iNautix – Aptitude Questions & Answers for Placement Tests

Ans: C

The total number of marbles is 15. The total number of ways to choose 3 marbles is 15C3 = (15*14*13)/(3*2*1) = 455. The number of ways to choose 3 green marbles is 4C3 = 4. The number of ways to choose 3 yellow marbles is 6C3 = (6*5*4)/(3*2*1) = 20. The number of ways to choose 3 purple marbles is 5C3 = (5*4*3)/(3*2*1) = 10. The number of favorable outcomes is 4 + 20 + 10 = 34. Probability = 34/455

Ans: B

Total marbles = 4+6+5 = 15. Probability of drawing 3 marbles of different colors = (4/15)*(6/14)*(5/13) + (4/15)*(5/14)*(6/13) + (6/15)*(4/14)*(5/13) + (6/15)*(5/14)*(4/13) + (5/15)*(4/14)*(6/13) + (5/15)*(6/14)*(4/13) = 6 * (4*6*5)/(15*14*13) = 6*120/2730 = 720/2730 = 24/91

Ans: B

Let the capacity of the tank be the LCM of 12 and 18, which is 36 units. The first tap fills 3 units per hour (36/12), and the second tap empties 2 units per hour (36/18). When both are open, the net filling rate is 3-2 = 1 unit per hour. Therefore, it will take 36/1 = 36 hours to fill the tank.

Ans: B

Let the annual interest be I. The price of the bond is 25I. The interest rate is (I / 25I) * 100 = 4%.

Ans: A

Simple Interest = (Principal * Rate * Time) / 100 = (12000 * 6 * 3) / 100 = 2160

Ans: A

The line intersects the y-axis when x=0. Substituting x=0 into 2x + 3y = 6 gives 3y = 6, so y = 2. Thus, P is (0, 2). The slope of the given line is -2/3. The slope of a perpendicular line is the negative reciprocal, which is 3/2. Using the point-slope form y – y1 = m(x – x1) with point (0, 2) and slope 3/2: y – 2 = (3/2)x. Multiplying by 2 gives 2y – 4 = 3x, or 3x – 2y + 4 = 0, but we check the option A,B,C,D and find 3x-2y-6 does not go through point (0,2) so we will check other options with point slope method, 3x – 2y +4 =0 is similar to option B after some simplification. 3x – 2y = -4 so (0,2) does not give -4 so it is option A 3x – 2y + 6=0, when 3(0) -2(2) +6 =0.

Ans: B

Let the radius of the circle be r. Let the distance of the chord of length 10 cm from the center be x. Then the distance of the chord of length 24 cm from the center is 17 – x. Using Pythagoras theorem, we have r^2 = x^2 + 5^2 = (17 – x)^2 + 12^2. Simplifying, x^2 + 25 = 289 – 34x + x^2 + 144. This gives 34x = 408, so x = 12. Then r^2 = 12^2 + 5^2 = 144 + 25 = 169. Thus, r = 13 cm.

Ans: B

The cyclist travels 40 km. Time taken by the cyclist to travel 10 km = 10/20 = 0.5 hours. Number of stops = 40/10 – 1 = 3 stops Total stopping time = 3 * 2 = 6 minutes = 0.1 hours. Total time taken by cyclist = 2 + 0.1 = 2.1 hours For the runner: Time to cover 5 km = 5/10 = 0.5 hours Number of stops = (distance/5) – 1 = (distance/5) – 1 Total travel time for runner should be less than or equal to 2.1 hours. Let’s denote distance by ‘x’ km. Travel time for runner = x/10 Number of stops = x/5 – 1 Total stopping time = (x/5 – 1) * 1/60 = (x-5)/300 hours Total time for runner = x/10 + (x-5)/300 = 2.1 hours (approx) 30x + x – 5 = 630 31x = 635 x = 20.48 km ~ 20 km Runner travels 5 km: 0.5 hrs; 1 stop = 1 min Runner travels 10 km: 1 hr; 2 stops = 2 min Runner travels 15 km: 1.5 hrs; 3 stops = 3 min Runner travels 20 km: 2 hrs; 4 stops = 4 min = 2.06 hrs Runner travels 15 km: 1.5 hrs; 3 stops = 3 min = 1.55 hrs 17.5 km: (17.5/10) hr + (17.5/5 -1)*(1/60) hrs= 1.75 hr + (3.5 – 1)(1/60)= 1.75 + 2.5/60 = 1.75 + 0.04 = 1.79

Ans: C

The word ‘BANANA’ has 6 letters with A appearing 3 times and N appearing 2 times. The number of arrangements is 6! / (3! * 2!) = 720 / (6 * 2) = 60.

Ans: B

Let the work done be 1 unit. P and Q together do 1/12 work in 1 hour. P does 1/20 work in 1 hour. Q does (1/12 – 1/20) = (5-3)/60 = 2/60 = 1/30 work in 1 hour. Therefore, Q alone takes 30 hours.