# Aptitude [TCS Placement]: Sample Questions 117 - 119 of 174

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## Question 117

Aptitude

### Question

MCQ▾

100 students appeared for two examinations. 60 passed the first, 50 passed the second and 30 passed both. Find the probability that a student selected at random has failed in both the examinations?

Choice (4)

a.

b.

c.

d.

c.

### Explanation

• We know that,
• Let A be number of students who passed in first exam.
• Let B be number of students who passed in second exam.
• We are asked to find the probability of student who failed in both the examinations.
• So 80 passed in at least one of the exams.
• So, 100 - 80 = 20 students are there who failed in both exams.
• Probability of student who failed in both the exams

## Question 118

Aptitude
Edit

### Write in Short

A is 20 percent more efficient than B. If two persons can complete a piece of work in 60 days then in how many days A working alone can complete the work?

### Explanation

A is 20 % more efficient than B.

Ratio of time taken by A and B is .

If B can do work in 6x days then A can do the same amount of work in 5x days.

So,

A can complete the work in 5x days, i.e.. days.

## Question 119

Aptitude

### Question

MCQ▾

Four people each roll a fair dice once. Find the probability that at least two people will roll the same number?

### Choices

Choice (4)

a.

b.

c.

d.

Question does not provide sufficient data or is vague

c.

### Explanation

• First time probability of getting the same number will be .
• Second time when the die is thrown probability of getting the same number will be
• Third time when the die is thrown probability of getting the same number will be .
• Fourth time when the die is thrown probability of getting the same number will be
• We are asked to find the probability when at least two people will roll the same number.
• The probability of at least two persons will roll the same number = 1 - None of them rolls the same number

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