Amcat model questions set - 5

1. Which is greatest among 5^1/2 ,11^1/3, 123^1/6 ?
Explanation: Raising each term to their 6th power as the LCM of the denominators of the powers = 6, we get,
${\left( {{5^{{\textstyle{1 \over 2}}}}} \right)^6} = {5^3} = 125$
${\left( {{{11}^{{\textstyle{1 \over 3}}}}} \right)^6} = {11^2} = 121$
${\left( {{{123}^{{\textstyle{1 \over 6}}}}} \right)^6} = 123$
Hence, ${5^{{\textstyle{1 \over 2}}}}$ is greatest.

2. A fair is coin is tossed repeatedly. If head appears on first four tosses then what is the probability of appearance of tail in the fifth toss?
Explanation:
As the given coin is a fair coin, the probability of getting tail on the fifth toss is independent of the out comes in the previous 4 tosses. So probability = 1/2

3. Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should these be mixed to get an alloy 15 times as heavy as water ?
Explanation:
Let us say, water weighs 1kg/1 liter. Then Gold weighs 19 kgs and copper weighs 9 kgs.
Assume x kgs of gold and y kgs of copper required to get the required alloy.
We use weighted average formula = ${A_x} = \dfrac{{{n_1}.{A_1} + {n_2}.{A_2}}}{{{n_1} + {n_2}}}$
Therefore, $15 = \dfrac{{x.19 + y.9}}{{x + y}}$
15x + 15y = 19x + 9y
4x = 6y ⇒ x/y = 3 : 2
So Gold and Copper should be mixed in the ratio 3 : 2.

4. 7:11::31: ?
1. 33
2. 37
3. 39
4. 42
Explanation:
The prime number after 7 is 11, therefore the prime number after 31 is 37

5. From the given choices select the odd man out
1. 11, 3, 3, 17
2. 41, 5, 3, 47
3. 71, 7, 3, 17
4. 37, 14, 19, 7
5. 67, 71, 3, 5
Explanation:
All the numbers in those options are prime numbers except 14 in option 4.

6. Find the number of zero's in the expression 1^1 * 2^2 * 3^3 * 4^4 * 5^5 * ……..10^10.
Explanation:
To find the number of zero's we have to find the powers of 2's and 5's.
Powers of 2's = 2 + 4 + 6 + 8 + 10 = 26
But 4, 8 contains more 2's which are equal to 4 + 8 = 12
8 contains another eight 2's.
So total 2's = 46
Number of 5's = 5 + 10 = 15
So trailing zeroes = 15.

7. What are the unit's digits of 3⁶⁹, 6⁸⁶⁴, 4⁷²⁵ respectively ?
1. 9,6 and 6
2. 6, 6 and 6
3. 3,6 and 4
4. None of these
Explanation:
Cyclicity of 3 is 4. 3⁶⁹ = ${\left( {{3^4}} \right)^k}{.3^1}$ = ${\left( 1 \right)^k}{.3^1}$ = 3
Power of 6 always gives units digit 6 only.
If power of 4 is odd, then we will get 4 as units digit, if power of 4 is even, then we get 6 as units digit.
Hence, Option 3 is correct.

8. The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:
1. 1
2. 2
3. 3
4. 4
Answer: 2
Explanation:
Let the numbers be 13a and 13b.
Then, 13a × 13b = 2028
⇒ ab = 12
Here a and b are coprimes. Now, the co-primes with product 12 are (1, 12) and (3, 4).
[Note: Two integers a and b are said to be coprime or relatively prime if they have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1 ]
So, the required numbers are (13× 1, 13×12) and (13×3, 13×4).
Hence, there are 2 such pairs.

9. If 72X23Y is divisible by 72, then what is the value of X and Y?
1. X=0;Y=1
2. X=2;Y=3
3. X=7;Y=2
4. X=2;Y=2
Correct Option : 4
Explanation:
If a number has to be divisible by 72, then it has to be divisible by both 8 and 9.
Divisibility for 8 is last three digits should be divisible by 8. So Y takes only 2.
Now divisibility for 9 is sum of the digits should be divisible by 9. So by substituting Y = 2, the sum is divisible by 9 if X = 2.
So X = 2 and Y = 2

10. (((1/8)-1)-4)-1) =
1. 4096
2. - 4096
3. 4092
4. 4090
Correct Option:
Explanation:
We hae to use BODMAS rule. First simplify the terms in the bracket.
(((1/8)-1)-4)-1) = $\left[ {\left( {\dfrac{1}{8} - 1} \right) - 4} \right] - 1$ = $\left[ { - \dfrac{7}{8} - 4} \right] - 1$ = $ - \dfrac{{39}}{8} - 1$ = $ - \dfrac{{47}}{8}$

