TCS 安置文件 |多选题 1

这是一份用于能力准备的 TCS 模型安置论文。这份安置文件将涵盖 TCS 招聘活动中提出的能力问题，并严格遵循 TCS 面试中提出的问题模式。建议解决以下每个问题，以增加通过 TCS 面试的机会。

进行了考试并分析了以下内容。 4 名男子在 8 天内定期检查一些试卷，工作 5 小时。 2 个人在 20 天内检查双倍试卷的总时间是多少？
```
Answer: 8 hours
```
解决方案：

Assuming that 1 unit of work is done in 1 hour
Let’s calculate the total number of working hours:
=> 4 * 8 * 5 = 160 units
Now the work is doubled:
=> 160 * 2 = 320 units
Let ‘x’ be the number of hours taken by 2 men to complete the work in 20 days.
Therefore,
=> 2 * 20 * x = 320
=> x = 8 hours (Answer).

编程需要懂一点英语
从 101 到 150 的数字写作，101102103104105…146147148149150。这个总数除以 3 的余数是多少？
```
Answer: 2
```
解决方案：

The divisibility rule for 3 is that the sum of all digits of a number should be divisible by 3. Let’s calculate the sum of the digits:
There are 50 1’s (unit place) = 50
There are 10 1’s (tens place) = 10
There are 10 2’s (tens place) = 20
There are 10 3’s (tens place) = 30
There are 10 4’s (tens place) = 40
There is one 5 (tens place) = 5
For each number 1 to 9, there are 5 sets of sum 45(1+2+…+9) = 225
=> So sum of all digits = 380
=> 380 / 3 = 2 (Answer)

编程需要懂一点英语
如果字母按 a, bb, ccc, dddd, eeeee, ffffff, … 的顺序书写。第 120 个字母是什么？
```
Answer: O
```
解决方案：

It can be seen that the letter are in AP sequence, So applying the formula we get,

We find that n = 15 fits the equation
The 15th letter in the English alphabet = O
So 15th term contains O.

编程需要懂一点英语
有一个油箱，其 1/7 的部分装满了燃料。如果将 22 升燃油倒入油箱，指示器将上升到油箱的 1/5 标记处。那么油箱的总容量是多少？
```
Answer: 385
```
解决方案：

Let the total capacity of the tank be ‘x’ liters.
According to the question,
=> x/7 + 22 = x/5
=> x/5 – x/7 = 22
=> x = 385 litres(Answer)

编程需要懂一点英语
有多少个质数介于 3 到 100 之间（不包括值）满足条件：
- 4x + 1
- 5 年 – 1
```
Answer: 2
```
解决方案：

There are 23 prime numbers between 3 and 100 (excluding the values) of which all are odd.
For 5y – 1 to be odd, 5y must be even
For 5y to be even y should be even.
Taking y as 2 we get 5y – 1 as 9.
Now looking at all those prime numbers ending at 9 = 9, 19, 29, 39, 59, 79, 89
Out of these, the numbers satisfying both the equations(integer is assumed) are 9, 29 and 89.
We cannot consider 9 as it violates the constraint of number should be greater than 3.
Therefore answer is 2 (29 and 89)

编程需要懂一点英语
在给定的图中，求正方形的面积与三角形的面积之比：

a) 3:2
b) 2:3
c) 2:1
d) 1:2
```
Answer: c) 2:1
```
解决方案：

Let the side of the square be ‘2’ units
Area of the square = (side)^2 = = 4 unit
Side of triangle, using Pythagoras Theorem = $\sqrt{5}$ unit
Height of triangle = side of square (Using Pythgorean theorem)
Area of triangle = 1/2 * base * height
here, base = height = side
Area of triangle = 1/2 * (side)^2
=> 1/2 *2 * 2
=> 2 units
Therefore the ratio = 4:2
=> 2:1 (Answer)

编程需要懂一点英语
有一个仙岛，里面住着骑士、盗贼和间谍。你去那里遇到三个人，假设 A、B 和 C，其中一个是骑士，一个是流氓，一个是间谍。众所周知，骑士总是说真话，流氓总是说谎，间谍要么说谎，要么说实话。
- A 说：“C 是个无赖。”
- B 说：“A 是骑士。”
- C说：“我是间谍。”
那么谁是骑士，谁是流氓，谁是间谍？
```
Answer: A = Knight, B = Spy, C = Knave
```
解决方案：

Let us say A is the Knight, then he speaks the truth and C is Knave who lied and finally B is Knave, who speaks the truth regarding A. So this condition holds.
Let us say B is the knight. then it contradicts the answer since a knight always speaks the truth and there cannot be two knights.
Same goes with C.

编程需要懂一点英语
求给定序列 2013, 2020, 2027, ……………., 2300 中的完美平方数？（提示 44^2=1936）
a2
b) 1
c) 3
d) 以上都不是
```
Answer: b) 1
```
解决方案：

We can see that the series is in the form of AP with common difference of 7.
So the series is in the form of 2013 + 7d
The hint is actually a shortcut:
44^2 = 1936
45^2 = 2025
46^2 = 2116
47^2 = 2209
48^2 = 2304
Therefore among these numbers, we need to find which of them are in the form of 2013 + 7d
Only one number 2209 can be written in the form 2013 + 7*28.
Therefore the answer is 1.

编程需要懂一点英语
7^1+7^2+7^3+7^4…….+7^204+7^205数列中，单位位为3的数有多少个？
```
Answer: 51
```
Solution: According to the cyclicity of 7, the unit digit follows the pattern of 7, 9, 3, 1 and this repeats. So in every 4 numbers, we get one 3 in the unit place. Dividing 205 by 4 we get 51 which is the answer to the following question.

编程需要懂一点英语
找出 1728 的除数（包括 1 和数字本身）。
```
Answer: 28
```
解决方案：

There is a direct formula for this:
Number =
where p, q and r are prime numbers. Simply we need to prime factorize the Number.
Then, (a+1).(b+1).(c+1) is the number of divisors.
For 1728 =
Therfore, (6+1).(3+1) = 28

编程需要懂一点英语