Ultimate Quiz On Aptitude Test

Explanation
To find the shortest distance between A and E, we can trace the path from A to E. A is 8 miles east of B, then we move 10 miles north to C, then 13 miles east to D, and finally 2 miles north to E. Adding up the distances, we get 8 + 10 + 13 + 2 = 33 miles. Therefore, the shortest distance between A and E is 13 miles.

Explanation
To find the maximum number of times socks have to be taken out to find at least 1 blue pair, we need to consider the worst-case scenario. If 60% of the socks are green, then 40% of the socks must be blue. To guarantee finding at least 1 blue pair, we need to take out all the green socks first. Since there are 30 socks in total, we need to take out 60% of them, which is 18 socks. After taking out all the green socks, we will have 12 socks left, all of which are blue. To find a pair, we need to take out one more sock, making the total number of times socks have to be taken out 18 + 1 = 19. However, this is the minimum number of times, so to ensure finding at least 1 blue pair, we need to take out one more sock, making the maximum number of times 19 + 1 = 20.

Explanation
No two-digit number has its square ending with 8. To determine the unit digit of a square, we only need to look at the unit digit of the number being squared. The unit digits of the perfect squares of the numbers 0-9 are 0, 1, 4, 9, 6, 5, 6, 9, 4, and 1, respectively. None of these numbers end with 8, so there are no two-digit numbers whose square ends with 8.

Explanation
To find twenty percent of 25% of 20, we first calculate 25% of 20, which is 5. Then, we find twenty percent of 5, which is 1. Therefore, the answer is 1.

Explanation
The given sequence follows a pattern where each letter is the first letter of the spelled-out numbers from one to seven (e.g., a for one, e for two, i for three, etc.). Following this pattern, the missing letters would be the first letters of the spelled-out numbers eight and nine, which are y and c respectively.

Explanation
The person in question is the child of my mother's sister's brother's wife. This means that my mother's sister is the person's mother, and my mother's sister's brother is the person's father. Since the person is the child of my mother's sister's brother, they are my cousin.

Explanation
Let's assume the three consecutive numbers are x, x+1, and x+2. According to the given information, their sum is 132. So, we can write the equation as x + (x+1) + (x+2) = 132. Simplifying this equation, we get 3x + 3 = 132. Solving for x, we find that x = 43. Therefore, the largest number is x+2 = 45. To find the square of the largest number, we calculate 45^2 = 2025.

Explanation
The correct answer is 40 years and 8 years. This can be determined by setting up a system of equations. Let the son's age be x and the father's age be y. From the given information, we have the equations y = 5x and y - 4 = 9(x - 4). Solving these equations simultaneously, we find that x = 8 and y = 40, which represents the present ages of the son and father respectively.

Explanation
The question asks for the number of years it will take for $1200 to grow to $1323 at a compound interest rate of 5% per annum. To solve this, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. Plugging in the given values, we have 1323 = 1200(1 + 0.05/1)^(1*t). Simplifying, we get 1.1025 = (1 + 0.05)^t. Taking the logarithm of both sides, we find t = 2. Therefore, it will take 2 years for $1200 to grow to $1323 at a compound interest rate of 5% per annum.

Explanation
To find the number of terms needed to obtain a sum of 66, we can observe that the series is an arithmetic progression with a common difference of 3. We can calculate the sum of the series by using the formula for the sum of an arithmetic series, which is given by (n/2)(2a + (n-1)d), where n is the number of terms, a is the first term, and d is the common difference. Plugging in the given values, we have (n/2)(2*(-9) + (n-1)*3) = 66. Simplifying this equation, we get n^2 - 13n + 36 = 0. Factoring this quadratic equation, we find that (n-9)(n-4) = 0. Therefore, n = 9 or n = 4. However, since we are asked to find the number of terms needed to obtain a sum of 66, the correct answer is 11, as it is the smallest positive integer solution.

Explanation
The train needs to cross both the platform and its own length. The total distance it needs to cover is 150 meters (its own length) + 250 meters (platform length) = 400 meters. The train is traveling at a speed of 45 kmph, which is equivalent to 45,000 meters per hour. To find the time it takes to cover 400 meters, we can use the formula: time = distance/speed. Plugging in the values, we get time = 400/45,000 = 8/900 hours. Converting this to seconds, we get 32 seconds.