Amcat model questions - 4

1. Manav drives from his home to the nearest metro station at an average speed of 40km. From station, he boards a train that takes him to his office at a speed of 80km. the entire distance covered by him is 52km and the entire journey took him 1 hour. Find the distance between the station from where he boards the train and his office.
Explanation:
Let the distance from his home to station = x
Therefore, $\dfrac{x}{{40}} + \dfrac{{52 - x}}{{80}} = 1$
$ \Rightarrow \dfrac{{2x + 52 - x}}{{80}} = 1$
⇒ x + 52 = 80
⇒ x = 28
Hence, the distance from office to station = 52 - x = 52 - 28 = 24 km

2. Santa Singh was driving a car at a uniform speed. He saw a milestone showing number x0y. After travelling for an hour, he saw another milestone showing number yx. After another hour, he saw the next milestone showing the same two digits, but in the reverse order, i.e. xy. What was the average speed of the car?

Explanation:

The first milestone xoy in the decimal format = 100x + y

Second mile stone yx in the decimal format = 10y + x

Third mile stone xy in the decimal format = 10x + y

As the speed of the car is constant, difference between the two consecutive mile stones should be constant.

Therefore, 100x + y - (10y + x) = (10y + x) - (10x + y)

⇒ 99x - 9y = 9y - 9x

⇒ 11x - y = y - x

⇒ 12x = 2y

⇒ $\dfrac{x}{y} = \dfrac{1}{6}$
So the first mile stone = 106 and second mile stone = 61. Therefore, speed of the car = 106 - 61 = 45 kmph

3. If a and b are natural numbers and a-b is divisible by 3, then a³-b³ is divisible by:

1. 3 but not by 9

2. 9

3. 6

4. 27
Answer: 2

Explanation: ${a^3} - {b^3} = {(a - b)^3} + 3ab(a - b)$
Given that a - b is divisible by 3. So let a - b = 3k
Then, ${(3k)^3} + 3ab(3k)$ = $27{k^3} + 9abk$
So the given expression is divisible by 9.

4. A number becomes a perfect square when we subtract 1 from it.which of the following cannot be the last digit of that number

1. 2
2. 4
3. 5
4. 0
Answer: 2
Explanation:
Square of any number should end with 0, 1, 4, 5, 6, 9 only.
So the given number should end with, 1, 2, 5, 6, 7, 0. It cannot be 4.

5. 20 Men can do a job in 10 days, working 8 hrs a day if women is 33.33% more efficient than men. How many women will it take to finish the same job in 10 days working 6 hrs a day?

1) 10
2) 12
3) 15
4) 16
5) 20
Answer:
Explanation:
Let the capacity of each man = 3 units/hour, then capacity of woman = 4 units/hour. ($\because$ woman is 33.33% more efficient than man)
Total work done by man = 20 × 8 × 10 × 3 = 4800 units.
Now Let $x$ woman required to complete the job. Total work done by $x$ woman = $x$ × 4 × 6 × 10 = 240x
Equating the work, 240x = 4800 ⇒ x = 20.

6. Sujitha invests 7% i.e. 2170, of her monthly salary in mutual funds. Later she invests 18% of her monthly salary in recurring deposits, Also she invests 6% of her salary on NSC's . What is the total annual income invested by Sujitha ?
Explanation:

Let her monthly salary = x and she invests 7% of her salary in mutual funds which equal to Rs.2170

Therefore, 7%(x) = 2170 ⇒ x = 31000

Her total investments per month = 7%+18%+6% =31% of her monthly salary.

So per month she invests = 31% (31000) = Rs.9610

Her total investments per annum = 9610 × 12 = 1,15,320

7. Ishan spent 35,645 on buying a Bike, 24,355 on buying a Television ,and the remaining 20% of the total amount he had as cash with him. What was the total amount ?
Explanation:
He has 20% left. So he spent 80% of his money.
⇒80% (x) = 35,645 + 24,355 = 60,000
⇒ x = 75,000

8. Manoj sold an article for 15,000. Had he offered a discount of 10 % on the selling price, he would have earned a profit of 8 %. What is the Cost price?

Explanation:
If he offered 10%, then new selling price = 90% (15000) = Rs.13500
At this selling price, he got a profit of 8%.
So cost price = $\dfrac{{13500}}{{108\% }}$ = Rs.12,500.

9. A man bought oranges at the rate of 8 for Rs.34 and sold them at the rate of 12 for Rs.57. How many oranges should be sold to earn a net profit of Rs.45 ?
Explanation:
To solve these type of questions, equate oranges in both cases. Let us say, he bought 24 oranges.
Then, his cost price = Rs.102
Selling price = Rs.114
Profit = Rs.12.
So while selling 24 oranges he made a profit of Rs.12. i.e., For each rupee, he has to sell 2 oranges.
To make a profit of Rs.45, he has to sell 90 oranges.

10. Naresh purchased a TV set for Rs.11,250 after getting discount of 10% on the labeled price. He spent Rs.150 on transport and Rs.800 on installation. At what price should it be sold so that the profit earned would be 15% ?

