TCS Questions-3

TCS Questions – 3

 

1.    For climbing to the top of a hill 800 meters, Jack after climbing 16 meters in a minute takes two minutes rest, or one minute rest after climbing 20 meters in a minute. Paul takes one minute rest after climbing 10 meters in a minute and two minutes rest after climbing 16 meters in a minute. If the time allowed to reach the top of the hill is 2 hours (120 minutes) then what is the maximum number of rests that can be taken?

 

Answer : 40.

Let us take Jack first. He will take 50 minutes to climb the hill at 16 meters per minute. In the process he will take 50 times rest of 2 minutes. Thus the total time will be 50 + 100 = 150 minutes. (But the time allowed is only 120 minutes)

If he climbs at 20 meters in 2 minutes then the time to reach the top of the hill will be 80 minutes. He will 40 times rest of one minute each. The total time to reach the top will be 80 + 40 = 120 minutes. (Exactly the time allowed)

 

Now let us consider Paul. If he climbs 10 meters per minute then he will take 80 minutes to reach the top. In the process he will take rest for 80 times of one minute each. Thus the total time would be 80 + 80 = 160 minutes ( Time allowed is only 120 minutes). If he climbs at 16 meters per minute then the time take to reach the top of the hill will be 50 minutes. In the process he will take total rest time of 100 minutes. Hence the total time to reach the top will be 50 + 100 = 150 minutes ( Time allowed is only 120 minutes)

 

Thus the maximum number of rest that one of them can take is 40  

 

2.    If the 20^th term of an AP is 560 and the 30^th term of the AP is 840, then what is the sum of the 5^th term and 40^th term of the series?

 

Answer is : 1260

The 30^th term is 840 and the 20^th term is 560. Hence the 10^th term is 840 – 560 = 280.

The 5^th term is 280/2 = 140. The 40^th term is 30^th term + 10^th term ie 840 + 280 = 1120.  Hence the sum of 5^th term and 40^th term is  140 + 1120 = 1260.

 

3.    Raj tossed three dices. If the results are noted down, then what is the probability of Raj getting 10?

 

Answer is: 1/8

The possibility of Raj getting 10 is in the following manner: 136/145/154/163., 226/235/244/253/262; 316/325/334/343/352/361; 415/424/433/442/451/; 514/523/532/541/; 613/622/631/

27 possible manner as against total possibilities of 216 (6 x 6 x 6) ie 27/216 or 1/8

 

4.    The diagonal of a square is twice the side of equilateral triangle. What is the ratio of the area of the triangle to the area of the square?

 

Answer is: √3 : 8

 

                                                           

 

 

Let the sides of the equilateral triangle be ‘ a ‘  Then the area of the equilateral triangle will be √3/4 a^2.

 

The area of the square will be 2a^2/2 ie 4 a^2/2

 

Thus the ratio will be √3/4 a^2  :  2 a^2      ie √3 : 8

 

5.    Apple costs L rupees per kilogram for first 30 kg Q rupees per kg for each additional kilogram. If the price of 33 kg of apple is 11.67 and 36 kg of apple 12.48 then the cost of the first 10 kg of apples is how much?

Answer: 3.62

36 kg costs  12.48                                           Cost of 33 kg    11.67

33 kg costs  11.67    Hence,                           Cost of  3 kg      0.81

  3 kg costs    0.81                                           Cost of 30 kg    10.86           

                                                                Thus cost of   10 kg    10.86/3 = 3.62

 

6.    In the following series 1,2,2,3,3,3,4,4,4,4,1,1,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,…..

What is the number in the 2320 position of the sequence?

 

Answer is:  1

 

The first cycle in the sequence consists of 10 digits, the second 20 digits, the third 30 digits and so on.  So we have a series 10 + 20 + 30 + 40 + …………..  + x  where x is the nearer value of 2320. Thus we have 10 [ n (n+1)/2] nearer to 2320. N value 21 fill this condition and we have x = 2310. This completes the cycle and the next cycle begins with the digit 1.  Hence the answer is 1.

 

7.    How many 7’s are there between 0 and 400?

Answer: 79.   From 0 to 100 there are 19 7’s and for each 100 numbers thereafter there are 20 7’s.

 

8.    The letters in the word ABUSER are permuted in all possible ways and arranged in alphabetical order. Then what would be the word in the 49^th position of this alphabetical order?