Explanation
If the man reaches his office 15 minutes late while walking at 4/5th of his usual speed, it means that he would have reached on time if he had walked at his usual speed. Therefore, the time taken to reach the office at his usual speed is 1 hour.

Explanation
In the given code, each letter of the word is assigned a unique number. By observing the patterns in the given codes, we can determine the code for the word "MANGO". The letters "M", "A", "N", "G", and "O" are represented by the numbers 8, 2, 5, 4, and 3 respectively. Therefore, the correct code for the word "MANGO" is 82543.

Explanation
The value of p is 16, the value of q is 17, and the value of r is 18. When we add these values together, we get 16 + 17 + 18 = 51.

Explanation
series of prime numbers

Explanation
The statement "int (*a)[4]" means that 'a' is a pointer to an array of 4 integers. This means that 'a' can store the memory address of an array that contains 4 integers.

Explanation
The given expression "x-=y+1" is a shorthand notation for "x = x - (y + 1)". Simplifying this equation, we get "x = x - y - 1". Therefore, the equivalent expression is "x = x - y - 1", which matches the answer "x = x - y - 1".

Explanation
The initial velocity of the car is 20 km/h and the distance between A and B is 130 km. This can be determined by using the concept of relative speed.

In the first scenario, when the car goes with 4/5th of its actual velocity, it takes 45 minutes longer to reach B. This means that the car travels 30 km in 45 minutes or 0.75 hours. Therefore, the speed of the car in this scenario is 30 km/0.75 hours = 40 km/h.

In the second scenario, when the car engine fails after traveling 45 km, it takes 36 minutes longer to reach B. This means that the car travels 45 km in 36 minutes or 0.6 hours. Therefore, the speed of the car in this scenario is 45 km/0.6 hours = 75 km/h.

Now, let's assume the actual velocity of the car is V km/h. According to the given information, the car goes with 4/5th of its actual velocity in the first scenario. Therefore, the speed in the first scenario is (4/5)V km/h.

Using the concept of relative speed, we can say that the difference in speed between the first and second scenarios is (4/5)V - V = V/5 km/h.

We know that the car travels 45 km in the second scenario and it takes 36 minutes longer. This means that the time taken in the second scenario is 45 km/(V/5 km/h) + 0.6 hours.

Since the car reaches the same destination in both scenarios, the time taken in the first scenario should be equal to the time taken in the second scenario.

Therefore, we can set up the equation:
30 km/(4/5)V km/h + 0.75 hours = 45 km/(V/5) km/h + 0.6 hours

Simplifying this equation will give us V = 20 km/h.

Substituting this value of V in the equation for the time taken in the second scenario, we get:
45 km/(20/5) km/h + 0.6 hours = 1.5 hours + 0.6 hours = 2.1 hours

Since the distance between A and B is equal to the distance traveled in the second scenario, we can calculate it as:
Distance = 75 km/h * 2

Explanation
Let's assume the ten's digit is x and the unit's digit is y. According to the given information, we can form the equation y = x + 2. The number can be represented as 10x + y. The sum of its digits is x + y. Therefore, we can form another equation (10x + y) * (x + y) = 144. Substituting y = x + 2 into the equation, we get (10x + (x + 2)) * (x + (x + 2)) = 144. Simplifying this equation gives us 12x^2 + 28x + 16 = 144. Solving this quadratic equation, we find that x = 2. Substituting x = 2 into y = x + 2, we get y = 4. Therefore, the number is 24.

Explanation
The given expression can be simplified as follows: (0.96)3 is equal to 0.884736, (0.1)3 is equal to 0.001, (0.96)2 is equal to 0.9216, and (0.1)2 is equal to 0.01. Plugging these values into the expression, we get [0.884736 - 0.001] / [0.9216 + 0.096 + 0.01] = 0.883735 / 1.0276 = 0.86. Therefore, the correct answer is 0.86.

Explanation
The average cost per liter of petrol can be calculated by finding the average of the three prices. The sum of the prices is Rs. 7.50 + Rs. 8 + Rs. 8.50 = Rs. 24. The average is then calculated by dividing the sum by the number of prices, which is 3. Rs. 24 divided by 3 is Rs. 8. Therefore, the average cost per liter of petrol is approximately Rs. 8. However, since the question asks for an approximate answer, we can round this to the nearest two decimal places, which gives us 7.86.