Explanation:
Here labelled price is irrelevant. His total costprice = 11,250 + 150 + 800 = 12,200
Selling price to get 15% profit = 115% (12200) = 14030

Amcat model questions set - 1

1. Rahul purchased 7 DVDs each of which costs Rs.17. He gave a five hundred rupee note to the shopkeeper. The amount returned to him is divisible by?

A. 3

B. 7

C. 9

D. 11

Answer: A

Explanation:

7 DVD's cost = Rs.17×7 = Rs.119

Amount returned by the shopkeeper = 500 – 119 = 381

Checking from the options, This is divisible by 3

2. An investment earns 4 paisa per rupee invested. If at the end of the year, the interest earned by an investment is Rs.100,then the investment is equal to?

A. 3000

B. 2500

C. 3500

D. 1500

Answer: B

Explanation:

Interest rate = $\dfrac{{{\rm{Interest}}}}{{{\rm{Principal}}}}{\rm{ \times 100}}$ = $\dfrac{\text{4 ps}}{\text{100 ps}}{\rm{ \times 100}}$ = 4%
Given that R% (P) = Rs.100 ⇒4%(P) = 100 ⇒P = 2500

3. The time in the clock is 8:20. What is its mirror image?

A. 3: 20

B. 3: 40:40

C. 2: 25

D. 4: 20

Answer: B

Explanation:

There is a simple formula to find the mirror image. Subtract the given time from 11:60. So mirror image = 11:60 - 8:20 = 3:40

4. In a school, for a student out of 100 he got 74 of average for 7 subjects and he got 79 marks in the 8th subject. what is the average of all the subjects?

A. 76.251

B. 80.25

C. 74.265

D. 74.625

Answer: D

Explanation:

Average = $\dfrac{\text{Sum of observations}}{\text{Number of observations}}$
Sum of all the marks = 74×7 + 79 = 597
Average = $\dfrac{{597}}{8}$ = 74.625

Alternative method:
In the 8th subject he additionally got 5 marks and these 8 marks are distributed to all 8 subjects equally. Hence average = 74 + 5/8 = 74.625

5. Amaranth told to Amanda in front of a Photo that “He is the son of my father’s son”. Find who is in the picture if Amaranth have no brothers and sisters.

A. Amaranth himself

B. Amaranth’s Uncle

C. Amaranth’s Father

D. Amaranth’s son

Answer: D

Explanation:

Amarnath's father's son is Amarnath himself as he is the only son. Now the photo is son of Amarnath.

6. A train travelling at 250 Km/h overtakes a cyclist who is moving at 10km/h in 45 seconds. Find the length of train in meters?

A. 3000 m

B. 5400 m

C. 6000 m

D. 10800 m

Answer: A

Explanation:

We know that Distance = Speed × Time.

Here Distance = Length of the train; Speed = Relative speed.

Therefore, Length of train = relative speed × time = (250 – 10) $\dfrac{5}{{18}}$ × 45 s = 3000 m

7. The Tremors of earthquake were felt at intervals of 15 seconds. The first tremor was felt at 8:54:57 and last tremor was felt at 10:45:12. How many times were the tremors felt?

A. 484

B. 485

C. 441

D. 525

Answer: C

Explanation:

Difference of times = 10:45:12 - 8:54:57 = 9:104:72 - 8:54:57 = 1:50 :15 = 3600 + 3000 + 15 = 6615 seconds.

Now tremors are felt at the intervals of 15 seconds.

Total = $\dfrac{{6615}}{{15}}$ = 441

8. Soha Ranks 5th in the class. How many students are there in the class?

I) One of her friends got 40th rank which is second last rank

II) Her rank is 17th from the middle

A. Statement I is alone sufficient

B. Statement II is alone sufficient

C. Both the statements put together are sufficient

D. Both the statements put together are not sufficient

E. Either of the statements are sufficient

Answer: E

Explanation:

Statement 1: "One of her friends got 40th rank which is second last rank"

Therefore total no of student is 40+1 = 41

Statement 2: "Her rank is 17th from the middle"

1) Soha Ranks 5th in the class

i.e. There are 4 student ahead of Soha .

2) Her rank is 17th from the middle

i.e. There are 15 students between Soha and middle student

Therefore total students on either side of middle student = 15 + 4 + 1 = 20

Total no of student = 20 (left side of middle student) + 20(right side middle student) + 1(middle student) = 41 ( student)

Hence either of the statements are sufficient.

9. A person is rock climbing at an altitude of 800 m. He go up by 7 mph. and come down by 9 mph. what was his average speed?