 

Answer:  ARBESU

 

Arrange the letters of ABUSER in the dictionary order; It will be ABERSU

Now keep the first two letters AB. The remaining 4 letters can be arranged in 4! Ways. ie 24 ways. Now take the next letter after B and keep AE aside. The remaining four letters can again be arranged in 4! Ways ie 24 ways. Thus we have completed 48 ways. The next is 49^th way. Take A and R as first two letters and the remaining four follow in the dictionary order. Thus we have the 49^th word as ARBESU

 

9.    15 students join a summer course. Every day 3 students are to stay back after classes to clean the class room. After the course was over it was observed that each pair of students were on duty only for one day. How many days the course lasted?

 

Answer: 105 days.

 

 The answer to this question can be arrived at n two ways. Out of the 15 students it was observed that each pair had worked only once. Hence the course lasted for 15C2 days. ie 105 days.

 

The second way:  Three students are to stay back and clean the class rooms. If we number the students from 1 to 15 then we have the following interesting thing.

 

Student No 1 would have worked with the other students 14 days.

Student No 2 would have worked with the other students  13 days

Student No 3   …………………………………………………12 days. As you go down

…….

……..

The last Student would have worked with the other for         1 day only.

If you total the number of days you will get 105 days which is the duration of the course.

 

10.  Next number in the series:  1, 7, 8, 49, 50, 56, 57, 343, ?

 

Answer: 344

 

The series goes in the following manner:  1*7 =7    7 + 1 = 8

                                                                    7*7 = 49  + 1   = 50

                                                                    7*8 = 56  + 1   = 57

                                                                   7*49 = 343 + 1 = 344

 

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TCS-Questions-2

TCS Questions-2TCS Questions – 2

1.    If the sum of each row, each column and each diagonal are the same then, find the value of ( Y + Z ).

V	50	W
196	X	Y
269	Z	123

There are two possible way of arriving at the solution.

269 + 196 + V = V + 50 + W.  Cancelling out V on both sides we can arrive at the value of W as 415. Likewise

269 + 196 + V = 123 + X + V. Again cancelling out V on both sides we get the value of X as 342. Now we have the total of one diagonal as 269 + 342 + 415 = 1026. It is now easy to arrive at the value of the other alphabets:  V = 561, Y = 488, and Z = 634.

Hence the value of Y + Z = 488 + 634 = 1122

		Z
	V		W
Y		X		196
	269		123
		50

Re-arrange the grid in the following manner. You will be surprised to find the difference between each two digits is 73. This is one simple way of solving 3 x 3 grid Sudoku type questions.

The value of X will be 269 + 73 = 342

The value of W will be 342 + 73 = 415

The value of Y will be 415 + 73 = 488

The value of V will be 488 + 73 = 561

The value of Z will be 561 + 73 = 634

2.    Please find the value of ( Y + Z ) in the following grid.

V	-16	W
-2	X	Y
5	Z	-9

The difference between the digits is 7 and going by either of the two methods mentioned earlier the

Answer is 66

3.    Find the value of 7*A + 7*B + 6*C*D in the following simple subtraction where some digits are represented by Alphabets.

    A  7  C  2

-        4  B  6  8

 5  4   3  D

                                                                     ---------------

Proceed from the final value and move upwards. You will get the values for A-9, B-2,

C- 0 and D- 4.  Answer is 77.

4.    What is the reminder when 50! Is divided by 16^15?

The answer is 1. 16^15 can be written as (2^4)^15. Ie  2 ^ 60.  In 50! All factorials after 2! Are divisible by 2 and only 1! is not divisible by 2. Hence the answer is 1.

5.    What is the value of the 30^th term in the following series:

1, 5, 6, 25, 26, 30, 31, 125, 126, 130, 131, 150, 151, 156, ……….

Answer is 780.  If you look at the pattern of the series you will note the first term multiplied by 5 gives the second term, the second term multiplied by 5 gives the fourth term, the fourth term multiplied by 5 gives the 8^th term and so on. Hence the 30^th term is obtained by multiplying the 15^th term by 5. (156 x 5 = 780)

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TCS Questions

TCS QuestionsTCS – Latest Questions

1.    x^y + y^x  = 46. Find the values of x and y.

Ans: either 45 and 1 or 1 and 45.

2.    3 White chips, 7 Blue chips and 16 Green chips are there. If 2 chips are drawn at random in succession from the box then what is the probability that one is Blue and the other White?

Total no of chips is 26. The probability of getting a blue in the first take is 7C1/26C1 ie 7/26. After this take there will remain only 25 chips and the probability of getting a white chip is 3C1/25C1 ie 3/25. Thus the probability of picking a Blue first and White followed will be (7/26 x 3/25). The picking of the chips could be the other way also, white being first and blue being the second. In this case the probability works as (3/26 x 7/25). Hence the answer to the question is [ (7/26 x 3/25) + (3/26 x 7/25) ] ie 21/ 13 x 25

3.    A person works continuously for 8 days and gets the 9^th day as his rest day. If he starts work on a Monday, then what day it would be of his 12^th rest day.

