Quantitative Aptitude

1. The ratio of age of A and B is x:y. If A’s age is increased by 3 years and B’s age is increased 2 years then new ratio of their ages becomes 24:25.Given that the sum of their actual ages is 93 years. Find the actual ratio of their ages.

(a) 21 : 22

(b) 42 : 45

(c) 45 : 48 

(d) can’t be determined

2. a : b = 4 : 9 if 4 is added to both of the numbers then the new ratio becomes 21 : 46. What is the difference between a and b?

(a) 80

(b) 100

(c) 125

(d) 130

3. 6 pumps of kirlosker can fill a tank in 7 days and 2 similar pumps of USHA can fill the same tank in 18 days. What is the ratio of the efficiency of a Kirlosker pump and a USHA pump?

(a) 6 : 7

(b) 7 : 6

(c) 7 : 54

(d) can’t be determined

4. 16 person can reap 1/5th field in 6 days. How many person (with same efficiency) are required to reap rest of the field in 8 days?

(a) 27 

(b) 54 

(c) 48

(d) 64

5. Pertrol is 7 times heavy than Kerosene and Castrol mobil is 18 times as heavy as Kerosene. What should be the ratio of petrol and mobil in the new mixture to get the mixture which must be 11 times as heavy as kerosene?

(a) 3 : 4

(b) 7 : 4

(c) 9 : 19

(d) 9 : 10

6. A girl buys 2 pigeons for Rs. 182. She sells one at a loss of 5% and another at a profit if 8%. But she neither gains nor loses on the whole. Find the price of pigeon which has sold at a profit:

(a) Rs. 112

(b) Rs. 85

(c) Rs. 70

(d) can’t be determined

7. The ratio of price of Cello and Parker pens in 2000 were in the ratio of 3 : 5. In 2005 the price of Cello pen trebles itself and the price of Parker pen is increased by Rs. 100, then the new ratio of prices of the same pens becomes 4 :5. What was the original price of the Parker pen in 2000?

(a) Rs. 60 

(b) Rs. 80

(c) Rs. 100

(d) Rs. 120

8. A goldsmith has 361 rings of gold. He sells some of them at a loss of 4% and rest at a profit of 15% marking overall profit of 8%. Find the no. of rings sold at a profit of 15%:

(a) 171

(b) 133

(c) 218

(d) 228

9. Michel travelled from New York to New Jersey covering total distance of 250 miles in 8 hr. partly by car at 30 miles/hr. and rest by train at 35 miles/hr. The distance travelled by car is:

(a) 150 miles

(b) 80 miles

(c) 220 miles

(d) 180 miles

10. A rabit takes 22 leaps for every 17 leaps of cat and 22 leaps of a rabit are equal to 17 leaps of the cat. What is the ratio of the speeds of rabit and cat?

(a) 1 : 1

(b) 484 : 289

(c) 17 : 22

(d) none of these

Solution

1. x+y=93  ……………(i)

And (X+3)/(y+2)=24/25

25x-24y=(-27) ……….(ii)

From equation number (i) and (ii)

x=45 and y=48

2. a/b=4x/9x and (a+4)/(b+4)=21/46

a=80 and b=180 

∴b-a=100 

3. The number of days required by a single Kirlosker pumps to fill the tank=6×7=42 days and the number of days required by a single USHA pump to fill the same tanks=2×18=36 days.

Now, since efficiency is inversely proportional to the number of days. Hence,

(Efficiency of on K-pump)/(Efficiency of U-pump)=36/42=6/7 

4. 1/5th field can be reaped by 96 man days

∴4/5th field can be reaped by 96×4=384 man days

Now, since there are only 8 days so required number od men=384/8=48  men

5. If the weight of kerosene be k kg/unit volume, then 

Weight of petrol= 7 k/unit volume

Weight of Castrol=18 k/unit volume

Required weight of the mixture=11 k/unit volume

By Alligation 

The required ratio is 7 : 4. 

6. By Alligation 

The ratio of price of pigeons sold at loss and profit respectively are in the ratio of 8 : 5

∴ Cost price of profitable pigeon=5/(8+5)×182=Rs.70.

