Placement Papers - Akamai

1. What will be the reminder when (1234567890123456789) ^24 is divided by 6561 (1 Marks)?

A. 0
B. 1
C. 2
D. 3

Explanation:

sum of digits of denominator 6+5+6+1=18 1+8=9
sum of digits of numerator =90= 9+0=9
both numerator and denominator will be divisible by 9 without any remainder i.e. 0 remainder.

2. There is a 3*3 matrix. u have 2 colors red and blue. in how many ways u can fill the colors in the boxes so that if u rotate the matrix by 180 degrees we get the same matrix? (1 Marks)

A. 8
B. 16
C. 32
D. 48

Explanation:

2 2 2
2 2 1
1 1 1
(each element are represented no. of ways--hence 2^5=32.

3. A bag contains 6 balls of one or more colors. A ball is picked and is found to be red. What is the probability that the bag initially had exactly 6 red balls? (1 Marks)

A. 2/7
B. 1/5
C. 3/5
D. 4/5

Explanation:

If we have 1 red ball, then the probability of drawing 1 red ball out of 6 balls is 1/6.
If there are 2 red balls then the probability of drawing 1 red ball out of them is 2c1/6.
Similarly the other cases 3/6 4/6 5/6 6/6.

Now the probability of drawing 1 red ball when all the six are red is [6/6]/ [(1/6) +(2/6) +(3/6) +(4/6) +(5/6) + 6/6)] = 6/21=2/7.

4. 2 oranges, 3 bananas and 4 apples cost rs.15. 3 oranges,2 bananas and 1 apples cost rs.10. what is the cost of 3 oranges, 3 bananas and 3 apples? (1 Marks)

A. 5
B. 10
C. 15
D. 20

Explanation:
Given,
2 oranges + 3 bananas + 4 apples = Rs 15 ------------------(i)
and,
3 oranges + 2 bananas + 1 apples = Rs.10. ------------------(ii)

Add both equations. Which will be 5o + 5b + 5a=25. Now divide it by 5.
i.e. o + b +a = 5.
So now multiply it by 3 i.e. 3o+3b+3a=15.
Hence, the required number is 15.

5. Sehwag and Ganguly were sharing an apartment and cooked the food by themselves. One day Sehwag made 5 pizzas for himself and Ganguly made 3 for himself. At the time of lunch Tendulkar came in. So all three of them sat together and ate all the pizzas equally. After eating them Tendulkar gave them 8 expensive cricket bats and left. As Ganguly was running out of form he started quarrelling and asked for 4 bats which Sehwag refused to give. Finally, David shepherd was called to give the right decision which he did. How many bats Sehwag and Ganguly were given finally? (2 Marks)

A. 5,3
B. 7,1
C. 4,4
D. 3,5
Explanation:

8 pizzas were equally divided...hence each gets 8/3 pizzas
so for sachin,
sehwag provided: 5 - 8/3 = 7/3 pizzas, and
sourav provided: 3 - 8/3 = 1/3 pizzas
Hence their ratio being 7:1, sehwag gets 7 bats and sourav gets 1 bat.

6. Veena wants to make a cuboidal box with length 8cm, width 7 cm and height 6 cm, using 1 cubic cm cubes. What is the number of cubes she would require to make the box? (1 Marks)

A. 49
B. 136
C. 236
D. 336

Explanation:

The volume is (8*7*6) cm^3
The volume of one box is 1 cm^3
The no is (8*7*6) =336

7. 5 printers can print 5 sheets in 5 seconds. If I need to print 20 sheets in 20 seconds, how many additional printers should I install in my office? (1 Marks)

A. 0
B. 10
C. 15
D. 20

Explanation:

As 5 printers can print 20 pages in 20 second.

8. A three-digit number was divided successively in order by 4, 5 and 6 leaving out the remainders. The remainders were respectively 2, 3 and 4. How many such three digit numbers are possible? (1 Marks)

A. 3
B. 5
C. 7
D. 9

Explanation:

When a three-digit number is divided by 4,5,6 successively, the final quotient will be a single digit (as 4*5*6 = 120 and the max three-digit number 999 is not more than 9*120).

Let the number be x and the quotient after division by 4 be a and the quotient after division by 5 be b and the quotient after division by 6 be c.