Answer is Wednesday. Simple logic.

4.    How many liters of 90% concentrated Acid need to be mixed with 75% concentrated acid to get 30 liters of 78% concentrated acid?

Answer:  Let xlires of 90% concentrated acid be in the final mixture. Then the 75% concentrated acid will be (30-x) liters. We can now use a simple equation taking the % concentration in to account in the following manner:

90x + 75(30-x) = 30 x 78.  The value of x will be 6 liters.

5.    Three cars A, B and C are in the race. A is twice likely to win as B and B is thrice likely to win as C. What is the probability B will win the race if only one car wins the race?

Let probability of C winning be x. Then probability of B winning is 3x and probability of A winning 6x. Hence the probability of B winning the race is  3x/ 6x+3x+x

ie 3/10.

6.    A Cow and Horse were bought for Rs 2000.00. The Cow was sold for profit of 20% and Horse sold at a loss of 10%. If the overall gain in the transaction is Rs 40.00 then what is the cost price of Cow?

Answer: Let the price of Cow and Horse be C and H. Then we have C + H = 2000  (i)

Cow is sold at a profit of 20% or 1/5 C. Horse is sold at 10% loss or H/10. Thus we

have the second equation C/5 – H/10 = 40.00   (ii)

Equating (i) and (ii) you will get the value of Cow as Rs 800.00.

7.    The sum of three consecutive numbers of the four numbers A, B, C, and D are 4613, 4961, 5010 and 5099. What is the largest number among A, B, C, and D?

Solution:   Let the sum of the numbers be  A+B+C  = 4613

                                                                     B+C+D = 4961

                                                                     C+D+A = 5010

                                                                     D+A+B =  5099

Totalling all the four                             3(A+B+C+D) = 19683

                                                                 A+B+C+D  =  6561

It is now easy to find the values of A, B, C and D individually. The highest value

Is 1948.

8.    George printing press can print an edition of a newspaper in 12 hours while Paul’s printing press can print the same in 18 hours. What is the total no. of hours the press working together but independent of each other to print the same edition?

This question has two possible answers depending upon how you interpret the question.

Assuming the two press work together in producing the edition then the time taken will be 12 x 18 /12 + 18 ie 7.2 hours.

If they work independent of each other then the time taken will be 12+18 =30/2 ie 15 hours.

9.     Find the 87^th number in the series 2, 10, 26, 50, ……..

Solution:  1^st term = 1² + 1     2^nd term = 3² + 1     3^rd term = 5² + 1   4^th term = 7² + 1

On this basis the 87^th term will be 173² + 1  ==  29930.

10.  What is the next number in the series 70, 54, 45, 41, ?

Answer : 40

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Know thy meaning

Know thy meaning - 2

gross domestic product (GDP)

   Definition

The value of a country's overall output of goods and services (typically during one fiscal year) at market prices, excluding net income from abroad.

Gross Domestic Product (GDP) can be estimated in three ways which, in theory, should yield identical figures. They are (1) Expenditure basis: how much money was spent, (2) Output basis: how many goods and services were sold, and (3) Income basis: how much income (profit) was earned. These estimates, published quarterly, are constantly revised to approach greater accuracy. The most closely watched data is the period to period change in output and consumption, in real (inflation adjusted) terms. If indirect taxes are deducted from the market prices and subsidies are added, it is called GDP at factor cost or national dividend. If depreciation of the national capital stock is deducted from the GDP, it is called net domestic product. If income from abroad is added, it is called gross national product (GNP). The main criticisms of GDP as a realistic guide to a nation's well-being are that (1) it is preoccupied with indiscriminate production and consumption, and (2) it includes the cost of damage caused by pollution as a positive factor in its calculations, while excluding the lost value of depleted natural resources and unpaid costs of environmental harm.

elasticity of demand 

Definition

The degree to which demand for a good or service varies with its price. Normally, sales increase with drop in prices and decrease with rise in prices. As a general rule, appliances, cars, confectionary and other non-essentials show elasticity of demand whereas most necessities (food, medicine, basic clothing) show inelasticity of demand (do not sell significantly more or less with changes in price). Also called price demand elasticity. See also cross price elasticity of demand.

market penetration pricing  

Definition

A strategy adopted for quickly achieving a high volume of sales and deep market penetration of a new product. Under this approach, a product is widely promoted and its introductory price is kept comparatively low.

This strategy is based on the assumption that (1) the product does not have an identifiable price-market segment, (2) it has elasticity of demand (buyers are price sensitive), (3) the market is large enough to sustain relatively low profit margins, and (4) the competitors too will soon lower their prices.