7. C/R=3x/5x

Again  C/R=(3x)3/(5x+100)=4/5

x=16 

∴ Price PARKER pen in 2000 was Rs. 80.

8. By Alligation

Now, we get the ratio of no. rings sold at a loss and profit is 7 : 12

∴ Number of rings sold at profit=12/19×361=228

Alternatively: Go through options. 

9. Best way is to go through option consider option (d) 

180/30+70/35=6+2=8 hrs

Hence, (d) is correct.

Alternatively: x/30+(250-x)/35=8

x=180 miles 

Alternatively: Since the Average Speed=(Total Distance)/(Total time)=250/8 miles/hr

∴ By Alligation 

Therefore, the ratio of time taken @ 30 m/hr and @ 35 m/hr is in the ratio of 3 : 1. It means he has travlled @ 30 m/hr for 6 hr.

Therefore, the distance travelled by car is 180.

(∵ Distance=Speed×Time).

10.22/22:17/17=1∶1

Quantitative Aptitude

1. In a shower, 5 cm of rain falls. The volume of water that falls on 2 hectares of ground, is

(a) 100 m^3

(b) 1000 m^3

(c) 10000 m^3

(d) 10 m^3

2. The LCM of two prime numbers x and y (x>y) is 161. The value (3y-x) is 

(a) -2 

(b) -1

(c) 1

(d) 2

3. A is thrice as good as a workman B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in 

(a) 20 days

(b) 221/2 days

(c) 25 days

(d) 30 days

4. 94 is divided into two parts in such a way that fifth part of the first and eighth part of the second are in the ratio 3 :4. The first part is 

(a) 27

(b) 30

(c) 36

(d) 48

5. Of the three numbers, the ratio of the first and the second is 8 : 9 and that of the second and third is 3 : 4. If the product of the first and third number is 2400, then the second number is

(a) 45

(b) 40

(c) 30

(d) 35

6. In what ratio must a grocer mix teas worth Rs. 60 a kg and Rs. 65 a kg so that by selling the mixture at Rs. 68.20 a kg he may gain 10%?

(a) 3 : 2

(b) 3 : 4

(c) 3 : 5

(d) 4 : 5

7. A boat is rowed downstream at 15.5 km/h and upstream at 8.5 km/h the speed of the stream is 

(a) 3.5 km/h

(b) 5.75 km/h

(c) 6.5 km/h

(d) 7 km/h

8. A sum of money amounts to Rs. 6690 after 3 yr and to Rs. 10035 after 6 yr on compound interest. The sum is

(a) Rs. 4000

(b) Rs. 4445

(c) Rs. 4460

(d) Rs. 4520

9. If p=999, then the value of ∛(p(p^2+3p+3)+1) is 

(a) 1000

(b) 999

(c)  998

(d) 1002

10. If (x+1)/x=3, then the value of (x^5+1)/x^5  is 

(a) 123

(b) 126

(c) 113

(d) 129

Answer Key:
1.b
2.a
3.b
4.b
5.a
6.a
7.a
8.c
9.a
10.a

Quantitative Aptitude

1. Which among 2^(1/2),3^(1/3),4^(1/4),6^(1/6) and 12^(1/12) is the largest?

(a) 2^(1/2)

(b) 3^(1/3)  

(c) 4^(1/4)

(d) 6^(1/6) 

2. Consider a sequence where the nth term, tn=n/(n+2),n=1,2,……. . The value of t3×t4×t5×……..×t53 equals-

(a) 2/495

(b) 2/477

(c) 12/55

(d) 1/1485

3. If 1/b=1/3,b/c=2,c/d=1/2,d/e=3  and e/f=1/4, then what is the value of abc/def ?

(a) 3/8

(b) 27/8

(c) 3/4

(d) 27/4

4. If x=-0.5, then which of the following has the smallest value?

(a) 2^(1/x)

(b) 1/x

(c) 1/x^2  

(d) 2^x

5. The sum of four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can possibly be one of these four numbers?

(a) 21

(b) 25

(c) 41

(d) 67

6. When you reverse the digits of the number 13, the number increases by 18. How many other two digit numbers increase by 18 when their digits are reversed?

