Deloitte – Aptitude Questions & Answers for Placement Tests

Ans: C

We can use the property of modular arithmetic. We want to find 3^41 mod 13. First, let’s find a pattern: 3^1 mod 13 = 3 3^2 mod 13 = 9 3^3 mod 13 = 27 mod 13 = 1 Since 3^3 mod 13 = 1, we can write 3^41 as 3^(3*13 + 2) = (3^3)^13 * 3^2 So, 3^41 mod 13 = (1)^13 * 3^2 mod 13 = 1 * 9 mod 13 = 9.

Ans: C

The pattern is (2^n) – 1, where n starts from 2 and increases by 1 for each subsequent element.

Ans: B

Total marks scored in 10 exams = 10 * 80 = 800. To have an average of 85 across 15 exams, total marks required = 15 * 85 = 1275. Marks required in the next 5 exams = 1275 – 800 = 475. Average score required in the next 5 exams = 475 / 5 = 95.

Ans: A

X’s salary = 25% of 20000 = 5000. Remaining profit = 20000 – 5000 = 15000. Let X’s investment be ‘x’. Let X’s share be Px and Y’s share be Py. Then Px – Py = 8000. Since the profit is divided in the ratio of investment, so (x/10000) = (Px/Py). Also, Px+Py = 15000. So, Px = Py + 8000, then (Py+8000)+Py = 15000, 2*Py = 7000, Py = 3500. So Px= 11500. (x/10000) = 11500/3500, therefore x = 10000 * 11500/3500 = 32857 approx. But Px = 5000+share which is 11500, total X’s earnings = 11500+5000 = 16500. Y’s earnings is 3500. So if we calculate it differently, Let X’s investment = a. X’s earnings: 5000 + (a/(a+10000))*15000 Y’s earnings: (10000/(a+10000))*15000 5000 + (a/(a+10000))*15000 – (10000/(a+10000))*15000 = 8000 5000 + 15000(a-10000)/(a+10000) = 8000 15000(a-10000) = 3000(a+10000) 5(a-10000) = a+10000 5a-50000= a+10000 4a = 60000 a = 15000

Ans: B

We need to find 3^102 mod 100. We can observe a pattern: 3^1 = 03 mod 100 3^2 = 09 mod 100 3^3 = 27 mod 100 3^4 = 81 mod 100 3^5 = 43 mod 100 3^6 = 29 mod 100 3^7 = 87 mod 100 3^8 = 61 mod 100 3^9 = 83 mod 100 3^10 = 49 mod 100 3^20 = (3^10)^2 = 49^2 = 2401 = 01 mod 100 Since 3^20 = 1 mod 100, then 3^100 = (3^20)^5 = 1 mod 100. Therefore, 3^102 = 3^100 * 3^2 = 1 * 9 = 9 mod 100.

Ans: A

The subject of the sentence is “the chef”. The phrase “along with the sous chefs” is a modifying phrase and doesn’t affect the verb conjugation. Therefore, the verb should agree with the subject which is singular.

Ans: A

The word BANANA has 6 letters, with ‘B’ appearing once, ‘A’ appearing three times, and ‘N’ appearing twice. The number of different words is 6! / (3! * 2!) = 720 / (6 * 2) = 60.

Ans: B

Subtle suggests that the clue was not obvious.

Ans: A

Since the bacteria population doubles every minute, the dish was half full one minute before it was full.

Ans: B

Let the capacity of the cistern be the LCM of 12 and 18, which is 36 units. The first tap fills 36/12 = 3 units per hour. The second tap empties 36/18 = 2 units per hour. When both taps are open, the net filling rate is 3 – 2 = 1 unit per hour. Therefore, the cistern will be filled in 36/1 = 36 hours.

Ans: B

The pattern is adding consecutive even numbers: 2 + 4 = 6, 6 + 6 = 12, 12 + 8 = 20, therefore, 20 + 10 = 30

Ans: B

The incorrect sum of weights is m*48. The error is 54-36=18 kg. The correct sum of weights is m*48 – 18. The corrected average is (m*48 – 18)/m = 48 – 18/m. The new average decreased by 0.5, so 48 – 18/m = 48 – 0.5. Thus, 18/m = 0.5, therefore m = 18/0.5 = 36.

Ans: D

Both arguments present valid points for and against the idea.

Ans: B

Let the present ages of the father and son be 7x and 2x respectively. After 10 years, their ages will be 7x + 10 and 2x + 10. According to the problem, (7x + 10) / (2x + 10) = 9/4. Cross-multiplying, 28x + 40 = 18x + 90. 10x = 50, so x = 5. The father’s present age is 7x = 7 * 5 = 35 years.

Ans: A

Let x be the time spent at 20 km/h. Then (6-x) is the time spent at 35 km/h. Thus, 20x + 35(6-x) = 180. Simplifying, 20x + 210 – 35x = 180, -15x = -30, x = 2. The distance covered at 20 km/h is 20 * 2 = 40 km.

Ans: C

Let the original salary be 100. After a 20% increase, the salary becomes 120. After a 20% decrease on 120, the salary becomes 120 – (20/100)*120 = 120 – 24 = 96. The change is 100-96=4, which is a 4% decrease.

Ans: C

Prime factorization of 12 = 2^2 * 3, 36 = 2^2 * 3^2, and 48 = 2^4 * 3. LCM is the product of the highest powers of all prime factors: 2^4 * 3^2 = 16 * 9 = 144

Ans: B

The last digit of powers of 4 follow the pattern: 4, 6, 4, 6,… Since 2024 is an even number, the last digit will be 6.

Ans: A

The woman’s mother’s only daughter is the woman herself. Therefore, the man’s mother is the woman. Hence, the man is the woman’s son.

Ans: A

The sentence needs a verb that shows the company’s success is a result of the employees’ hard work. “Reflects” fits this meaning.

Ans: C

The pattern is: 2+1=3, 3+2=5, 5+4=9, 9+8=17, 17+16=33. The numbers being added are powers of 2 (2^0, 2^1, 2^2, 2^3, 2^4)

Ans: D

The first train has a 3-hour head start (from 6:00 AM to 9:00 AM) and covers 60 km/hr * 3 hr = 180 km. The relative speed of the second train with respect to the first is 90 km/hr – 60 km/hr = 30 km/hr. Time taken for the second train to cover the 180 km gap is 180 km / 30 km/hr = 6 hours. The second train starts at 9:00 AM, so it will overtake the first train at 9:00 AM + 6 hours = 3:00 PM.

Ans: A

This is a right-angled triangle problem. The distance is the hypotenuse, calculated using the Pythagorean theorem: sqrt(12^2 + 9^2) = sqrt(144 + 81) = sqrt(225) = 15

Ans: A

Aanya walks 8m North, then 4m East, then 8m South (back to the same horizontal level as the starting point), and finally 8m West. This forms a rectangle. The distance from the starting point is the length of the remaining side which is 4m + 8m = 12m.