A. 7.875 mph

B. 7.125 mph

C. 7 mph

D. 7.5 mph

Answer: A

Explanation:

If distance is same in both cases, average speed = $\dfrac{\text{total distance}}{\text{Total time}}$ = $\dfrac{{2xy}}{{x+y}}$

Given that, x = 7 mph, y = 9 mph

Average speed = $\dfrac{{2 \times 7 \times 9}}{{7 + 9}}$ = 7.875 mph

10. In the reading room of a library, there are 23 reading spots. Each reading spot consists of a round table with 9 chairs placed around it. There are some readers such that in each occupied reading spot there are different numbers of readers. If in all there are 36 readers, how many reading spots do not have even a single reader?

A. 8

B. none

C. 15

D. 16

Answer: C

Explanation:

As there are 23 spots so there are 23 tables and at each table there are 9 chairs.

The condition is:

Each table occupies different no. of people and as there are 36 people so these people can be arranged in each table: 1, 2, 3, 4, 5, 6, 7, 8.

⇒ 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36.

⇒ 8 tables are occupied.

So (23 – 8) = 15 tables have no single reader.

Amcat model questions set - 2

1. What is the largest power of 20 contained in 100!?

A. 56

B. 1

C. 24

D. 2

Answer: C

Explanation:

20 = 5×2^2.

Power of 2 in 100!= $\left[ {\dfrac{{100}}{2}} \right] + \left[ {\dfrac{{100}}{4}} \right]$ + $\left[ {\dfrac{{100}}{8}} \right] + \left[ {\dfrac{{100}}{{16}}} \right]$ + $\left[ {\dfrac{{100}}{{32}}} \right] + \left[ {\dfrac{{100}}{{64}}} \right]$ = 97

Here [ ] is greatest integer function. So only integer parts should be considered for positive numbers.
So highest power of 4 in 100! = ${\left( 2 \right)^{97}} = {\left( {{2^2}} \right)^{48}} \times 2$ = 48 times.
Highest power of 5 in 100! = $\left[ {\dfrac{{100}}{5}} \right] + \left[ {\dfrac{{100}}{{25}}} \right]$ = 24

so, Power of 20 in 100! = least of the two powers = 24

2. A seller uses 900 gm in place of 1 kg.Find his actual percentage of profit or loss when he sells his articles at 5% loss on cost price?

A. 5

B. 6

C. 5.55

D. 20

Answer: C

Explanation:
Let us assume one grams costs Rs.1.
He gives only 900 gm for 1 kg. So cost price = Rs.900
But he collects 5% less on the cost price. So he collects Rs.950 from the customer. ($\because$ This
reduction should be calculated on Rs.1000 as the customer does not know about his cheating).

Profit % = $\dfrac{{50}}{{900}} \times 100$ = 5.55%

3. A coin is tossed thrice. What is the probability that first toss of the coin lands head, second lands tail and third lands tail as well

A. 1/3

B. 1/ 6

C. 1/8

D. 1/10

Answer: C

Explanation:

Total ways when 3 coins are tossed = $2^3$ = 8

Now HTT is one of the way. So required probability = 1/8

Alternative method:

If a coin is tossed, getting heads or tails has the probability = 1/2

We have 3 such cases here so = 1/2 × 1/2 × 1/2 = 1/8

4. If the LCM of a and (a>b) is 667 the the value of 7b – 5a is

Answer: 16
Explanation:
667 can be written as 29 × 23. So a = 29, b = 23.
7b – 5a = 7×29 – 5×23 = 16

5. The money at compound interest amount to thrice it self in 16 years. So,in how many years it will be 27 times itself ?

Answer: 48
Explanation:
Let P be the principal.
It will thrice itself in 16 years. So it becomes = 3×P = 3P.
After another 16 years it will be 3×3P = 9P
Another after 16 years it will be 3×9P = 27P
So it will take 48 years to become 27 times.

6. INGENUITY (OPPOSITE)

A. skillfulness
B. cunning
C. inventive
D. dullness

Answer: 48

Explanation:

Ingenuity means the quality of being original, clever. It came from the root 'genuine' which is nobility. So dullness can be opposite to this.

7. PRANKISH (OPPOSITE)
A. whimsical
B. Machiavellian
C. impish
D. serious
Answer:

Explanation: D

Prank means childish behaviour , to put pranks on others. So opposite to this is serious. Machiavellian means cunning, and impish means lack of seriousness.

8. PERT (OPPOSITE)

A. impudent
B. brash
C. savvy
D. polite

Answer: D

Explanation:

Pert means shameless boldness. Impudent also means the same. Brash means the same as impertinent, impudent. Savvy means knowledgeable. So Polite is opposite to pert.

9. GAUNT (OPPOSITE)

A. emaciated
B. sombre
C. plump
D. piquant

Answer: C

Explanation:

Guant means lean and haggard, especially because of suffering, hunger, or age. Opposite to this is plump - having a full rounded shape. Emaciated means weak and thin. Sombre means gloomy, dark and dull. Piquant has two meanings. 1. having sharp taste 2. interesting

10. He protracted illness has reduced him ________ skeleton
A. THROUGH
B. TILL
C. TO
D. ROUND
E. FROM

Answer: C
Reduced is followed by the preposition to.