(a) 5

(b) 6

(c) 7

(d) 8

7. The number of employees in Obelix Menhir Co. is a prime number and is less than 300. The ratio of the number of employees who are graduates and above, to that of employees who are not, can possibly be

(a) 101 : 88

(b) 87 : 100

(c) 110 : 111

(d)97 : 84

8. The rightmost non-zero digit of the number 30^2720 is

(a) 1

(b) 3

(c) 7

(d) 9

9. Let x=√(4+√(4-√(4+√(4-(……..) ∞)) ) ) . Then, x equals

(a) 3

(b) ((√13-1)/2)

(c) ((√13+1)/2)

(d) √13

10. A rectangular floor is fully covered with square tiles of identical size. The tiles on the edges are white and the tiles in the interior are red. The number of white tiles is the same as the number of red tiles. A possible value of the number of tiles along one edge of the floor is

(a) 10

(b) 12

(c) 14

(d) 16 

Answers:
1. (b); LCM of 2, 3, 4, 6, 12=12
(2^1/2)^12, (3^1/3)^12, (4^1/4)^12, (6^1/6)^12, (12^1/12)^12
=(2)^6, (3)^4, (4)^3, (6)^2, (12)^1 
=64, 81, 64, 36, 12
Hence, 3^(1/3) is the largest.

2. Given t_n=n/(n+2), n=1,2,….
Therefore, t_3=3/5, t_4=4/6, t_5=5/7, …., t^53=53/55 
Therefore  t_3 × t_4 × t_5 ×….×t_53 
=3/5 × 4/6 × 5/7 × 6/8 ×…..×51/53 × 52/54 × 53/55 
=(3×4)/(54×55) = 2/495

3. (a); Given that a/b=1/3, b/c=2, c/d=1/2, d/e=3  and e/f=1/4 
Therefore  a/b × b/c × c/d = 1/3 × 2 × 1/2= 1/3 
a/d=a/3   and  c/d × d/e=1/2 × 3 = 3/2 
c/e=3/2 
and e/f  × d/e × b/c × c/d=1/4 × 3 × 2 × 1/2 = 3/4 
b/f= 3/4 
therefore, abc/ def= a/d × c/e × b/f = 1/3 × 3/2 × ¾ = 3/8 

4. (b); Using options, we can solve the question easily. 
Put x=- ½ 
(a) 2^(-2)= ¼ 
(b) 1/(- ½) = -2 
(c) 1/(- a/2)^2 = 4 
(d) 2^(-1/2)=1/√2 
(e) 1/√-(1/2) = √2 

5. (c); Using options, we find that four consecutive odd numbers are 37, 39, 41 and 43. The sum of these 4 numbers is 160, when divided by 10, we get 16 which is a perfect square. 
Therefore, 41 is one of the odd numbers.

6. (b); Let the number be (10x+y), so when the digits of number are reversed the number becomes (10y+x). According the question, (10y+x)-(10x+y)=18
9(y-x)=18      y-x=12
So, the possible pairs of (x, y) are
(1, 3), (2, 4), (3, 5), (4, 6), (5, 7), (6, 8)  and (7, 9). 
But we want the number other than 13. Thus, there are 6 possible numbers ie, 24, 35, 46, 57, 68, 79.
So, total number of possible numbers are 6.

7. (d); Using options, we find that sum of numerator and denominator of 97 : 84 is (97+84)=181 which is a prime number. Hence, it is the appropriate answer.

8. (a) [(30^4]^680 hence, the rightmost non-zero digit is 1. 

9. (c); x=(√(4+√(4-x))  
(x^2-4)=4+√(4-x) 
Now, put the values from option only option (c) satisfies the condition.

10. (b); Let the rectangle has m and n tiles along its length and breadth respectively. 
The number of white tiles 
W=2m+2(n-2)=2(m+n-2)
And the number of red tiles=R=mn-2(m+n-2) 
Given W=R          4(m+n-2)=mn
mn-4m-4n=-8
(m-4) (n-4)=8
m-4=8 or 4  
M=12 or 8 

Therefore 12 suits the option.

