International Business Machines Corporation model aptitude test papers

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1. In a computer institute 9 languages can be taught. The module is of 6 months duration and of the six languages only one can be taught each month . In addition to that BASIC is always taught and should be in first month itself
WORD PERFECT is to be taught in the preceeding week of WORD STAR. FORTRAN can not be taught until COBAL is taught prior to that BINO, FIFO can never be taught in single module languages are BASIC, WORD STAR, WORD PERFECT, FORTRAN, COBAL, BINO, FIFO, LOTUS, C
i) If word star is in 3rd month , what could be in 6th month.
ii) If COBAL is in the 2nd month and BINO in 6th month. FORTRAN will be taught in which month.

2. The values of shares (in Rs).of A, B and C from January to June are as follows.
Month A B C
January 30 60 80
February 35 65 85
March 45 75 65
April 40 75 82
May 55 75 85
June 50 75 80
i) During this period which share has undergone maximum fluctuation?
ii) In which month it is possible to buy B and C selling A?
iii) In which month the share values are very low?
iv) By purchasing one share of A and 4 each of B and C in the beginning of the period,
when should these be sold to get maximum profit?
Ans. i). the greatest amount by which the contract price can change, up or down, during one trading session, as fixed by exchange rules in the contract specification.
So, Answer is (C)
ii). In March, because the value of A is decrease in April, and of B and C are increase in total.
iii). January , the month in which the value of A+B+C is least.
Hence answer is
iv). value of A,B and C are highest in the month of May. Hence May is the answer.

3. A person has Rs 100/- in his pocket, he can as 25 pencils or 15 books. He kept 15% of the money for traveling expenses and purchased 5 pencils. So how many books he can purchase with the remaining money.
Ans> cost of 15 books is 100 rupee
so cost of 3 books is 20 rupee
and cost of 25 pencils is 100 rupee
so cost of 1 pencil is 4 rupee
traveling expenses = 15 % = 15 rupee
cost of 5 pencils = 5*4 = 20 rupee
remaining amount = 100 - 35 = 65 rupee
cost of 9 books is 20*3 = 60 rupee
so total 9 books can be purchased and 5 rupee will remained.

4. In 1978, a kg of paper was sold at Rs25/-. If the paper rate increases at 1.5% more than the inflation rate which is 6.5% a year, then what will be the cost of a kg of paper after 2 years?
(a) 29.12
(b) 29.72
(c) 30.12
(d) 32.65
(e) none of these
Ans> If the paper rate increases at 1.5% more than the inflation rate which is 6.5%
This means paper rate increase is 1.5+6.5 = 8% per year
For the first year the increase is 8 % or (8/100)x25 = 2
So the new cost is 25+2 = 27
For the second year the increase is the same = (8/100)x27 = 2.16
So the cost = 27+2.16 = 29.16

5. In a company printing work is done by two machine 5% of the work done by machine A are wasted , and 40% of work done by machine B are wasted. if the 80% of the total work is done by machine A. then what is the total percentage of wastage.
Ans> If total 100 units of job is done, then
80 units on machine A and 20 units of machine B.
wasted work by A = .05*80 = 4 units
wasted work by B = .4* 20 = 8 units
total wasted work = 12 units.
12%

6. Company A taken a truck on rent of $1280 per month another company B bought the truck in $40000 and send $120 per month. After 4 years what will be the difference in the amount spent by the both companies on the TRUCK
Ans> Difference in amt spent = 1280*48 - ( 40000+120*48)
=> 48*(1280-120)- 40000 = 48*1160-40000
=> 15680 Answer.

7. Rectangular room has width half of its length. When 6 is decreased from both length and width then its area is differed by 108 so find the width.

Ans. Let the length be 2x, Then width will be x
The area : 2x^2
After decrease: Length(2x-6) & Width(x-6)
Now, the area:2x^2-18x+36
Hence, the eq. is 2x^2-(2x^2+18x+36)=108
Solving, we get x=8,(width)

8. We have 171 kg rice costing 7 rs/kg.we have rice at 11 rs/kg and 2 rs/kg .then after mixing 11 rs/kg and 2 rs/kg rice. What is quantity of 11 rs/kg rice.
Ans. A = 11 rs/kg rice
b = 2 rs/kg rice
11a= cost of 11 rs/kg rice
2b= cost of 2 rs/kg rice
a+b = 171
11a+ 2b = 7 x 171
solving above equation
a = 95 & b = 76

9. In a library there are 5 cluster and each is having 44 books(module). In first weak 75 books are used, in second 95, in third 95 and in fourth 160 books are used.then tell how much fraction of books are used.
Ans> Total modules that can be used every week = 44*5 = 220
Total modules that can be used in 4 weeks = 4*220 = 880
modules used in 4 weeks = 75+95+95+160 = 425
fraction used = 425/880 = 0.483 or 48.3 %

