1.
X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days, Y joined him till the completion of the work. How long did the work last?
Correct Answer
B. 10 days
Explanation
X can do 1/20th of the work in one day, and Y can do 1/12th of the work in one day. After 4 days, X has completed 4/20th or 1/5th of the work. So, the remaining work is 4/5th. When X and Y work together, their combined rate is 1/20 + 1/12 = 8/60 = 2/15th of the work per day. To complete the remaining 4/5th of the work, it will take 4/5 ÷ (2/15) = 6 days. Therefore, the total duration of work is 4 days + 6 days = 10 days.
2.
In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?
Correct Answer
C. 120960
Explanation
The word 'MATHEMATICS' has 11 letters, including 4 vowels (A, E, A, I). To arrange the letters such that the vowels always come together, we can consider the group of vowels (AEA) as a single entity. This reduces the problem to arranging the 7 entities (M, T, H, M, T, C, S) and the group of vowels (AEA). The number of ways to arrange these entities is 8!, but we need to account for the repeated letters (M and T), so we divide by 2!. The number of ways to arrange the vowels within the group is 4!, but we need to account for the repeated vowels (A), so we divide by 2!. Therefore, the total number of arrangements is (8!/2!) * (4!/2!) = 120960.
3.
Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After a further 8 years, how many times would he be of Ronit's age?
Correct Answer
A. 2 times
Explanation
Let's assume Ronit's current age is x. According to the given information, the father's current age is 3x. After 8 years, Ronit's age would be x+8 and the father's age would be 3x+8. It is given that after 8 years, the father would be two and a half times Ronit's age, so we can write the equation 3x+8 = 2.5(x+8). Solving this equation, we get x = 8. Therefore, Ronit's current age is 8 and the father's current age is 24. After a further 8 years, Ronit's age would be 16 and the father's age would be 32, which is exactly 2 times Ronit's age.
4.
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
Correct Answer
C. 9/20
Explanation
The probability that the ticket drawn has a number which is a multiple of 3 or 5 can be calculated by finding the total number of tickets that are multiples of 3 or 5 and dividing it by the total number of tickets. Out of the numbers 1 to 20, there are 6 multiples of 3 (3, 6, 9, 12, 15, 18) and 4 multiples of 5 (5, 10, 15, 20). However, the number 15 is counted twice as it is a multiple of both 3 and 5. Therefore, there are 9 tickets that are multiples of 3 or 5. The total number of tickets is 20. So, the probability is 9/20.
5.
Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number.
Correct Answer
A. 3
Explanation
The correct answer is 3. To find the number, let's assume it as x. According to the given information, when the number is increased by 17, it becomes equal to 60 times the reciprocal of the number. Mathematically, this can be represented as x + 17 = 60 * (1/x). Simplifying this equation, we get x^2 + 17x - 60 = 0. Factoring this quadratic equation, we get (x + 20)(x - 3) = 0. Therefore, the possible values for x are -20 and 3. Since we are looking for a positive number, the correct answer is 3.
6.
Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:
Correct Answer
B. 273m
Explanation
The angle of elevation from each ship to the top of the lighthouse allows us to form two right-angled triangles. The height of the lighthouse is the opposite side of both triangles. By using trigonometry, we can determine that the adjacent side of the 30° triangle is (100/tan(30°)) and the adjacent side of the 45° triangle is (100/tan(45°)). The distance between the two ships is the sum of these adjacent sides, which simplifies to 100(√3 + 1). Evaluating this expression gives us 273m.
7.
When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?
Correct Answer
D. Rs. 25,300
Explanation
If the owner loses 15% when selling the plot for Rs. 18,700, it means that the selling price is only 85% of the original price. To calculate the original price, we can divide Rs. 18,700 by 0.85. This gives us approximately Rs. 22,000.
To gain 15% on this original price, we need to add 15% of Rs. 22,000 to the original price. 15% of Rs. 22,000 is Rs. 3,300. Adding this to Rs. 22,000 gives us Rs. 25,300. Therefore, the plot must be sold for Rs. 25,300 in order to gain 15%.
8.
Which of the following has the most number of divisors?
Correct Answer
C. 176
Explanation
The number with the most divisors will be the one with the highest prime factorization. Among the given options, 176 has the highest prime factorization of 2^4 * 11. This means that 176 can be divided evenly by 2, 4, 8, 11, 22, 44, 88, and 176 itself, resulting in a total of 8 divisors. Therefore, 176 has the most number of divisors among the given options.
9.
Look at this series: 544, 509, 474, 439, ... What number should come next?
Correct Answer
A. 404
Explanation
The series is decreasing by 35 each time. Starting with 544, subtracting 35 gives 509, subtracting 35 again gives 474, and so on. Therefore, the next number in the series should be 439 - 35 = 404.
10.
Which of the following is not a leap year?
Correct Answer
A. 700
Explanation
A leap year is a year that is evenly divisible by 4, except for years that are divisible by 100 but not divisible by 400. In this case, 700 is not a leap year because it is divisible by 100 but not divisible by 400.
11.
10, 25, 45, 54, 60, 75, 80
Correct Answer
C. 54
Explanation
The given sequence appears to be a list of numbers that are increasing, but with some numbers missing. The missing numbers are 25, 60, and 80. However, the number 54 does not fit the pattern as it is not missing and does not follow the increasing trend. Therefore, the correct answer is 54.
12.
A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?
Correct Answer
C. 30
Explanation
By walking diagonally across the square lot, the man took the shortest distance possible from one corner to the opposite corner. If he had walked along the edges of the square, he would have had to cover a longer distance. The percent saved can be calculated by finding the difference between the diagonal distance and the edge distance, dividing it by the edge distance, and then multiplying by 100. In this case, the percent saved is approximately 30%.
13.
At what time between 5.30 and 6 will the hands of a clock be at right angles?
Correct Answer
C. 40 min past 5
14.
One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:
Correct Answer
C. 144 min.
Explanation
The faster pipe fills the tank three times faster than the slower pipe. So, if the slower pipe takes x minutes to fill the tank, the faster pipe will take x/3 minutes. Together, they can fill the tank in 36 minutes. Therefore, the equation becomes x + x/3 = 36. Solving this equation, we find that x = 27. Hence, the slower pipe alone will be able to fill the tank in 27 minutes, which is equal to 144 minutes.
15.
ZA_{5}, Y_{4}B, XC_{6}, W_{3}D, _____
Correct Answer
C. VE7
Explanation
The pattern in the given sequence involves alternating between a letter, a number, and another letter. Following this pattern, the next item in the sequence should be a letter, followed by a number, and then another letter.
Given this pattern, the correct option is: VE7