Elitmus previous questions - 1

Elitmus previous questions - 1

1. If a number x is in octal form and having zero as unit place then if we change that number x in decimal form then what is the probability that number x having zero as unit place?
Explanation:
When you convert a decimal number into octal form, think which numbers end with zero.  The multiples of 8. For example (8)10=(10)8${\left(8\right)}_{10}={\left(10\right)}_8$, (16)10=(20)8${\left(16\right)}_{10}={\left(20\right)}_8$, (24)10=(30)8${\left(24\right)}_{10}={\left(30\right)}_8$, (32)10=(40)8${\left(32\right)}_{10}={\left(40\right)}_8$, (40)10=(50)8${\left(40\right)}_{10}={\left(50\right)}_8$, . . .
So out of five numbers end with zero in octal form, only one (50)8=(40)10${\left(50\right)}_8={\left(40\right)}_{10}$ has zero in decimal format.  So the required probability is 1/5

My initial thinking:
Let the number be "ab0" in octal form.  Remember here a, b < 8.  So total possibilities are 64.
If we convert the given number into decimal format, then (ab0)₈ = 64a  + 8b.
We will find for how many values of 64a + 8b ends in zero.
64a + 8b = 60a + (4a + 8b)
For (0,0), (1, 2), (1, 7), (2, 4), (3, 1), (3, 6), (4, 3), (5, 5), (6, 2), (6, 7), (7, 4), (0, 0) the above expression gives unit digit 0.
So required probability = 11/64
(Imp: Still I am not comfortable with the solution I have written as it is not specified whether the given number is 3 digit or not.   Just learn how I tried to solve it. )

2. log xy³ = a; log x²y = b then then value of log y /log x
Explanation:
log xy³ = logx + 3logy = a - - - (1)
log x²y = 2logx + logy = b - - - (2)
Multiplying (1) by 2 and subtracting (2) from it
5logy = 2a-b
logy = 2a−b5${\displaystyle \frac{2a-b}{5}}$
Put the value of log y in equation (2),
2logx + 2a−b5${\displaystyle \frac{2a-b}{5}}$ = b
logx = 3b−a5${\displaystyle \frac{3b-a}{5}}$
logylogx=2a−b53b−a5${\displaystyle \frac{\log y}{\log x}}={\displaystyle \frac{{\displaystyle \frac{2a-b}{5}}}{{\displaystyle \frac{3b-a}{5}}}}$ = 2a−b3b−a${\displaystyle \frac{2a-b}{3b-a}}$

3. Einstein walks on an escalator at a rate of 5steps per second and reaches the other end in 10 sec. while coming back, walking at the same speed he reaches the starting point in 40secs. What is the number of steps on the escalator?
a) 40
b) 60
c) 120
d) 80
e) data insufficient
Explanation:
Escalator problems are similar to boats and streams problems.  If we assume man's speed as 'a m/s' and escalator speed as 'b m/sec' then while going up man's speed becomes 'a -b' and while coming down 'a + b'.
In this question, Let the speed of escalator be b steps per sec.  And length of escalator be L.   Einstein's speed = 5 steps/ sec
While going down,  L5+x=10${\displaystyle \frac{L}{5+x}}=10$ ⇒$\Rightarrow$ L = 50 + 10x
While coming up, L5−x=40${\displaystyle \frac{L}{5-x}}=40$ ⇒$\Rightarrow$ L = 200 - 40x
Multiply the first equation by 4, and add to the second, we get L = 80

4. Photography changed drastically _________ introduced in the market.
a) when polariod
b) as polaroid
c) since polaroid
d) that polaroid
Explanation:
There is no adequation information is given about details of subsequent changes.  So "when" is the right word. Option a. "As" inditates reason.

5. Data sufficiency question:
Is x has only '3' factors?
a) x^2 has only '5' factors.
b) one of its factor must be prime number
Explanation:
Only squares of primes has 3 factors.  For example, 4 has three factors. 1, 2, 4.
Now when we square 4, we get 16, which has 5 factors. 1, 2, 4, 8, 16.  So Statement 1 is sufficient.
Statement two says that one of the factor must be prime number.  10 has 4 factors.  i.e., 1, 2, 5, 10 and one of which is prime. but we cannot say whether numbers of this format always have three factors or not. So statement 2 is insufficient.