Quantitative Aptitude

Problems Based on Numbers 

The counting and exchanging of the articles had been felt by man as a necessity in life since the birth of our civilization. As the counting numbers N = 1, 2, 3,……….   has become a natural part of our life, they are simply called the ‘natural numbers’. The smallest natural number is 1 whereas there is no upper limit for the largest number. Further, if we count zero as the beginning number of N, the whole set viz. 0, 1, 2, 3,………… is called the ‘whole Numbers’. 

If we add or multiply any two natural the result is a natural number. On the other hand, the result of the subtraction or division of two natural numbers may not be a natural number. 

1. Integers : The positive, zero and the negative natural constitute INTEGERS i.e.           

 I=  -3,-2,-1, 0, 1, 2, 3,... 

2. Prime Numbers : Any number which cannot be divided by any other number without the remainder. For instance, there are twenty six prime numbers in the first hundred viz.  2, 3, 5, 7, 11,13,17,19, 23, 29, 31,37,41,43,47,53, 59, 61, 67, 71, 73, 79, 83, 89 and 97. Thus, there are 25 prime numbers in the first hundred. 

3. Composite Numbers : All non-prime numbers are referred as the composite numbers. 

     3. (a) Even Numbers : The numbers divisible by two e.g. 2, 4, 6, 8, 10, 12,……….   

     3. (b) Odd Numbers : The numbers which are not divisible by 2, e.g. 3, 5, 7, 9, 11, 13, 15, 17, 19, 21,……..

4. Consecutive Numbers : A series of numbers in which each number is greater OR smaller than its succeeding or proceeding number by unity e.g. if x is a number, its consecutive are x-1, x, x+1. 

5. Rational Numbers : If p is any integer and q is a non-zero integer, then R = p/q is called a rational number e.g. 2/3,5/6,11/12…….

In general, p can be positive, zero OR negative integers but q > 0. q cannot be zero i.e. q≠0, otherwise R becomes infinite. 

1. The sum of the squares of first ten natural numbers is

(a) 281

(b) 402

(c) 385

(d) 502

2. The sum of the first seventeen prime number is

(a) 440

(b) 329

(c) 498

(d) 382

3. The sum of the prime number below 100 is

(a) 1061

(b) 1058

(c) 1160

(d) None of these

4. The number of prime numbers upto the counting 100 is

(a) 26

(b) 24

(c) 25

(d) 23

5. The multiplication of seven first odd numbers divided by the sum of nine even numbers provides the answer as

(a) 1501.5

(b) 1877.2 

(c) 2413.1

(d) None of these

6. The product of two odd prime numbers is 

(a) even

(b) odd

(c) either even or odd

(d) It depends upon the numbers chosen

7. Zero is counted as

(a) Whole number

(b) Prime number

(c) Integer

(d) a and c both are correct

8. Search the prime numbers from the given list 

2, 12, 21, 37, 53, 101, 72,

(a) 2, 21, 53

(b) 12, 37, 53, 101

(c) 2, 37, 53, 101

(d) 2, 72, 101

9. Two rational numbers lying between 4/5 and 6/7 are

(a) 71/35,5/6

(b) 29/21,5/6

(c) 29/35,57/70

(d) None of these

10. The square root of a number which is divisible by 2, 4, 5 and 8 is 

(a) 900

(b) 800

(c) 1600

(d) 400

Answer Key:
1.c
2.a
3.d
4.c
5.a
6.b
7.d
8.c
9.c
10.c

Quantitative Aptitude

Q1. Two pipes A and B can fill a tank in 20 minutes and 30 minutes respectively. If both pipes are opened together, the time taken to fill the tank is: a) 50 minutes b) 12 minutes c) 25 minutes d) 15 minutes

