Mu Sigma – Aptitude Questions & Answers for Placement Tests
Reviewing Previous Year Questions is a good start. Prepare Aptitude thoroughly to Clear Placement Tests with 100% Confidence.
Q.1 A bag contains 5 red, 7 green, and 3 yellow balls. If two balls are drawn at random without replacement, what is the probability that both balls are green?
Check Solution
Ans: A
The total number of balls is 5 + 7 + 3 = 15. The probability of drawing a green ball on the first draw is 7/15. After drawing one green ball, there are 6 green balls left and a total of 14 balls. The probability of drawing another green ball is 6/14. The probability of both events occurring is (7/15) * (6/14) = 42/210 = 1/5. However, the options do not have 1/5. Thus, we made an error in the multiplication, (7/15) * (6/14) = 1/5. Now let’s analyze the given options: (7/15) is incorrect, (7/30) is not correct. The probability is (7/15) * (6/14) = 1/5
Q.2 The third term of an AP is 11 and the fifth term is 18. Find the sum of the first 10 terms.
Check Solution
Ans: A
Let the first term be ‘a’ and common difference be ‘d’. a + 2d = 11 …(1) a + 4d = 18 …(2) Subtracting (1) from (2), 2d = 7, d = 3.5 Substituting in (1), a + 2(3.5) = 11, a = 4 Sum of first 10 terms, S10 = (10/2) * [2a + (10-1)d] = 5 * [2(4) + 9(3.5)] = 5 * [8 + 31.5] = 5 * 39.5 = 197.5. The question is wrong in it’s initial set up. However, the closest answer is 200.
Q.3 The average age of a group of friends is 24 years. The ratio of the number of boys to girls in the group is 3:2, and the average age of the boys is 25 years. What is the average age of the girls?
Check Solution
Ans: A
Let the number of boys be 3x and the number of girls be 2x. The total age of the group is 24 * (3x + 2x) = 120x. The total age of the boys is 25 * 3x = 75x. Therefore, the total age of the girls is 120x – 75x = 45x. The average age of the girls is 45x / 2x = 22.5 years. However, given the options are all whole numbers, there is probably an error in the question, but 22 is the closest.
Q.4 What is 25% of 60% of 2/3 of 900?
Check Solution
Ans: A
(25/100) * (60/100) * (2/3) * 900 = (1/4) * (3/5) * (2/3) * 900 = 1/10 * 900 = 90
Q.5 A shopkeeper buys a television for Rs. 8000 and sells it at a profit of 20%. What is the selling price of the television?
Check Solution
Ans: C
Selling price = Cost price + Profit. Profit = 20% of 8000 = (20/100)*8000 = 1600. Selling price = 8000 + 1600 = 9600.
Q.6 A milkman has 20 liters of milk and he mixes 5 liters of water with it. He sells the mixture at the cost price of pure milk. His profit percent is:
Check Solution
Ans: B
Let the cost price of 1 liter of milk be Rs. x. Total cost price of 20 liters of milk = 20x. Total volume of mixture = 20 + 5 = 25 liters. Selling price of 25 liters of mixture = 25x. Profit = 25x – 20x = 5x. Profit % = (Profit / Cost Price) * 100 = (5x / 20x) * 100 = 25%.
Q.7 Two trains start simultaneously from stations A and B, 400 km apart, and travel towards each other. They meet after 4 hours. If the speed of one train is 10 km/h faster than the other, what is the speed of the slower train?
Check Solution
Ans: B
Let the speeds of the trains be x and x+10 km/h. In 4 hours, they cover 400 km. Therefore, 4x + 4(x+10) = 400, which simplifies to 8x + 40 = 400. Solving for x, we get 8x = 360, and x = 45 km/h.
Q.8 A boat travels 30 km upstream in 3 hours and the same distance downstream in 2 hours. What is the speed of the boat in still water?
Check Solution
Ans: A
Let the speed of the boat in still water be ‘b’ km/hr and the speed of the stream be ‘s’ km/hr. Upstream speed = b – s Downstream speed = b + s Distance = Speed x Time Upstream: 30 = (b – s) * 3 => b – s = 10 Downstream: 30 = (b + s) * 2 => b + s = 15 Adding the two equations: 2b = 25 => b = 12.5 km/hr
Q.9 A train departs from Delhi at 6:00 AM, traveling towards Mumbai at 60 km/hr. Another train departs from Mumbai at 8:00 AM, traveling towards Delhi at 70 km/hr. The distance between Delhi and Mumbai is 1000 km. At what time will the two trains meet?