6.  Data sufficiency question:
If solution (x) with alcohol (14%) and solution (y) with alcohol (20%) mixed together to form 24 liters of mixture.  Then the amount of solution(x) is?
a) The alcohol in solution(mixture) is 15%
b) If we inter changed the amounts of solutions 'x' and 'y' we get mixture of alcohol %,44%
Explanation:
Let a liters of first solution, and 'b' liters of second solution has been taken.
So using weighted average formula = n1×a1+n2×a2n1+n2${\displaystyle \frac{n_1\times a_1+n_2\times a_2}{n_1+n_2}}$ = n1×14+n2×20n1+n2=15${\displaystyle \frac{n_1\times 14+n_2\times 20}{n_1+n_2}}=15$
⇒n1=5n2⇒n1n2=51$\Rightarrow n_1=5n_2\Rightarrow \frac{n_1}{n_2}=\frac{5}{1}$
As total volume was given as 24 liters, first solution = 16×24=4${\displaystyle \frac{1}{6}}\times 24=4$
So statement 1 is sufficient.

Let us take volume of the first solution is 'a' liters. Then volume of the second = 24 - a.
Again by using the question statement, and statement 2, (24−a)×14+a×2024=44${\displaystyle \frac{(24-a)\times 14+a\times 20}{24}}=44$
From this also, value of 'a' can be calculated.  So Statement 2 also sufficient.

7. How many solution  does the expression x+3−−−−√=xx+3−−−−√$\sqrt{x+3}=x\sqrt{x+3}$ has?
Explanation:
Squaring on the both sides, x+3=x2(x+3)$x+3=x^2(x+3)$
Bring x+3 to one side and take common, (x2−1)(x+3)$\left(x^2-1\right)\left(x+3\right)$
So roots are, 1, -1, 3. But -1 is not a root. So 1, -3 are the roots.

(∵$\because$ when you square the equation additional roots may be generated. So finally you have to check manually, whether the given roots satisfy the original equation or not)

8. In 2 bags, there are to be put together 5 red and 12 white balls, neither bag being empty. How must the balls be divided so as to give a person who draws 1 ball from either bag-
(i) the least chance of drawing a red ball ?
(ii) the greatest chance of drawing a red ball ?
Explanation:
(1) Put 1 white in first bag, and all the remaining ball in second bag.  Probability = 12×0+12×516${\displaystyle \frac{1}{2}}\times 0+{\displaystyle \frac{1}{2}}\times {\displaystyle \frac{5}{16}}$ = 532${\displaystyle \frac{5}{32}}$
(2) To maximize, we put 1 red in the first bag, and all the remaining in the second. Probability = 12×1+12×432${\displaystyle \frac{1}{2}}\times 1+{\displaystyle \frac{1}{2}}\times {\displaystyle \frac{4}{32}}$ = 916${\displaystyle \frac{9}{16}}$

9. The dairy condensed milk has only 20% water while the cow milk has 90% water. How many litres of milk maid will be obtained from 72 litres of milk?
a) 7.2l
b) 8l
c) 9l
d) 14.4l
Answer: 9
Explanation:
In this question, Pure milk in condensed milk = Pure milk in cow milk
80% (x) = 10% (72)
Therefore, x = 9 Liters.

10. How many two digit numbers are there such that the product of their digits after reducing it to the smallest form is a prime number? for example if we take 98 then 9*8=72, 72=7*2=14, 14=1*4=4. Consider only 4 prime numbers (2,3,5,7)
Explanation:
2 = 12 or 21 So 1×2, 2×1, 3×4, 4×3, 2×6, 6×2, 3×7, 7×3
3 = 13 or 31 So 1×3, 3×1
5 = 15, 51 So 1×5, 5×1, 3×5, 5×3, 7×5, 5×7
7 = 17 or 71 So 1×7, 7×1
15 = 3×5 = 5×3
So total 18 numbers = 12,13,15,17,21,26,31,34,35,37,43,51,53,57,62,71,73,75

Wipro previous placement questions - 1

Wipro previous placement questions - 1

1. A starts business with Rs. 35,000 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2:3. What is B’s contribution in the capital?