Then, x = 4a+2,
=> a = 5b +3
=> b = 6c + 4.
Now, start with c=1, b=10, a=53, x=214.
when c=2, b=16, a=83, x=334,
c=3, b=22, a=113, x=454 and so on with an increment of 120.
Thus the 3 digit numbers possible are 214, 334, 454, 574, 694, 814, 934.

The answer is 7 such numbers are possible.

9. Jack, twenty-one years old, is three times as old as his brother. How old will Jack be when he is twice as old as his brother? (1 Marks)

A. 24
B. 28
C. 32
D. 36

Explanation:

Currently Jack \\'s age =21, his brother \\'s age=21/3=7.
Let x be years further when Jack is twice as old as his brother.
=> 21+x = 2 (7+x), solving x=7.
Hence Jack \\'s age will be 21+7 = 28.

10. If x and y are the two digits of the number 653xy such that this number is divisible by 80, then what is x + y =? (1 Marks)

A. 2 or 6
B. 4 or 6
C. 4
D. 8

Explanation:

Since, 80 = 2 * 2 * 2 * 2 * 5, which means the number should be divisible by 2 and 5.
Hence y=0.

Now 653x0 should also be divisible by 8 (as 80 = 8 *10) which means 3x0 should be divisible by 8. (For a number to be divisible by 8 last 3 digits should be divisible by 8).
Thus x can be 2 or 6.

So x+y can be 2+0 = 2 or 6+0 = 6.
Answer is option A) 2 or 6.

11. Three dice are rolled. What is the probability of sum of the numbers on the faces being 10? (1 Marks)

A. 15/216
B. 10/216
C. 9/25
D. 1/8

Explanation:

The combination of 10 can occur when we have (1,3,6) (1,4,5) (2,2,6) (2,3,5) (2,4,4), (3,3,4) = 6 patterns.
(1,3,6) can be 1,3,6 or 1,6,3 or 3,1,6 or 3,6,1 or 6,1,3 or 6,3,1 that is in 3! ways.
Set having repeating digits like 2,2,6 can be ordered in 3! /2 ways = 3 ways (like 2,2,6 or 2,6,2 or 6,2,2)
Hence over all occurrences = 6 + 6 + 3 + 6 + 3 + 3 = 27 ways.
Probability = 27/216 = 3/24 = 1/8.

12. A man has three grandchildren. The age of the eldest grand child is four times the age of youngest grandchild. The second grand child\'s age is half of the eldest grandchild. The sum of the ages of all three grandchildren is 63. What is the age of eldest grand child? (1 Marks)

A. 18
B. 24
C. 30
D. 36

Explanation:

Let the age of youngest be x. Eldest =4x
and the other = 2x.
Now 7x=63, x=9.
Age of eldest grandchild = 4x = 36.

13. The cost price of a cow and a horse is 3 lakhs. The cow is sold at 20% profit and horse at 10% loss. Overall gain is Rs.4200. What is the cost price of the cow? (1 Marks)

A. 114000
B. 140000
C. 141000
D. 144000

Explanation:

Let C.P of cow = c and horse =h.
=> c + h =300000 --------------- Eq1
=> 1.2c + 0.9h = 300000 + 4200,
Using Eq1, 1.2c + 0.9(300000-c) = 304200,
=> 0.3c = 304200 - 270000,
=> c=34200/0.3 = 342000/3
=> Rs. 114000

14. Vinod ordered for 6 blue toys and some green toys. The price of a blue toy is 2.5 times that of a green toy. While preparing the bill, the clerk interchanged the number of blue and green toys which increased the bill by 145%. Find the number of green toys. (1 Marks)

A. 9
B. 12
C. 15
D. 18

Explanation:

Let price of green toy be a. Price of blue toy = 2.5a.
Let the number of green toys purchased be x.
Actual price = 6 * 2.5a + ax = 15a + ax
Increased bill = 2.5ax + 6a
=> 2.5ax + 6a = 145/100 * (15a + ax)
Cancelling a,
2.5x + 6 = 1.45*15 + 1.45x, on Solving we get x= 15.

