All questions of Amazon for Interview Preparation Exam

Solution:

We are given two equations:

9x - 3y = 12 ...(1)
3x - 5y = 7 ...(2)

We need to find the value of 6x - 2y, which can be obtained by manipulating the given equations.

Method 1: Elimination method

Multiplying equation (2) by 3 and equation (1) by -1, we get:

-9x + 15y = -21 ...(3)
-9x + 3y = -12 ...(4)

Adding equations (3) and (4), we get:

12y = -33

y = -33/12

Substituting this value of y in equation (1), we get:

9x - 3(-33/12) = 12

9x + 11/4 = 12

9x = 41/4

x = 41/36

Therefore, 6x - 2y = 6(41/36) - 2(-33/12) = 41/6 + 11/2 = 83/6 = 13.83

Therefore, the correct option is not given in the choices.

Method 2: Substitution method

Solving equation (2) for x, we get:

x = (7 + 5y)/3

Substituting this value of x in equation (1), we get:

9(7 + 5y/3) - 3y = 12

21 + 15y - 9y = 36

6y = 15

y = 2.5

Substituting this value of y in equation (2), we get:

x = (7 + 5(2.5))/3 = 4

Therefore, 6x - 2y = 6(4) - 2(2.5) = 24 - 5 = 19

Therefore, the correct option is not given in the choices.

Hence, we can conclude that none of the given options is the correct answer.

It's a two pattern series.
1) bc, de, fg
2) cde, efg,?
so, in (2) following the pattern we get "ghi"

Solution:

Given:
- 9 men working 6 hours a day can complete a work in 88 days.

To find:
- How many days will it take for 6 men working 8 hours a day to complete the same work?

Assumptions:
- The amount of work is the same in both cases.
- The efficiency of each man remains the same.

Let's solve this step by step:

Step 1: Calculate the total work
- In the given scenario, 9 men working 6 hours a day complete the work in 88 days.
- So, the total work done by these 9 men is given by the formula:
Total work = Number of men * Hours per day * Number of days
Total work = 9 * 6 * 88 = 4752 units

Step 2: Calculate the work done by 6 men working 8 hours a day
- We need to find the number of days it will take for 6 men working 8 hours a day to complete the same work.
- Using the formula for total work, we can calculate the time required:
Time required = Total work / (Number of men * Hours per day)
Time required = 4752 / (6 * 8) = 99 days

Therefore, 6 men working 8 hours a day can complete the work in 99 days.

Hence, the correct answer is option 'B' (99).

Understanding the Sequence
The sequence provided is: 21, 9, 21, 11, 21, 13, 21, ...
Identifying the Pattern
- The first and every alternate number in the sequence is 21.
- The numbers in between follow a separate pattern: 9, 11, 13...
Analyzing the Middle Numbers
- The sequence of the middle numbers starts at 9 and increases by 2 each time:
- 9 (first middle number)
- 11 (second middle number, 9 + 2)
- 13 (third middle number, 11 + 2)
Predicting the Next Middle Number
- Continuing this pattern, the next middle number after 13 would be:
- 13 + 2 = 15
Final Sequence Construction
- Based on the established pattern:
- The next number in the sequence after 21 and 13 will be 21 (first number).
- The next middle number will be 15.
Therefore, the complete sequence would continue as 21, 9, 21, 11, 21, 13, 21, 15, ...
Conclusion
Thus, the correct answer is option B: 15. This is derived from the clear pattern observed in the sequence of middle numbers.

Given information:
The total of the ages of Amar, Akbar, and Anthony is 80 years.

Let's assume:
Let's assume the ages of Amar, Akbar, and Anthony are A, B, and C respectively.

Formulating the equation:
According to the given information, we can write the equation as:
A + B + C = 80

Three years ago:
Three years ago, the ages of Amar, Akbar, and Anthony would have been A-3, B-3, and C-3 respectively.

Calculating the total of their ages three years ago:
The total of their ages three years ago can be calculated by adding their individual ages three years ago:
(A-3) + (B-3) + (C-3) = A + B + C - 9

Simplifying the equation:
We know that A + B + C = 80, so we can substitute this value in the equation:
(A-3) + (B-3) + (C-3) = 80 - 9
A + B + C - 9 = 71

Conclusion:
Therefore, the total of their ages three years ago was 71 years, which is option (a).