A) Rs .7500
B) Rs. 8000
C) Rs. 8500
D) Rs. 9000
Answer: D
Explanation:
Ratio in which profit is to be divided = 2 : 3
Assume that B's contribution to the capital = b
⇒ 3500 × 12 : b × 7 = 2 : 3
⇒ 3500 × 12/7 b = 2/3
⇒ b = (3500 × 12 × 3)/(2 × 7) = 500 × 6 × 3 = 9000

2. Anand and Deepak started a business investing Rs. 22,500 and Rs.35,000 respectively.  Out of a total profit of Rs.13,800, Deepak’s share is _____
A) Rs.5,400
B) Rs.7,200
C) Rs.8,400
D) Rs.9,400
Answer: A
Explanation:
Ratio of their investments = 22500 : 35000 = 9 : 14
So Deepak' s  share =  923${\displaystyle \frac{9}{23}}$ × 13800 = Rs.5,400

3. Narasimha, Madhu and pavan started a business by investing Rs.1,20,000, Rs.1,35,000 and Rs 1, 50,000 respectively.  Find the share of Pavan, out of an annual profit of Rs.56,700.
A) Rs.16,800
B) Rs.18,900
C) Rs.21,000
D) none
Answer: C
Explanation:
Ratio of their investments = 120000 : 135000 : 150000 = 8 :  9 : 10
Share of Pavan = 1027${\displaystyle \frac{10}{27}}$ × 56700 = 21,000

4. Out of four numbers ,the average of first three is 16 and that of the last three is 15.  If the last number is 18,the first number is :
A) 20
B) 21
C) 23
D) 25
Answer: B
Explanation:
Let the numbers be a,b,c,d
Given, a + b + c = 48,  b + c + d = 45
Now, d = 18
thus, b + c + 18 = 45 ⇒ b + c = 27
Putting the value of b + c in a + b + c = 48
a + 27 = 48 ⇒ a = 21

5. A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3 . Find his average after 17th inning.
A) 39
B) 38
C) 38.5
D) 39.5
Answer: A
Explanation:
Consider the avg for first 16 innings is x.
Then total runs scored till 16 innings is 16x.
Total runs after 17 innings = 16x + 87.
Thus,  16x+8717=x+3${\displaystyle \frac{16x+87}{17}}=x+3$ ⇒ x = 36
So his average after 17 innings = 39.

6. Three years ago , the average age of A, B and C was 27 years and that of B and C 5 years ago was 20 years. A’s present age is :
A) 30 yrs
B) 35 yrs
C) 40 yrs
D) 48 yrs
Answer: C
Explanation:
Sum of the present ages of A, B and C = (27× 3 + 3 × 3) years = 90 years.
Sum of the present ages of B and C = (20 × 2 + 5 × 2) years = 50 years.
A's present age = 90 – 50 = 40 years.

7.The average of six numbers is 30.  If the average of first four is 25 and that of last three is 35, the fourth number is :
A) 25
B) 30
C) 35
D) 40
Answer: A
Explanation:
Let the six numbers be, a, b, c, d, e, f.
a + b + c + d + e + f = 30 × 6 = 180 - - - -  (1)
a + b + c + d =  25 × 4 = 100 - - - -  (2)
d + e + f = 35 × 3 = 105 - - - - (3)
Add 2nd and 3rd equations and subtract 1st equation from this.
d = 25

8. A and B are partners in a business. A contributes 1/4 of the capital for 15 months and B received 2/3 of the profit .  For how long B’s money was used.
A) 6 months
B) 9 months
C) 10 months
D) 1 year
Answer: C
Explanation:
B received 2/3 of the profit ⇒Their profits ratio = A : B = 1 : 2
Let the total capital = 4 units
Then A's capital = 1
B's capital = 3
Assume B's money was used for b months
Then A : B = 1 × 15 : 3 × b = 1 : 2
⇒ 15 : 3b = 1 : 2
⇒ 153b=12${\displaystyle \frac{15}{3b}}={\displaystyle \frac{1}{2}}$
⇒ b = 10

9.  At an election a candidate who gets 84% of the votes is elected by a majority of 476 votes. What is the total number of votes polled?
A) 672
B) 700
C) 749
D) 848
Answer: B
Explanation:
Let the total votes are 100x. Then winning candidate got 84x, and losing candidate got 16x.
⇒ 84x – 16 x = 476
⇒ 68 x = 476
⇒ x = 7
Total votes are 700.