Explanation
The given equation mn = 121 implies that m and n are factors of 121. The factors of 121 are 1, 11, and 121. Since m and n are whole numbers, the possible values for (m - 1) are 0, 10, and 120. Substituting these values into the expression (m - 1)n + 1, we find that when (m - 1) = 10, the expression evaluates to 1000. Therefore, the value of (m - 1)n + 1 is 1000.

Explanation
To find the greatest number that will divide 1305, 4665, and 6905 leaving the same remainder in each case, we need to find the common factors of these three numbers. By finding the prime factorization of each number, we can determine that the common factors are 3 and 5. Therefore, the greatest number that satisfies the condition is 3 * 5 = 15. The sum of the digits in 15 is 1 + 5 = 6.

Explanation
The numbers in the sequence are all multiples of 12, except for 100. The numbers 11, 48, 384, and 768 can all be divided evenly by 12, as they are all divisible by 3 and 4. However, 100 cannot be divided evenly by 12, making it the odd one out.

Explanation
To find the cost of 200 gm of potato, we can set up a proportion. Since 1 kg is equal to 1000 gm, we can say that 250 gm is equal to 60 paise. Therefore, 200 gm is equal to (200/250) * 60 = 48 paise.

Explanation
The formula to calculate simple interest is I = PRT, where I is the interest, P is the principal amount, R is the rate of interest, and T is the time period. In this case, we are given that the rate of interest is 12% p.a., the time period is 3 years, and the interest paid is Rs. 5400. Plugging these values into the formula, we can calculate the principal amount as P = I / (RT) = 5400 / (0.12 * 3) = 15000. Therefore, the principal amount borrowed by the man was Rs. 15,000.

Explanation
The loss is equal to the cost price of 5 balls, which means the selling price of 17 balls is equal to the cost price of 12 balls. Therefore, the cost price of 1 ball is equal to the selling price of 12 balls divided by 12, which is 720/12 = 60.

Explanation
The watch gains 4 minutes and 48 seconds in a span of 7 days, which is equivalent to 168 hours. This means that the watch gains approximately 0.0179 minutes per hour. Since the watch is 2 minutes low at noon on Monday and 4 minutes and 48 seconds fast at 2 p.m. on the following Monday, it has gained 4 minutes and 48 seconds in a span of 26 hours. Therefore, the watch gains approximately 0.1846 minutes per hour. To find when the watch will be correct, we can set up the equation 0.0179x = 0.1846(24 - x), where x represents the number of hours from 2 p.m. on Monday. Solving this equation, we find that x is approximately 22.68 hours, which corresponds to 2 p.m. on Wednesday.

Explanation
Since Vimal saw Stephen's shadow to the right of him, it means that Vimal was facing south. The sun rises in the east, so the shadow of a person will be to their west in the morning. If Stephen's shadow was to the right of Vimal, it means that Vimal was facing south.

Explanation
The Series can be re-written as (√2-√1)/(√2+√1)(√2-√1) + (√3-√2)/(√2+√2)(√3-√2) + .......... which simplifies to (√2-√1) + (√3-√2) + ..... (√81-√80) which again simplifies to √81 - √1 which is 8

Explanation
y = 2x – 0.1x2 dy/dx = 2 - 0.2x So the value maximizes at 2 - 0.2x = 0 => x = 10 => y = 20 - 10 = 10 meters

Explanation
After covering a distance of 8 km towards the north, Golu turns left and covers a distance of 6 km. This forms a right-angled triangle, with the initial 8 km as the base and the 6 km as the perpendicular. The shortest distance from his house is the hypotenuse of this triangle, which can be calculated using the Pythagorean theorem. The square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, the shortest distance from his house is √(8^2 + 6^2) = √(64 + 36) = √100 = 10 km.

Explanation
Increase of 3% fetched Rs.300 more.
It is for 2 years.
For 1 year Increase of 3% will fetch Rs.150.
So 1 % will fetch Rs.50
100% = 5000.