10. Printer A prints 8192 character per min and printer B prints 13862 character per min four character are equal to one word. Printer A starts at 7:15 am while Printer B starts at 7:29 am then at what time both will have same no of words printed.
Ans. rate * time = words.
Ra = 8192/4 = 2048 words/minute.
Rb = 13862/4 = 3465.5 words/minute.
Ra(T+14) = Rb*T
=> T = 20.22

11. The rate of color toner increases $33 to $35 and rate of black&white toner increases $28 to $29. If company spends $1540 in which 3/5 is color toner then how much is total expenditure increases after the cost hike.
Ans. Total spend amount = $1540
3/5 is color-toner = 3/5 * 1540 = $924.
Number of color toner = 924/33 = 28.
Number of black and white toner = 22.
Total expenditure after hike= 28*35 + 22*29 = $1618.
Increase in total expenditure = 1618-1540 = $78.

12. A printer started its work at 8.15 a.m and ended its work at 9.20 p.m. It was interrupted twice for the time duration of 42 min. It can print 100 instructions per hour. Approximate how many instructions it can print?
Ans. Time duration from 8.15am to 9.20pm = 13 hours 5 min = 785 minutes
stoppage for 2*42 min= 84 min
effective running time = 701 min
in 60 min 100 instructions are printed
in 1 min = 100/60 instructions
in 701 min , we have 701*100/ 60 = 1168.33 instructions

13. If a company produces 15 different model of tv sets of 2 inches screen and 4 different model of 4 inches screen size. Then how many model should vendor has for all the model so that all models will displayed in the showroom.
Ans. 15 models of 2 inches screen =15
4 models of 4 inches screen = 4
15+4= 19

14. In A,B,C are having some marbles with each of them. A has given B and C the same number of marbles each of them already have. Then, B gave C and A the same number of marbles they already have. Then C gave A and B the same number of marbles they already have. At the end A,B,and C have equal number of marbles.

If the total number of marbles are 72, then the number of marbles with A at the starting
(a) 20
(b) 30
(c) 32
(d) 39
Ans. go from the end.
at end each having equal no.of marbles.
totally we have 72 marbles.
so at end all are having 24,24,24.
previous step C gave A and B the same number of marbles they already have...
so
A B C
24 24 24
if c gave same amount means in previous steps it look like
12 12 48
if b gave same amount means in previous steps it look like
6 42 24
so intially a gave to b and c
39 12 12
Ans:39

15. Rs 50000 is divided into two parts One part is given to a person with 10% interest and another part is given to a person with 20 % interest. At the end of first year he gets profit 7000 Find money given by 10%?
Ans. let x was given to a with 10% interest.
then b got 50,000 - x
interest = p*t*r /100
so
7000 =((50000 - x)*1*20)/100 +(x*1*10)/100
700000 = 1000000 - 10x
x = 30000

16. The price of sugar increases by 20%, by what % house-wife should
reduce the consumption of sugar so that expenditure on sugar can be
same as before
Ans. As price increase and consumption are inversely proportional,
if one increases by 1/x then other should reduce by 1/(x+1)
hence 20% is 1/5, consumption should reduce by 1/6 = 16.66%

17. Machine A is got for rent and maintatence cost of 250$ is spent per month. Another machine B is purchased for 1500$ and cost of maintenance is 75$ per month. what is the expenditure difference?
Ans. (250*12) - (1500+75*12)

18. A computer shop consists 3 brand’s laptop .Laptop of brand A is sold 3/16, B is sold 1/16 and c is sold ¾ then what fraction is sold by the shop in all.
Ans. A+B+C = 3/16 + 1/16 + 3/4 = 3/16 + 1/16 + 12/16 = 16/16.
A+B+C = 1
A,B, and C make up 100% of the laptops.

19. If a car starts from A towards B with some velocity. Due to some problem in the engine after traveling 30km, the car goes with 4/5 th of its actual velocity The car reaches B 45 min later to the actual time. If the car engine fails after traveling 45km, the car reaches the destination B 36min late to the actual time What is the initial velocity of car and what is the distance between A and B in km
Ans. let x is distance from A to B
and y is initial speed.
30/y+(x-30)5/4y -x/y = 3/4
=> 4x-12y=120 ----(1).
45/y + (x-45)5/4y -x/y=3/5
=> 5x-12y=225 -------(2).
From equ (1) and equ (2) we will get.
x=25 and y=105
so initial speed is 25 km/hr
and Distance From A to B is 105 km

20. Person A can finish 2/5 of work and person B can finish 3/5 of work. If A completed some 1/9 of his work and B completed 5/18 of his work. what fraction of work is not yet completed by both?
Ans. Total work is 2/5+3/5=1
so, A use to do 2/5th work ,but he has completed =2/5*1/9 = 2/45 work
II,y B use to do 3/5th work ,but he has completed =3/5*5/18= 1/6work
left out work = 1-(2/45 +1/6)= 10/9

21. In a square, all the mid points are joined. The inner square is shaded. If the area of the square is A, what is the area of the shaded area?
Ans. the shaded area is half the area of the square (having area A). Therefore answer is A/2.