10.  A man buys a cycle for Rs.1400 and sells it at loss of 15%.  What is the selling price of the cycle?
A) Rs.1090
B) Rs.1160
C) Rs.1202
D) Rs.1190
Answer: D
Explanation:
S.P = 85% of Rs.1400  ⇒ Rs.(85100${\displaystyle \frac{85}{100}}$ ×1400) = Rs.1190.

11. A shopkeeper purchased 70 kg of potatoes for Rs.420 and sold the whole lot at the rate of Rs 6.50 per kg .What will be his gain percent?
A) 4 1/6 %
B) 6 1/4 %
C) 8 1/3 %
D) 20%
Answer: C
Explanation:
Price per 1 kg = 42070${\displaystyle \frac{420}{70}}$ = Rs.6.
Profit per 1 kg = Rs.6.5 – Rs.6 = Rs.0.5
Profit for 70 kg = 0.5 × 70 = Rs.35
Gain % = 35420${\displaystyle \frac{35}{420}}$  × 100= 8.33% = 8 1/3

12.  By selling 300 apples a seller gains the selling price of 60 apples. The gain percent of the seller is
A) 200
B) 20%
C) 25%
D) 16 2/3%
Answer: C
Explanation:
We know that SP − CP = Profit
⇒300SP - 300CP = 60SP
⇒240SP = 300CP
⇒ SPCP=300240${\displaystyle \frac{SP}{CP}}={\displaystyle \frac{300}{240}}$ = 54${\displaystyle \frac{5}{4}}$
Let SP = 5, and CP = 4
So profit percentage = 14×100=25%${\displaystyle \frac{1}{4}}\times 100=25\mathrm{\%}$

13. The average monthly salary of 8 workers and one supervisor in a factory was 430.Whenthesupervisor,whosesalarywas$430.Whenthesupervisor,whosesalarywas$870 per month, retired, a new person was appointed and then the average salary of 9 people was $400 per month. The salary of the new supervisor is:
A. $700
B. $600
C. $430
D. $400
Answer: B
Explanation:
Total salary of 8 workers and supervisor together = 9 × 430 = 3870
Now total salary of 8 workers = 3870 − 870 = 3000
Total salary of 9 workers including the new supervisor = 9 × 400 = 3600
Salary of the new supervisor = 3600 − 3000 = 600

14. The average of the first five prime numbers greater than 20 is:
A. 32.20
B. 31.00
C. 31.01
D. 32.00
Answer: A
Explanation:
Required prime numbers are 23, 29, 31, 37, 4.
Average will be (23 + 29 + 31 + 37 + 41)/5 = 32.20

15. The average score of 35 students in a class is 37. If every student is given 3 grace marks, the new average of the class is:
A. 45
B. 34
C. 43
D. 40
E. None of these
Answer: D
Explanation:
Average score = 37
Grace mark 3 is given to 35 student then its average will be 3.
Hence new average = 37 + 3 = 40

16. The average age of a group of 10 students is 14 years. If 5 more students join the group, the average age rises by 1 year. The average age of the new students is:
A. 15 years
B. 17 years
C. 16 years
D. 18 years
E. None of these
Answer: D
Explanation:
Total age of the 10 students = 10 × 14 = 140
Total age of 15 students including the newly joined 5 students = 15 × 15 = 225
Total age of the new students = 225 − 140 = 85
Average age = 85/5 = 17 years

17. It rained as much as on Wednesday as on all the other days of the week combined. If the average rainfall for the whole week was 3 cms, How much did it rain on Wednesday?
A. 3 cms
B. 10.5 cms
C. 15 cms
D. 2.62 cms
E. 4.5 cms
Answer: B
Explanation:
Let the rainfall on wednesday = 6x.
∴ Rainfall on the remaining days = 6x
Given,
(6x + 6x )/7 = 3
⇒12x = 21
⇒6x = 10.5