Q2. A swimming pool has 3 drain pipes. The first two pipes A and B, operating simultaneously, can empty the pool in half the time C, the 3rd pipe, alone takes to empty it. Pipe A working alone, takes half the time taken by pipe B. Together they take 6 hours 40 minutes to empty the pool. Time taken by pipe A to empty the pool, in hours is a) 15 b) 10 c) 30 d) 7 Q3. The percentage of loss when an article is sold at rs 50 is the as that of the profit when it is sold at Rs 70. The above mentioned percentage of profit or loss on the article is a) 10% b) 50/3% c) 20% d) 68/3% Q4. A man had 100 kgs of sugar part of which he sold at 7% profit and rest at 17% profit. He gained 10% on the whole. How much did he sell at 7% profit? a) 65 kg b) 35 kg c) 30 kg d) 70 kg Q5. A shopkeeper lists the price of an article as Rs 500. But he gives a certain discount which allows a certain discount which allows the buyer to pay Rs 500 for the article including 10% sales tax. The rate of discount is a) 10% b) 111/115% c) 100/11% d) 11% Q6. A trader allows a trade discount of 20% and a cash discount of 26/4% on the marked price of the goods and gets a net gain of 205 of the cost. By how much above the cost should the goods be marked for the sale? a) 40% b) 50% c) 60% d) 70% Q7. A sum of money invested at compound interest amount to Rs 650 at the end of first year and Rs 676 at the end of second year. The sum of money is: a) Rs 6000 b) RS 5400 c) Rs 6250 d) Rs 5600 Q8. A loan of Rs 12300 at 5% per annum compound interest, is to be repaid in two equal annual instalments at the end of every year. Find the amount of each instalment. a) RS 6651 b) Rs 6615 c) Rs 6516 d) RS 6156 Q9. A shopkeeper bought 15 kg of rice at the rate of Rs 29 per kg and 25 kg of rice at the rate of rs 20 per kg. He sold the mixture of both types of rice at the rate of Rs 27 per kg. His profit in this transaction is a) Rs 125 b) Rs 150 c) Rs 140 d) Rs 145 Q10. A container contains 60 kg of milk. From this container 6 kg of milk was taken out and replaced by water. This process was repeated further two times. The amount of milk left in the container is a) 34.24 kg b) 39.64 kg c) 43.74 kg d) 47.64 kg Answer Key: 1.b 2.a 3.b 4.d 5.c 6.c 7.c 8.b 9.d 10.c

Quantitative Aptitude

1. A train passes a 50 m long platform in 14 s and a man standing on the platform train passe in 10 s. The speed of the train is?

(a) 24 km/h 

(b) 36 km/h

(c) 40 km/h 

(d) 45 km/h

2. The area of a circle of a radius 5 cm is numerically what per cent of its circumference?

(a) 200 

(b) 225

(c) 240 

(d) 250

3. If 16 men or 20 women can do a piece of work in 25 days, in what time will 28 men and 15 women do it?

(a) 14 2/7 days

(b) 33 1/3 days

(c) 18 3/4 days

(d) 10 days

4. A can go round a circular path 8 times in 40 min, If the diameter of the circle is increased to 10 times the original diameter, the time required by A to go round the new path once travelling at the same speed as before is?

(a) 25 min 

(b) 20 min

(c) 50 min 

(d) 100 min

5. The average wage of 500 workers was found to be Rs. 200. Later on it was discovered that the wages of two workers were misread as 180 and 20 instead of 80 and 220. The correct average wag is?

(a) Rs. 200.10 

(b) Rs. 200.20

(c) Rs. 200.50 

(d) Rs. 201.00

6. The sum of the squares of three consecutive natural numbers is 2030. Then, what is the middle number?

(a) 25 

(b) 26

(c) 27 

(d) 28

7. If doubling a number and adding 20 to the result gives the same answer as multiplying the number by 8 and taking away 4 from the product, the number is?

(a) 2 

(b) 3

(c) 4 

(d) 6

8. If the sum of two numbers is 22 and the sum of their squares is 404, then the product of the numbers is?

(a) 40 

(b) 44

(c) 80 

(d) 88

9.The compound interest on Rs. 10000 in 2 yr at 4% per annum, the interest being compounded half-yearly is?

(a) Rs. 636.80 

(b) Rs. 824.32

(c) Rs. 912.86 

(d) Rs. 828.82

10. If the 4th term of an arithmetic progression is 14 and the 12th term is 70, then the first term is?

(a) - 10 

(b) - 7

(c) + 7 

(d) + 10

ANSWER KEY:
01. d
02. d
03. d
04. c
05. b
06. b
07. c
08. a
09. b
10. b