AMCAT

# AMCAT previous questions

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
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
Explanation:
Interest rate = $\frac{\mathrm{I}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}}{\mathrm{P}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{p}\mathrm{a}\mathrm{l}}×100$ = $\frac{\text{4 ps}}{\text{100 ps}}×100$ = 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
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
Explanation:
Average = $\frac{\text{Sum of observations}}{\text{Number of observations}}$
Sum of all the marks = 74×7 + 79 = 597
Average = $\frac{597}{8}$ = 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
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
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) $\frac{5}{18}$ × 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
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 = $\frac{6615}{15}$ = 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
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
Explanation:
If distance is same in both cases, average speed = $\frac{\text{total distance}}{\text{Total time}}$ = $\frac{2xy}{x+y}$
Given that, x = 7 mph, y = 9 mph
Average speed = $\frac{2×7×9}{7+9}$ = 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
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.

1. What is the largest power of 20 contained in 100!?
A. 56
B. 1
C. 24
D. 2
Explanation:
20 = 5×22.
Power of 2 in 100!= $\left[\frac{100}{2}\right]+\left[\frac{100}{4}\right]$ + $\left[\frac{100}{8}\right]+\left[\frac{100}{16}\right]$ + $\left[\frac{100}{32}\right]+\left[\frac{100}{64}\right]$ = 97
Here [ ] is greatest integer function.  So only integer parts should be considered for positive numbers.
So highest power of 4 in 100! = ${\left(2\right)}^{97}={\left({2}^{2}\right)}^{48}×2$ = 48 times.
Highest power of 5 in 100! = $\left[\frac{100}{5}\right]+\left[\frac{100}{25}\right]$ = 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
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 % = $\frac{50}{900}×100$ = 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
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
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 ?
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
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

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
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
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
Reduced is followed by the preposition to.

1. EGREGIOUS
A. pious
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.

2. GARNISH
A. paint
B. garner
D. abuse
E. banish
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

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

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
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

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
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.

A. fallible
B. enthusiastic
C. unsuspecting
D. unrealistic
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

10. The angry villagers have lynched two suspected child-lifters already.
A. beaten up
B. captured
C. killed
D. mutilated
Lynch means killing without legal trial.  Mutilated means causing injury.

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, $\frac{x}{40}+\frac{52-x}{80}=1$
$⇒\frac{2x+52-x}{80}=1$
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
$\frac{x}{y}=\frac{1}{6}$
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
Explanation: ${a}^{3}-{b}^{3}=\left(a-b{\right)}^{3}+3ab\left(a-b\right)$
Given that a - b is divisible by 3. So let a - b = 3k
Then, $\left(3k{\right)}^{3}+3ab\left(3k\right)$ = $27{k}^{3}+9abk$
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
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
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 = $\frac{13500}{108\mathrm{%}}$ = 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

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,
${\left({5}^{\frac{1}{2}}\right)}^{6}={5}^{3}=125$
${\left({11}^{\frac{1}{3}}\right)}^{6}={11}^{2}=121$
${\left({123}^{\frac{1}{6}}\right)}^{6}=123$
Hence,  ${5}^{\frac{1}{2}}$ 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 = ${A}_{x}=\frac{{n}_{1}.{A}_{1}+{n}_{2}.{A}_{2}}{{n}_{1}+{n}_{2}}$
Therefore, $15=\frac{x.19+y.9}{x+y}$
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
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) = $\left[\left(\frac{1}{8}-1\right)-4\right]-1$ = $\left[-\frac{7}{8}-4\right]-1$ = $-\frac{39}{8}-1$ = $-\frac{47}{8}$