Amcat model questions - 3

For the following questions find the word which is similar to the sentence or word given.

1. EGREGIOUS

A. pious
B. outrageous
C. anxious
D. sociable
E. gloomy

Answer: B
Explanation:
Egregious means very bad or outrageous. Pious means having belief in God. Sociable means being friendly. Gloomy means dull.

2. GARNISH

A. paint

B. garner

C. adorn

D. abuse

E. banish

Answer: C

Explanation:

Garnish means decorate. You hear this word mostly on TV in culinary episodes. After preparing a dish the anchor says that you have to adorn this with badam or something to give some good taste or look!! Adorn is similar to this. Garner means collect. Abuse means criticize. Banish means eradicate or remove.

33. EMACIATED

A. garrulous
B. primeval
C. vigorous
D. disparate
E. thin
Answer: E

Explanation:

Emaciated means very thin or weak. Garrulous means talkative or chatter box. Primeval means earliest time in history. Vigorous means intense. Disparate means separate and cannot be compared.

4. Flowers and insects or anything lasting only for a day.

A. Transitional
B. Ephemeral
C. Transient
D. Transitory
E. Monumental
Answer: B

Explanation:

One word substitution for the above definition is Ephemeral. Transient also similar. But for flowers we can use ephemeral. Transient smile means which lasts for short time. Transitory is not permanent. Monumental means something which is very important.

5. The liberal school of thought trusts in education reform, and the sporadic use of force to remedy the depravity of certain isolated individuals
or groups.
A. Infrequent, irregular
B. Persistent, constant
C. Continuous
D. Sparing
E. Corrective and preventive both

Answer: A

Explanation:

Sporadic means happening at irregular intervals. Persistent means stubborn which won't move. Sparing means spending economically.

6. He has got a meretricious style which does not produce a lasting effect.
A. Capricious
B. Whimsical
C. Flamboyant
D. Pretentious
E. Showily attractive

Answer: E

Explanation:

Meretricious means showy but has no real value. Whimsical means something lasts for short time like fashion. Flamboyant means having attraction due to their charm. Pretentious means trying to attract others.

7. His style is quite transparent.

A. verbose

B. involved

C. lucid

D. witty

Answer: C

Explanation:

Transparent means clear. So lucid is the synonym. Verbose means using more words than necessary.

Witty remarks are using words in such a way that creates humor.

8. Only those who are gullible take every advertisement seriously.

A. fallible

B. enthusiastic

C. unsuspecting

D. unrealistic

Answer: C

Explanation:

Gullible people are who easily believes everything. So unsuspecting is the right synonym. Fallible means capable of making mistakes.

9. We didn't believe in his statement, but subsequent events proved that he was right.

A. later

B. many

C. few

D. earlier

Answer: A

10. The angry villagers have lynched two suspected child-lifters already.

A. beaten up

B. captured

C. killed

D. mutilated

Answer: C

Lynch means killing without legal trial. Mutilated means causing injury.

Accenture Previous questions - 4

1. There are two bags A and B. A contains 6 red flowers and 3 pink flowers. where as bag B contains 2 red flowers and 7 pink flowers. One flower is chosen from a bag randomly. What is the probability that the flower chosen is pink?
a. 4/9
b. 1/3
c. 5/4
d. 5/9
Answer : d
Explanation:
Bag A 6 red + 3 pink
Bag B 2 red + 7 pink
Probability of picking 1 pink from bag A is 3/9
Probability of picking 1 pink from bag B is 7/9
Total = 3/9 + 7/9 = 10/9
And probability of selecting a bag is 1/2
So finally probability of choosing a pink flower = 1/2(10/9) = 5/9

2. The sum of a number and its square is 1406. What is the number?
1) 38
2) 39
3) 37
4) 29
Answer: 3
Explanation:
By option Verification 37 + 37 × 37 = 1406

3. How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
A. 40
B. 400
C. 5040
D. 2520
Answer: C. 5040
Explanation:
The Word LOGARITHMS is contain 10 letters.
To find how many 4 letter word we can find from that = 10 × 9 × 8 × 7 = 5040.

4. At 6′o a clock ticks 6 times. The time between first and last ticks is 30 seconds. How long does it tick at 12′o clock
Answer: 66
Explanation:
For ticking 6 times, there are 5 intervals.
Each interval has time duration of 30/5 = 6 secs
At 12 o'clock, there are 11 intervals,
So total time for 11 intervals = 11 × 6 = 66 secs.

