 x 5 = 275 marks

amongst them. This leaves 325 marks to be shared amongst the top 5 students. Let’s call them a, b, c,

d and e. Now, in order to maximize what the top scorer “e” gets, all the others have to get the least

possible scores (and at the same time, they should also get distinct integers.)

The least possible score of the top 5 should be at least equal to the highest of the bottom 5.

Now we want to make sure that the highest of the bottom 5 is the least possible. This can be done by

Making all scores equal to 55. If some scores are less than 55, some other scores have to be higher

than 55 to compensate and make the average 55. Thus the highest score is the least only when the

range is 0.

So now, we have the lowest value that the top 5 can score, which is 55. The others have to get

distinct integer scores, and as few marks as possible, so that “e” gets the maximum.

So, 55 + 56 + 57 + 58 + e = 325

e = 99 marks.

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**3) 3L of milk are drawn from a container containing 30L of milk. It is replaced by water and the process is repeated 2 times. What is the ratio of milk to water at the end?**

a) 729/271

b) 2187/100

c) 81/19

d) 743/229

**Answer: Option a****Explanation: **

Formulae (derived using allegation):

Milk left = Capacity * (1 – fraction of milk withdrawn)^{n}

Therefore, milk left = 30 * 0.9^{3}

=> 30 * 9/ 10 * 9/ 10 * 9/ 10

=> 2187/ 100

So, Water in container = (30 – 2187)/ 100

=> (3000 − 2187)/100

=> 813/ 100

Therefore, Milk : Water = 2187 : 813 = 729 : 271

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**4) a, b, c are real numbers in a Geometric Progression (G.P.) such that |a + b + c| = 15. The median of these three terms is a, and b = 10. If a > c, what is the product of the first 4 terms of this G.P.?**

a) 40,000

b) 32,000

c) 8,000

d) 2,500

**Answer:** Option a**Explanation: **

a + b + c cannot be 15.

a + b + c = –15

10/r + 10 + 10r = -15 ⇒ 2/r + 2r = -5

Solving the quadratic, we will get r = −1/2 or -2.

The sequence is either – 5, 10, – 20 or – 20, 10, – 5.

a > c ==> the sequence has to be – 5, 10, – 20.

The product of the first 4 terms = – 5 * 10 * –20 * 40 = 40000.

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**5) B takes 12 more hours than A to complete a task. If they work together, they take 16 fewer hours than B would take to complete the task. How long will it take A and B together to complete a task twice as difficult as the first one?**

a) 16 hours

b) 12 hours

c) 14 hours

d) 8 hours

**Answer:** Option a

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**6) A number, when divided by 18, leaves a remainder 7. The same number, when divided by 12, leaves a remainder n. How many values can n take?**

a) 1

b) 2

c) 0

d) 3

**Answer:** Option b**Explanation: **Number can be 7, 25, 43, 61, 79. Remainders, when divided by 12, are 7 and 1. n can take exactly 2 values.

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**7) In how many ways can we stack n different coins so that two particular coins are not adjacent to each other? [ Note that m! = (1)(2)(3)…(m) ]**

a) (n − 2) * (n − 1) !

b) (n − 2) !

c) (n − 1) * (n − 1) !

d) (n) * (n − 2) !

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**8) For how many integer values does the following inequality hold good? (x + 2) (x + 4) (x + 6)…(x + 100) < 0**

**9) Consider the set S = {8, 5, 1, 13, 34, 3, 21, 2}. Akshay lists all the two element subsets of S and takes the larger of the elements in each set. If he sums all these numbers, the sum he will obtain is __________**

**Answer:** 484**Explanation:**

{8,5},{8, 1},{8, 13},{8, 34},{8, 3},{8, 21},{8, 2},{5, 1},{5, 13},{5, 34},{5, 3},{5, 21},{5, 2},{ 1, 13},

{ 1, 34},{ 1, 3},{ 1, 21},{ 1, 2},{ 13, 34},{ 13, 3},{ 13, 21},{ 13, 2},{ 34, 3},{ 34, 21},{ 34, 2},{ 3, 21},{ 3, 2},

{ 21, 2},

8+8+13+34+8+21+8+5+13+34+5+21+5+13+34+3+21+2+34+13+21+13+34+34+34+21+3+21 = 484

**10) Set P comprises all positive multiples of 4 less than 500. Set Q comprises all positive odd multiples of 7 less than 500, Set R comprises all positive multiples of 6 less than 500. How many elements are present in P ∪ Q ∪ R ?___________**

**11) How many 10-digit strings of 0’s and 1’s are there that do not contain any consecutive 0’s? ****Do not enter whitespaces before or after the answer.**

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**12) Each of Alia, Betty, Carol, and Dalia took a test. Each them answered at least one question correctly, and altogether they answered 67 questions correctly. Alia had more correct answers than anyone else. Betty and Carol together answered 43 questions correctly. How many correct answers did Dalia have? Do not enter whitespaces before or after the answer.**

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**13) Of a set of 30 numbers, the average of first 10 numbers is equal to the average of last 20 numbers. Then the sum of the last 20 numbers is**

a) sum of the first ten numbers

b) 2 x sum of the first ten numbers

c) Cannot be determined with the given data

d) 2 x sum of the last ten numbers

**14) The number of integers n with 100 < n < 300 such that 16 divides (n^2-n-2) and 25 divides (n^2 + 2n – 3) is**

a) 4

b) 2

c) 1

d) 3

**15) George’s salary is 20% more than Mark’s, Harry’s salary is 30% greater than George’s. Tony’s salary is 40% more than Albert’s. Albert’s salary is 20% lesser than George’s. What is Albert’s salary as a percentage of Tony’s salary (to the nearest percentage point)?**

a) 82%

b) 76%

c) 69%

d) 60%

**16) A Sudoku grid contains digits in such a manner that every row, every column, and every 3×3 box accommodates the digits 1 to 9, without repetition. In the following Sudoku grid, find the values at the cells denoted by**

a) 113

b) 79

c) 59

d) 129

**17) In a family, there are four daughters Aasha, Eesha, Trisha, and Usha. Each girl has exactly one necklace and one bracelet. Each of these eight ornaments was bought in either 2007, 2008, or 2009. The eight ornaments were bought in a manner consistent with the following conditions:**

- The necklace for each girl was bought either in an earlier year than or in the same year as the bracelet for that girl.
- The necklace for Eesha and the bracelet for Aasha were bought in the same year.
- The necklace for Trisha and the bracelet for Usha were bought in the same year.
- The necklace for Eesha and the necklace for Trisha were bought in different years.
- The necklace for Aasha and the bracelet for Trisha were bought in 2008.

If the necklace for Trisha was bought in an earlier year than the bracelet for Trisha was, then which one of the following statements could be true?

a) The bracelet for Usha was bought in 2008

b) The necklace for Eesha was bought in 2008

c) The necklace for Usha was bought in 2008

c) The necklace for Eesha was bought in 2007

**18) A rectangle of height 100 squares and width 200 squares is drawn on a graph paper. It is colored square by square from top left the corner and moving across in a spiral turning right whenever a side of the rectangle or a colored square is reached. Which square is colored last? (give its row and column numbers – the bottom right square is on row 100 and column 200)**

a) 50,50

b) 51,50

c) 51,150

d) 50,150

**19) If 12 divides ab313ab (in decimal notation, where a, b are digits > 0, the smallest value of a+b is**

a) 7

b) 6

c) 4

d) 2