22. If a team consists 20 members in which 20% are mathematician then how many member should they hire sothat the ratio would become 10/11.
Ans. 20*20/100=4,so there are 4mathematician,'x' be the number of members added together,so x+4/x+20=10/11.therefore x=156.

23. You have two jars, 50 red marbles and 50 blue marbles. A jar will be picked at random, and then a marble will be picked from the jar. Placing all of the marbles in the jars, how can you maximize the chances of a red marble being picked? What are the exact odds of getting a red marble using your scheme?

24. Using the numerals 1,7,7,7 and 7 (a "1" and four "7"s) create the number 100. As well as the five numerals you can use the usual mathematical operations +, -, x,/ and brackets ().
Ans. (7+7) × [7+(1 / 7)] = 100

25. A girl, a boy, and a dog start walking down a road. They start at the same time, from the same point, in the same direction. The boy walks at 5 km/h, the girl at 6 km/h. The dog runs from boy to girl and back again with a constant speed of 10 km/h. The dog does not slow down on the turn. How far does the dog travel in 1 hour?
Ans. 10km. Because the dog's speed is 10 km/h.
Where the boy and girl are has no effect on answering this puzzle.

26. There are 2 trees in a garden (tree "A" and "B") and on the both trees are some birds.
The birds of tree A say to the birds of tree B that if one of you come to our tree, then our population will be the double of yours. Then the birds of tree B tell to the birds of tree A that if one of you come here, then our population will be equal to that of yours. How many birds in each tree?
Ans. Let the birds on Tree A = x
Birds on Tree B = y
According to question :
When 1 bird fly from tree B to tree A
Trees of A = x + 1
Trees on B = y - 1
x + 1 = y - 1
=> y-x = 2........(i)

When 1 bird fly from tree a to tree b
Birds on Tree A = x - 1
Birds on Tree B = y +1
y + 1 = 2 ( x - 1 )
2x-y = 3............(ii)
From equation (i) and (ii), we get
x= 5 and y = 7.

27. There are two bags, one of which contains 5 red and 7 white balls and the other 3 red and 12 white balls. A ball is to be drawn from one or other of the two bags ; find the chances of drawing a red ball.
Ans. 37/120

28. Karthik started a business investing Rs.9000. After 5 months, Shyam joined with a capital of Rs.8000. If at the end of the year, they earn a profit of Rs.6970, then what will be the share of Shyam in the profit?
Ans. 2380

29. A Black Smith was given a chain torn into equal sections of 3 links each and asked to fix it. How many links(minimum) would he has to open up and reforge ?
Ans. To join 2pieces of 3links one link must be open and to join next two pieces one more link needs to be opened. so, total no. of links which needs to be opened is 2.

30. A square plate of some size is cut at four corners. Equal squares of the same size are cut and is formed as open box. If this open box carries 128 ml of oil. What is the size of the side of the plate?
(a) 17
(b) 14
(c) 13
(d) None of these
Ans. Let, side of original plate be =x
Also, side of the square at the corners= a
so, when the square at the corner is cut off, the length of the box is=x-2a
similarly, the breadth of the box is=x-2a
the height of the box would be invariably=a
so, the dimension of the open box=(x-2a)*(x-2a)*a=a*(x-2a)^2
so, we need to factorize 128 so that we get a square term & an integer.
case 1. 128=2*2*2*2*2*2*2=(2*2*2*2*2)*2*2=32*2*2
so, a=32, x-2a=2, x=2*32+2=66
case 2. 128=2*2*2*2*2*2*2=(2*2*2)*(2*2)*(2*2)=8*4*4
so, a=8, x-2a=4, x=2*8+4=20
case 3. 128=2*2*2*2*2*2*2=2*(2*2*2)*(2*2*2)=2*8*8
so, a=2, x-2a=8, x=2*2+8=12
so, the possible values of the side of the original square plate are 66, 20 & 12
none of these match the answer options provided in a. , b. or c.
so, the correct choice is (d) None of these.