5. A man travelled from the village to the post-office at the rate of 25 kmph and walked back at the rate of 4 kmph. If the whole journey took 5 hours 48 minutes, find the distance of the post-office from the village
Answer: 20 km
Explanation:
Average speed = (2 ×a × b)/(a + b) here a = 25 b = 4
Average speed = 2 × 25 × 4/(25 + 4) = 200/29 kmph.
Distance covered in 5 hours 48 minutes = Speed × time
Distance = (200/29) × (29/5) = 40 kms
Distance covered in 5 hours 48 minutes = 40 kms
Distance of the post office from the village = (40/2) =20 km.

6. One year payment to the servant is Rs. 200 plus one shirt. The servant leaves after 9 months and receives Rs. 120 and a shirt.Then find the price of the shirt.
Answer: 120
Explanation:
12 months == Rs 200 + shirt --(1)
9 months == Rs 120 + shirt --(2)
After subtracting equation (2) from (1) we get,(shirt is cancelled)
3 months = Rs 80
12 months = (80 × 12)/3= 320
Hence from equation (1) we get 320 = 200 + shirt
Therefore shirt = 120 Rs/-

7. In a class there are 45 pupil, out of them 12 are in debate only and 22 in singing only. Then how many in both?
Answer: 11
Explanation:Total pupil = 45
Debate + Singing = 12 + 22 = 34
The intersection for two = 45 – 12 – 22 = 11 play both games.

8. Silu and Meenu were walking on the road.
Silu said, "I weigh 51 Kgs. How much do you weigh?"
Meenu replied that she wouldn't reveal her weight directly as she is overweight.
But she said, "I weigh 29 Kgs plus half of my weight."How much does Meenu weigh?
Answer: 58
Explanation:
It is given that Meenu weighs 29 Kgs plus half of her own weight.
It means that 29 Kgs is the other half. So she weighs 58 Kgs.
Solving mathematically, let's assume that her weight is A Kgs.
A = 29 + A/2
2 × A = 58 + A
A = 58 Kgs.

9. What is the 56743 rd term in the series 1234567891011121314…….?
a) 1
b) 3
c) 7
d) 5
Answer: C
Explanation:
1 to 9 = 9 no.s 1 digit each no.
9 to 99 = 90 no.s 2 digit each,Total digit = 90 × 2 = 180 terms
99 to 999 = 900 no.s 3 digit each,total digit = 900 × 3 = 2700
999 to 9999 = 9000 no.s 4 digit each,total digit = 9000 × 4 = 36,000
Till Now 999,we have = 9 + 180 + 2700 = 2889 digits
Upto 9999 we have = 2889 + 36000 = 38889 digits
56743 – 38889 = 17854
After 9999 each no. has 5 digit
So 17584/5= 3570 with remainder 4.
3570th no after 9999 =9999+3570=13569
Next term=13570.
4th digit =7 so answer=7

10. A cycled from P to Q at 10 kmph and returned at the rate of 9 kmph. B cycled both ways at 12 kmph. In the whole journey B took 10 minutes less than A. Find the distance between P and Q.
Answer: 3.75 km
Explanation:
Let the distance between P and Q = d km
A - time = d/10 + d/9 = 19 d/90 hours
B - time = 2 d/12 = d/6 hours
10 minutes = 1/6 hours
Thus 19 d/90 – d/6 = 1/6
(19 d – 15 d)/90 = 1/6
4 d/90 = 1/6
thus d = 15/4 km = 3.75 km

11. A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:
A. 18
B. 24
C. 42
D. 81
Answer:
Explanation:
Just go in reverse order.
Check the options with th subtracting 18 from each option for getting reverse number.
42 – 18 = 24 (which is in reverse).
So answer is 42.

Accenture previous placement papers - 5

1. If a certain computer is capable of printing 4900 monthly credit card bills per hour, while a new model is capable of printing at a rate of 6600 per hour, the old model will take approximately how much longer than the new model to print 10000 bills?
Answer: 31 minutes
Explanation:
Old model is capable of printing at a rate of 4900 per hour
New model is capable of printing at a rate of 6600 per hour
Old model time taken to print 10000 cards = 10000/4900 = 100/49
New model time taken to print 10000 cards = 10000/6600 = 100/66
Old model – new model: 100/49 - 100/66 = 1700 /(49 × 66) = 850/(49 × 33) = 0.525 hrs => 31 mins
Therefore, the old model will take approximately 31 mins longer than the new model to print 10000 bills

2. 3 men and 8 women complete a task in same time as 6 men and 2 women do. How much fraction of work will be finished in same time if 4 men and 5 women will do that task.
1) 5/6
2) 6/13
3) 7/9
4) 11/12
5) 11/15
6) 13/14
Answer: 6
Explanation:
3 m + 8 w = 6 m + 2 w
3 m = 6 w
1 m = 2 w
Therefore 3 m + 8 w = 14 w
4 m + 5 w =13 w
Answer is 13/14

3. How can a cake(circular) be cut into 8 pieces by making just 3 cuts?
Explanation:
Cut the cake using three mutually perpendicular planes. It leaves 8 pieces, one each in each octant.