To find the greatest number of four digits which is divisible by 15, 25, 40, and 75, we need to find the least common multiple (LCM) of these numbers.

1. Finding the LCM of 15 and 25:
To find the LCM of 15 and 25, we need to find the prime factors of both numbers.

Prime factors of 15: 3, 5
Prime factors of 25: 5, 5

The LCM is the product of the highest powers of all the prime factors involved. Therefore, the LCM of 15 and 25 is 3 * 5 * 5 = 75.

2. Finding the LCM of 75 and 40:
To find the LCM of 75 and 40, we need to find the prime factors of both numbers.

Prime factors of 75: 3, 5, 5
Prime factors of 40: 2, 2, 2, 5

The LCM is the product of the highest powers of all the prime factors involved. Therefore, the LCM of 75 and 40 is 2 * 2 * 2 * 3 * 5 * 5 = 600.

3. Finding the LCM of 600 and 1000:
To find the LCM of 600 and 1000, we need to find the prime factors of both numbers.

Prime factors of 600: 2, 2, 2, 3, 5, 5
Prime factors of 1000: 2, 2, 2, 5, 5, 5

The LCM is the product of the highest powers of all the prime factors involved. Therefore, the LCM of 600 and 1000 is 2 * 2 * 2 * 3 * 5 * 5 * 5 = 6000.

Since we are looking for the greatest number of four digits, we need to find the highest multiple of 6000 that is less than 10000.

The greatest multiple of 6000 less than 10000 is 9600. Therefore, the correct option is c) 9600.

Understanding Medians in Right-Angled Triangle
In triangle ABC, where angle A is a right angle, we have two medians: BL and CM. The lengths of these medians are crucial for solving the problem.
Given Information
- Length of side BC = 5 cm
- Length of median BL = 3 - 5/2 cm = 3 - 2.5 cm = 0.5 cm
Finding Length of CM
1. Medians in Right-Angled Triangle:
- In any triangle, the median from a vertex to the midpoint of the opposite side can be calculated using the formula, but in a right triangle, it's simpler due to the properties of right angles.
2. Using the Formula:
- The median length from vertex A (right angle) to the hypotenuse BC can be calculated as:
Length of median = 1/2 * sqrt(2AB^2 + 2AC^2 - BC^2)
3. Finding Lengths AB and AC:
- Since we are working with a right angle at A and BC as the hypotenuse, we assume:
- AB = x cm
- AC = y cm
- Using Pythagoras theorem:
x^2 + y^2 = 5^2 = 25
4. Calculating CM:
- The length of CM can also be derived through its relation to the sides.
- For a right triangle, the median to the hypotenuse (CM) is equal to half the length of the hypotenuse:
CM = 1/2 * BC = 1/2 * 5 = 2.5 cm
Final Answer
Thus, the length of median CM = 2.5 cm, which corresponds to option 'A' as 2 5.

To solve this problem, let's assume the number of sums the student got right is x. According to the given information, the student got twice as many sums wrong as he got right. Therefore, the number of sums the student got wrong is 2x.

We are also given that the student attempted 48 sums in total. This means the number of sums the student got right plus the number of sums the student got wrong should be equal to 48.

So, we can write the equation as:

x + 2x = 48

Simplifying the equation, we get:

3x = 48

Dividing both sides of the equation by 3, we find:

x = 16

Therefore, the student solved 16 sums correctly.

Answer: Option B) 16

Definition of Encode:
Encode means to convert information into a particular form for storage, transmission, or processing. It involves transforming data into a code or format that can be understood by a computer or other device.

Synonym for Encode:
- Code
- Cipher
- Encipher

Explanation:
The term "encode" is often used interchangeably with "code" or "cipher" when referring to the process of converting information into a specific format or representation. In this context, all of the above options can be considered synonyms for the word "encode" as they all involve the transformation of data into a coded form.

In summary, when looking for a synonym for "encode," options such as "code," "cipher," and "encipher" can be used to convey the same meaning of converting information into a particular format or code.

Monday   1        2         3          4        5         6       7 sun     mon     tue      wed     thu      fri   sat today is Friday = 6 By question day after tomorrow is sunday day before sunday is saturday now 2 days after saturday is monday. hence answer is monday. [Don't confuse it with Tuesday.the correct answer is Monday]

3. There is no error in the sentence.