**AMCAT**

# AMCAT previous questions

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?

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?

Given that R% (P) = Rs.100 ⇒4%(P) = 100 ⇒P = 2500

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?

Sum of all the marks = 74×7 + 79 = 597

Average = 59785978 = 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.

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?

Therefore, Length of train = relative speed × time = (250 – 10) 518518 × 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?

Total = 661515661515 = 441

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

A. Statement I is alone 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?

Average speed = 2×7×97+92×7×97+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?

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.

So highest power of 4 in 100! = (2)97=(22)48×2(2)97=(22)48×2 = 48 times.

Highest power of 5 in 100! = [1005]+[10025][1005]+[10025] = 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?

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. (∵∵ This

reduction should be calculated on Rs.1000 as the customer does not know about his cheating).

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

**Alternative method: **

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

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)

B. cunning

C. inventive

D. dullness

means the quality of being original, clever. It came from the root

‘genuine’ which is nobility. So dullness can be opposite to this.

A. whimsical

B. Machiavellian

C. impish

D. serious

Answer:

means childish behaviour , to put pranks on others. So opposite to

this is serious. Machiavellian means cunning, and impish means lack of

seriousness.

B. brash

C. savvy

D. polite

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.

B. sombre

C. plump

D. piquant

– 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

A. THROUGH

B. TILL

C. TO

D. ROUND

E. FROM

Reduced is followed by the preposition to.

B. outrageous

C. anxious

D. sociable

E. gloomy

Explanation:

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

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

B. primeval

C. vigorous

D. disparate

E. thin

Answer: E

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.

B. Ephemeral

C. Transient

D. Transitory

E. Monumental

Answer: B

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

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

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.

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

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

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, x40+52−x80=1×40+52−x80=1

⇒2x+52−x80=1⇒2x+52−x80=1

⇒ x + 52 = 80

⇒ x = 28

Hence, the distance from office to station = 52 – x = 52 – 28 = 24 km

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?

So the first mile stone = 106 and second mile stone = 61. Therefore, speed of the car = 106 – 61 = 45 kmph

Answer: 2

Given that a – b is divisible by 3. So let a – b = 3k

Then, (3k)3+3ab(3k)(3k)3+3ab(3k) = 27k3+9abk27k3+9abk

So the given expression is divisible by 9.

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.

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?

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. (∵∵ woman is 33.33% more efficient than man)

Total work done by man = 20 × 8 × 10 × 3 = 4800 units.

Now Let xx woman required to complete the job. Total work done by xx woman = xx × 4 × 6 × 10 = 240x

Equating the work, 240x = 4800 ⇒ x = 20.

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:

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

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?

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 = 13500108%13500108% = Rs.12,500.

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.

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% ?

Here labelled price is irrelevant. His total costprice = 11,250 + 150 + 800 = 12,200

Selling price to get 15% profit = 115% (12200) = 14030

Explanation: Raising each term to their 6th power as the LCM of the denominators of the powers = 6, we get,

(512)6=53=125(512)6=53=125

(1113)6=112=121(1113)6=112=121

(12316)6=123(12316)6=123

Hence, 512512 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 = Ax=n1.A1+n2.A2n1+n2Ax=n1.A1+n2.A2n1+n2

Therefore, 15=x.19+y.9x+y15=x.19+y.9x+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.

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 = (34)k.31(34)k.31 = (1)k.31(1)k.31 = 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) = [(18−1)−4]−1[(18−1)−4]−1 = [−78−4]−1[−78−4]−1 = −398−1−398−1 = −478−478