4. A number of cats got together and decided to kill between them 999919 mice. Every cat killed an equal number of mice. Each cat killed more mice than there were cats. How many cats do you think there were?
Answer:
Explanation: 991
999919 = 1000000 – 81 = $1000^2$ – $9^2$ = (1000 + 9)(1000 – 9) = 1009 × 991.
Since there were more mice than there were cats, 991 cats killed 1009 mice each.

5. An alloy of zinc and copper contains the metals in the ratio 5 : 3. The quantity of zinc to be added to 6 kg of the alloy so that the ratio of the metal may be 3 : 1 is:
A)3
B)6
C)8
D)9
Answer: C
Explanation:
In sixteen kg of alloy 10 kg of zinc and 6 kg copper is present
To make the ratio 3:1 we must add 8 kg of zinc to make it 18 kg of zinc and 6 kg copper
So answer is 8.

6. A class consists of 100 students, 25 of them are girls and 75 boys; 20 of them are rich and remaining poor; 40 of them are fair complexioned. The probability of selecting a fair complexioned rich girl is
Answer: 1/50
Explanation:
The probability of selecting girl is: 25/100 = 1/4
The probability of selecting rich is: 20/100 = 1/5
The probability of selecting fair complexioned is: 40/100 = 2/5
Three are independent;probability of rich and fair complexioned girl is:
(1/4) ×(1/5) × (2/5) = 1/50

7. If one-third of one-fourth of a number is 15, then three-tenth of that number is:
A. 35
B. 36
C. 45
D. 54
Answer: D
Explanation:
The number is 1/3 of 1/4 is =15 then 1/3 × 1/4 = 15
Number is 180 then 180 × 3/10 = 54

8. 100 oranges are bought at the rate of Rs. 350 and sold at the rate of Rs. 48 per dozen. The percentage of profit or loss is:
A) 100/7% gain
B) 15% gain
C) 100/7% loss
D) 15 % loss
Answer:A
Explanation:
C.P. of 100 orange=350
S.P. of 12 is 48 i.e, 4 of each now of 100 will be 400
So profit = 400 – 350 = 50
profit = $\dfrac{{profit × 100\% }}{{cp}}$ i.e 100/7% gain

9. If 3/p = 6 and 3/q = 15 then p – q = ?
A) 1/3
B) 2/5
C) 3/10
D) 5/6
E) None of the above
Answer: C
Explanation:
$\dfrac{{3}}{{p}}$ = 6 , p = $\dfrac{{3}}{{6}}$ = $\dfrac{{1}}{{2}}$and
$\dfrac{{3}}{{q}}$ = 15 , q = $\dfrac{{3}}{{15}}$ = $\dfrac{{1}}{{5}}$ then
p – q = 1/2 – 1/5 = 3/10

10. Two trains leaving from two station 50 miles away from each other with constant speed of 60 miles per hour, approaches towards each other on different tracks. if length of each train is 1/6 mile. when they meet How much time they need to pass each other totally ?
Answer: 10 seconds
Explanation:
The trains are coming towards each other so their relative speed is 60 + 60 = 120 mph
In this case the distance would be addition of lengths of trains.i.e 1/6 + 1/6 = 1/3 m
T = $\dfrac{{d}}{{s}}$ = $\dfrac{{1/3}}{{120}}$ = $\dfrac{{1}}{{1360}}$ h

Basics of share market and Buying shares online

Most of us are fascinated about stock markets. We have heard about numerous stories of people getting rich by investing in stock markets. Is it possible for us to become rich by investing in stockmarket? Yes. If you learn about the basics and fundas of stockmarket, you can surely invest and get benefited.

What is a share?
Let us assume a person named 'x' has got a good business idea. It requires an investment of $\$ $100. But he has only $\$ $20 with him. If this business idea gets into pipeline, it will create lots of jobs and benefits the economy a lot. But how to get started? There are many ways to raise funds, But I am discussing only two important ones. First, he approaches his nearest bank. Bank appraises the business proposal given by 'x' and tells him that they are willing to lend a loan of $\$ $20 to him. Still, our guy fell short by $\$ $60. Now this $\$ $60 will be divided into 60 parts of $\$ $1 each. These are called shares. That means,who ever buys these shares they actually become owners of the business!! Not really! but theoretically it is!! These people are called share holders.

So Mr.x got all the $\$ $100 and rolled out his business. Now the question is what is the benefit for the share holders of this company. Let us assume, Mr.x's company has done a business worth of $\$ $200 in the first year. This is called 'sales'. Now we have to subtract 'cost of goods sold'. This is nothing but raw materials and other consumables. Now we get gross profit. From this we have to subtract 'Over head expenses' which include salaries for employees, rents, power and other expenses. The result is EBITDA. This is nothing but Earnings before interest, tax, depreciation and amortization. The profit and loss account looks like below.