Check Solution
Ans: D
The first train travels for 2 hours (from 6:00 AM to 8:00 AM) before the second train starts. In these 2 hours, it covers 60 km/hr * 2 hr = 120 km. The remaining distance between the two trains is 1000 km – 120 km = 880 km. The relative speed of the two trains is 60 km/hr + 70 km/hr = 130 km/hr. Time to meet = 880 km / 130 km/hr = 6.77 hours (approximately 6 hours and 46 minutes). Since the second train departs at 8:00 AM, they meet around 2:46 PM. The closest option is 2:30 PM.
Q.10 Find whether the given content is alike or different: Date: 03/08/2024 : Date: 03/08/2024
Check Solution
Ans: A
Both the dates are identical.
Q.11 Pointing to a photograph, a man says, “She is the granddaughter of the father of my son.” How is the woman in the photograph related to the man?
Check Solution
Ans: A
The “father of my son” refers to the man himself. Therefore, “She is the granddaughter of the father of my son” implies she is the granddaughter of the man. This means she is the daughter’s daughter, so the woman in the photograph is his daughter.
Q.12 Sarah always walks her dog in the park every morning. The park has a large pond with ducks.
Check Solution
Ans: B
Since Sarah walks her dog in the park, it implies she spends time outdoors and therefore enjoys the outdoors.
Q.13 Find the statement that must be true according to the given information. Maya is a vegetarian. Her friend, Rohan, eats meat. They both enjoy cooking.
Check Solution
Ans: C
Since Rohan eats meat, he does not follow a vegetarian diet.
Q.14 When Michael realized his car had a flat tire, he called a taxi to take him to the mechanic. The mechanic informed him that the tire was beyond repair and needed to be replaced. Michael, annoyed, authorized the replacement and made a mental note to drive more carefully.
Check Solution
Ans: B
Michael authorized the replacement and was informed the tire needed replacement.
Q.15 Sarah always enjoyed attending the weekly book club meetings because of the stimulating discussions. Due to unforeseen circumstances, the book club is now meeting bi-weekly.
Check Solution
Ans: B
The frequency change directly impacts the opportunity for stimulating discussion, leading to a likely change in Sarah’s engagement.
Q.16 All successful people are risk-takers. Ram is a successful businessman. Conclusions: I. Ram is a risk-taker. II. Ram is an ambitious person.
Check Solution
Ans: A
The statement says all successful people are risk-takers. Ram is successful, therefore Ram is a risk-taker. The statement does not provide information to conclude about Ram’s ambition.
Q.17 All successful students are hardworking. Some intelligent students are not hardworking. Conclusions: I. All successful students are intelligent. II. Some successful students are not intelligent.
Check Solution
Ans: D
Neither conclusion I nor II follows.
Q.18 How much was the combined market value of ConnectTech and ByteWare a decade ago compared to Apex?
Check Solution
Ans: D
The passage states the combined value was one-eighth that of Apex.
Q.19 Transform the following sentence into indirect speech. The teacher said, “The Earth revolves around the Sun.”
Check Solution
Ans: B
The tense of the statement remains unchanged because it is a universal truth.
Q.20 Find the synonym of the following word: ELOQUENT
Check Solution
Ans: B
The word “eloquent” means fluent or persuasive in speaking or writing. “Fluent” is therefore a synonym.
Q.21 Find the Antonym of the following word: TRANSIENT
Check Solution
Ans: B
The word “transient” means lasting only for a short time, hence the antonym is “permanent”.
Q.22 The company is looking …… a new Marketing Manager.
Check Solution
Ans: B
The correct preposition to use is “for” when searching or seeking someone/something.
Q.23 The company decided to invest in new technology in order to improve their efficiency.
Check Solution
Ans: B
The correct phrase is “in order to improve”.
Q.24 The company’s profits increased considerably last year, more so than the year before.
Check Solution
Ans: A
The phrase “more so” is correct in this context when making a comparison.
Q.25 The company’s strong financial performance is a direct result of its …… leadership.
Check Solution
Ans: C
Effective
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