15. Mahesh spends 30% of his income on petrol. 1/4th of the remaining on house rent and the balance on food. If he spends Rs.300 on petrol, then what is the expenditure on food? (1 Marks)

A. 525
B. 450
C. 325
D. 175

Explanation:

Let income be x.
Petrol expense = 0.3x, House rent = 1/4 * 0.7x, food expense = 3/4 * 0.7x
As petrol expense = 300 = 0.3x, x=1000.
Hence food expense= 3/4 * 0.7 * 1000 = Rs.525

16. 60 men can complete a work in 40 days. 60 men start the work but after every 5 days, 5 men leave. In how many days the work will be completed? (2 Marks)

A. 50
B. 60
C. 75
D. None of these

Explanation:

Let the total work be 2400 (Product of 60 and 40) units of work.
Let us assume 1 man does 1 unit of work in a single day.
So in 5 days, 60 men do 5*60 = 300 units of work. Pending work = 2100 units.
From days 5-10, 55 men do 5*55 = 275 units of work. Pending work = 1825 units
From days 10-15, 50 men do 5*50 = 250 units of work. Pending work = 1575 units
In a similar fashion, after 20 days pending work = 1350 units, 25 days = 1150 units, 30 days = 975 units, 35 days = 825 units, 36 - 40 days (25 men) = 700 units, 41-45 days (20 men) = 725 units, 46-50 days (15 men) = 650 units, 51-55 days (10 men) = 600 units, 56-60 days (5 men) = 575 units.

Now as all men leave in the 60th day and still work is pending the work will never get completed.

17. Divide 50 into two parts so that sum of the reciprocal is 1/12? (1 Marks)

A. 10,40
B. 15,35
C. 30,20
D. 22,28

Explanation:

Let numbers be x and y.
=> x+y = 50.
=> y=50-x.
According to the question,
=>1/x + 1/y = 1/12
=> 1/x + 1/50-x = 1/12
=> 12 (50-x + x) = (50x - x^2)
=> x^2 -50x + 600 = 0, solving x=20 or x=30.
Hence the numbers are 20,30 (or can also be 30,20).

18. 146! /5^n what is the maximum value of n? (1 Marks)

A. 34
B. 35
C. 36
D. 37

Explanation:

Exponent of 5 in 146! = [146/5] + [146/5^2] + [146/5^3] = 29+5+1 = 35 i.e. 146! has a factor 5^35.
=>146! /5^n
=> n(max)=35.

19. Tim and Elan are 90 km from each other. They start to move towards each other simultaneously time at speed 10kmph and Elin 5kmph. If every hour they double their speed what is the distance that Tim will pass until he meets Elan. (1 Marks)

A. 57
B. 60
C. 63
D. 66

Explanation:

0..................90
AFTER 1ST HR
10................85
AFTER 2ND HR
30................75
AFTER 2.30MIN
50..............65
AFTER 2.45MIN
60.........60.

20. 3 persons A, B and C are standing in a queue. There are 5 persons between A and B and 8 persons between B and C. If there are 3 persons ahead of C and 21 persons behind A, what could be the minimum number of persons in the queue? (1 Marks)

A. 40
B. 41
C. 27
D. 28

Explanation:

positions: ---c--a-----b---------------
totally 28.

21. In a hotel where rooms are numbered from 101 to 130, each room gives an earning of Rs. 3000 for the first fifteen days of a month and for the latter half, Rs. 2000 per room. Find the average earning per room per day over the month. (Assume 30-day month) (1 Marks)

A. 2500
B. 2250
C. 2750
D. 3000

Explanation:

first 15 days = 15*3000
second 15 days = 15*2000
for a month= (15*3000 + 15*2000) = 75000
for a day = 75000/ 30 = 2500.

22. Lion tells lies on Mondays, Tuesday and Wednesday, Rat tells lie on Thursday, Friday and Saturday, both of them speak truth on other days. Lion tells, Yesterday was one of the days which, I tell lying? Rat also tells Yesterday was one of the days which I tell lying. What day was yesterday?

A. Monday
B. Tuesday
C. Wednesday
D. Thursday

Explanation:

Wednesday
if yesterday was Wednesday then today is Thursday. on Thursdays lion tells the truth whereas on Thursdays rat tells lies. therefore, "Yesterday was one of the days which, I tell lying?" said by lion is true and "Yesterday was one of the days which I tell lying " said by rat is false......