Share price change based on future profit

Interest: Mr.x has taken loan of $\$ $20 and he has to pay back to the bank.
Tax: Each corporate has to pay certain percentage of its profits as tax to the government.
Depreciation: Corporate has bought some equipment to generate goods. But over a period of time, these machines are to be replaced by new ones. So each year corporate, reduces the value of the machines by certain percentage and count it as expense.
Amortization: This is for intangible assets like a patent or license the corporate bought to product goods. This also expire after certain years and this will be counted as expense.

Now in the end, the corporate generates $\$ $17.50 as profit and this belongs to the share holders. We have a total of 60 shares. So earnings per share (EPS) is 17.5/60 = 0.291 per share. So each share generated 29.1% return for each dollar invested in this business. If some one keep their money in savings account or in time deposit, they give only 5 to 8% return.

Where to buy stocks and How to buy?
Suppose, you have some savings and you are interested in buying some good company shares.

This is where stock markets come in. There is an authority in each country which controls buying and selling of shares. In India, it is SEBI (Securities and Exchange board of India). There are two big stock exchanges in India. BSE (Bombay stock exchange), NSE (National stock Exchange). An individual is not allowed directly to buy or sell their share but through a financial intermediary called 'Stock broker'. These brokers buy and sell shares on behalf of you for which they charge some percentage (Usually 0.05% to 0.5%).

Share price appreciation:

As we have seen that $\$ $1 invested in this firm, has a capacity to pay 29.1% return, there are some people who wants to buy this share for more. Let us say, if some one buys this share for $\$ $2, then still this share gives return of 14.55% which is still good. So stock price automatically goes up because there is demand for that stock. Similarly, on the down side, if company has not done well in a particular financial year, the stock price may go down and investor looses his money temporarily. This is the risk associated with investing in stocks.

How to buy stocks online?
To buy and sell stocks online is called online trading. If you have "Demat account" and "Trading account", you can directly buy or sell stock from your home using online trading platform provided by your stock trading company. If buy shares using your trading account and your share will be saved in Demat account. To open these account you have to go to "Stock broking offices". There are many stock broking offices available. For example in India, Karvy, Kotak securities, Zen Money, HDFC securities are some examples. You can enquire in your city for well noted offices for stock trading. To see an example of stock Trading platform click here

Documents required to open a "Demat Account":
You need "PAN card", address proof, and Bank account statement. You need to carry these copies along with a crossed Cheque. There is an application form, where you need to sign the required documents and your account will be opened in 3 to 4 days.

Charges Associated with opening Demat and Trading accounts:
Usually the charges range from Rs.300 to Rs.800 depends on the broking firm.

Cryptarithmetic problems with explanations

Cryptarithmetic problems are where numbers are replaced with alphabets. By using standard arithmetic rules we need to decipher the alphabet.

General Rules:
1. Each alphabet takes only one number from 0 to 9 uniquely.
2. Two single digit numbers sum can be maximum 19 with carryover. So carry over in problems of two number addition is always 1.
3. Try to solve left most digit in the given problem.
4. If a × b = kb, then the following are the possibilities
(3 × 5 = 15; 7 × 5 = 35; 9 × 5 = 45) or (2 × 6 = 12; 4 × 6 = 24; 8 × 6 = 48)

Exercise

1. Find the sum of the values of A, B and C if $ABC = A! + B! + C!$ where ABC is a three digit number
a. 7
b. 8
c. 9
d. 10

2. Find the value of $T + E + N$ if

$$\begin{array}{*{20}{c}}
{ONE} \\
{ONE} \\
{ONE} \\
{ONE} \\\hline
TEN \\ \hline
\end{array}$$

a. 11
b. 12
c. 15
d. 17

3. The following questions are based on the following multiplication, where each digit has been replaced by an alphabet.
\[\begin{array}{r}
&J\ \ \ \ E\\
&\times \ \ \ \ \ \ \ \ \ \ B\ \ \ \ B\\
\hline
&J\ \ \ \ E\\
&J\ \ \ \ E\ \ \ \ A\\
\hline
&B\ \ \ \ A\ \ \ \ D\ \ \ \ E
\end{array}\]
Find the value of J.
a. 9
b. 8
c. 7
d. 6

4. From the multiplication below, What is the value of N + A + M + E?

a. 15
b. 17
c. 18
d. 19

5. Find the value of MAY in the following multiplication Table

a. 328
b. 239
c. 146
d. 319

6. If SEND + MORE = MONEY then find M + O + N + E + Y
\[\begin{array}{r}
&S\ E\ N\ D \\
+&M\ O\ R\ E \\
\hline
&M\ O\ N\ E\ Y
\end{array}\]
a. 11
b. 13
c. 14
d. 18

7. Find the value of B + A + D if each alphabet represent an unique single digit from 0 - 9