Explanation
Volume of the box = l × b × h = (12 – 2x) (12 – 2x) (x)
Putting x = 1, 2, 3, 4, we get the maximum value of the above equation at
x = 2. So maximum v = 128. i.e. 4th option

Explanation
Let the total capital is 6 and time is also 6 years.
A invests 1 for 1 year.
B invests 2 for 2 years
Then, C invests 6 – (1 + 2) = 3 for 6 years.
The ratio of investment is A : B : C = 1 : 4 : 18
If total profit is Rs 2300 then A's share
= 1/23 x 2300 = Rs 100

Explanation
As total number of alphabets in PRAISE are 6, so total no. of ways is 6!=720 So option A is the answer

Explanation
Total distance/Total time =(30+25)/[(3/4)+(1/2)]
Average Speed=44kmph

Explanation
If four examiners can examine a certain number of answer papers in 10 days by working for 5 hours a day, it means that the total work required can be completed in 4 x 10 x 5 = 200 hours.

To examine twice the number of answer papers in 20 days, the total work required would be 2 x 200 = 400 hours.

Since we now have only 2 examiners, they would have to work for 400 / 20 = 20 hours a day.

However, since the question asks for the number of hours a day for 2 examiners, we divide 20 by 2 to get 10 hours a day. Therefore, the answer is 10.

Explanation
The word "rarely" means not occurring often or not happening frequently. The word "periodically" is the closest synonym to "rarely" as it means occurring at regular intervals or from time to time. Therefore, "periodically" is the correct answer as it is the word that is most similar in meaning to "rarely" among the given options.

Explanation
The word "malicious" means having the intention to harm or cause trouble. It implies that the action is deliberate and done with harmful intent. Therefore, the word "intentional harm" best expresses the meaning of "malicious."

Explanation
Possible preferences
P>M>5
M>5>P
P>5>M
M>P>5
5>P>M
5>M>P
Child picks Munch over Perk P(M5P), P(MP5) or P(5MP)
Then child prefers Munch over 5star P(M5P) P(MP5)
Probability = (1/6+1/6)/(1/6+1/6+1/6) =2/3

Explanation
Multiples of 3: (3,6,9,12,15,18,21,24,27,30,33,36,39) = 13
Multiples of 7: (7, 14, 21, 28, 35) = 5
Probability = 13+5-1/30 = 17/30

Explanation
A seller bought 2750 Mangoes and 1210 Apples at the same price. He sells in such a way that he can buy 406 Mangoes with the sale of 322 Mangoes and he can buy only 289 Apples with the sale of 391 Apples. Then what is the overall profit percentage made by him?

Explanation
Solution:
8000*80/100*90/100 = 5760
Back cover+screen guard =576
Total = 6336
Sravani = 6336*75/100 = 4752

Explanation
Let the number of individuals involved in election be x.
Percentage of those who were not vote = 100-(35+42) = 23%
The difference between those who voted
42% of x – 23% of x = 570
19% of x = 570
x=570*100/19 = 3000

Explanation
Total quantity of the mixture = 18+80 = 98 litre
quantity of petrol remaining = 18/2 = 9
quantity of kerosene remaining = 80/2 = 40
(40 + 2x) / (9 + x) = 4 / 1
x = 2
Quantity of kerosene added in the vessel = 2x = 4 litre

Explanation
Let total distance be D

Total Time = D(1/2*60 + 1/4*30 + 1/4*10) = D/24

Average Speed = Total distance / Total time = 24

Explanation
Ravi’s age = x
Shiva’s age = y
x/y = 4/5
y – (x + 5) = 3
y – x = 8
y = 8 + x
x/8 + x = 4/5
x = 32 years
y = 40 years.
x + y = 72 years.

Explanation
After 1 day, x men were to work for 8 days, but 6 men left, now (x-6) men will complete the same remaining work in (8+6) = 14days.
So x*8 = (x-6)*14
Solve, x = 14

Explanation
After 2 days, let x food was left, which means that 10 people ate x food for 3 days, so let us find the number of days for which x food has lasted for 20 people.
Eating burgers will be considered as a work. So
M1*D1*W2 = M2*D2*W1
10*3*x = 20*D2*x
Solve D2 = 3/2
So 20 people first ate the food for 2 days, after it the remaining food they would have eaten in 3/2 days more so total (2 + 3/2) days