23. After allowing a discount of 11.11%, a trader still makes a gain of 14.28%. At how many per cent above the cost price does he mark on his goods? (2 Marks)

A. 28.56%
B. 35%
C. 22%
D. None

Explanation:

Let us consider cost price to be Rs.100
Thus, S.P. will be Rs.114.28 (i.e. 100+14.28)
Now discount=11.11%
Let marked price be Rs.x
thus, (100-11.11) =88.89% of x =Rs.114.28
=> x= (114.28 * 100)/ 88.89 =128.56%
Thus marked price is 28.56% above original cost price.

24. If \\'n integers taken at random and multiplied together, then what is the probability that the last digit of the product is 1, 3, 7 or 9? (1 Marks)

A. 2n/5n
B. 4n/5n
C. 2n/10n
D. None

Explanation:

2n/5n
As number of digits at end can b 0 to 9 and here it is asked only for 4 digits.
So, 4/10 is equal to 2/5.

25. In June, a baseball team that played 60 games had won 30% of its game played. After a phenomenal winning streak, this team raised its average to 50%. How many games must the team have won in a row to attain this average? (1 Marks)

A. 12
B. 20
C. 24
D. 30

Explanation:

Let the number of games required be x.
According to the question,
=> (50/100) (60+x) =18+x.
=> x =24.

26. A grocer bought 24 kg coffee beans at price x per kg.after a while one third of stock got spoiled so he sold the rest for $200 per kg and made a total profit of twice the cost what must be the price of x ( 1 Marks )

A. 44.44
B. 55.55
C. 66.66
D. 77.77

Explanation:

Given,
Spoiled eggs =24/3=8 and
Left eggs = 24-8=16.
Now 16*200$=3200$ which is sell price.
Now total cost=24*x and given that profit=2*total cost i.e. profit=48*x.
Now we know that profit+cost=sell price.
So, 24X + 48X=3200.
Now 72X=3200 from here X=44.44$.

27. In how many rearrangements of the word ERASED in the letter \\'A \\'positioned in between the 2 \\'E \\'s? (2 Marks)

A. 6!
B. 5!
C. 4!
D. 2!

Explanation:

Two E \\'s can be arranged in 1 way only (because Identical letters: [2! /2!])
then A can be arranged in between E \\'s is one-way.
These (EAE) treated as one group(letter).
Remaining letters(RSD)& That group(letter) =4.
So Four Letters can be arranged in 4places can be done in 4! Ways.

28. In how many ways a team of 11 must be selected from 5 men and 11 women such that the team must comprise of not more than 3 men? (1 Marks).

A. 1543
B. 2256
C. 2456
D. 1656

Explanation:

The team may consist of: -

0 men + 11 women,
1 men + 10 women,
2 men + 9 women,
or
3 men + 8 women.
So Number of ways are = (11C11) + (5C1x11C10)+ (5C2x11C9)+(5C3x11C8)= 2256.

29. Eisha bought 18 sharpeners for Rs.100. She paid 1 rupee more for each white sharpener than for each brown sharpener. What is the price of a white sharpener and how many white sharpeners did she buy? (1 Marks)

A. Rs.5, 10
B. Rs.6, 10
C. Rs.5, 8
D. Rs.6, 8

Explanation:

This question can be solved easily by going through options (Hit & Trial).

A. White sharpener total cost: Rs.5 x 10 = Rs.50. Brown sharpeners cost = Rs.4 x 8 = 32. Total cost is only Rs.82. Wrong option.

B. White sharpener total cost: Rs.6 x 10 = Rs.60. Brown sharpeners cost = Rs.5 x 8 = 40. Total cost is Rs.100. Correct option.

30. In how many different ways can the letters of the word \'LEADING\' be arranged in such a way that the vowels always come together?

A. 360
B. 480
C. 720
D. 5040
E. none of these

Explanation:

The word \'LEADING\' has 7 different letters.
When the vowels EAI are always together, they can be supposed to form one letter.
Then, we have to arrange the letters LNDG (EAI).
Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.
The vowels (EAI) can be arranged among themselves in 3! = 6 ways.
Hence, Required number of ways = (120 x 6) = 720.