NareshEXERCISE-1 NARESH ADAPA APTITUDE APTITUDE TRAINER TRAINER
1.
Find the number of prime factors of 720. a) 3 c) 4
b) 5 d) 6
2.
How many factors factor s of 720 are even? a) 15 b) 36 c) 8 d) 24
3.
Find the sum of the even factors of 300. a) 728 b) 625 c) 744 d) 600
4.
How many factors factor s of 600 are divisible by 5 but not divisible by 25? a) 24 b) 15 c) 12 d) 8
5.
6.
7.
If A, B and C are prime numbers such that A < B < C and their sum is 80, what is the value of A? a) 3 b) 5 c) Cannot be determined d) None of these When the digits of a two digit number are reversed, the value of the number increases by 27. How many such two digit numbers are possible? a) 3 b) 4 c) 5 d) 6 In the first 500 natural numbers, how many numbers have only three factors? a) 4 b) 5 c) 6 d) None of these
11. Find the last non –zero –zero digit in 100! a) 3 b) 4 c) 2 d) 5 12.
How many consecutive zeroes are at the end of 100!? a) 20 b) 12 c) 22 d) 24
13.
How many natural numbers less than 101 are divisible by either 2 or 3? a) 33 b) 50 d) 67 c) 83
14.
Find the unit digit of the number 17 a) 7 b) 9 c) 3 d) 1
15.
What is the unit digit in the expansion of 8^2^4^8^16^.....? a) 8 b) 4 c) 2 d) 6
16.
Find the unit digit digit of 1! + 2! + 3! + 4! + 5! + 6! + …..+ 100!? a) 3 b) 9 c) 4 d) 0
17.
If 17 + 13 is divided by 15, what is the remainder? r emainder? a) 3 b) 9 c) 0 d) 1
18.
If 18 a) 0 c) 3
19.
If N! has 26 zeroes at the end, what is the maximum value of N? a) 105 b) 134 c) 114 d) 125
8.
In a three digit number, how many numbers have 6 as atleast one of its digits? a) 252 b) 256 c) 189 d) 216
9.
How many three digit numbers are not 20. divisible by 3? a) 333 b) 267 c) 300 d) 600
10.
If a 100 digit number consisting of all 7’s is divided by 8, what is the remainder? a) 5 b) 1 c) 3 d) 4
15
2003
.
15
201
is divided by 7, what is the remainder? b) 1 d) 9
If a person wants to type numbers from 0 to 200, find the number of times he needs to press the number key on the typewriter? a) 200 b) 480 c) 692 d) 492
EXERCISE - 2 1.
2.
3.
4.
5.
Find the sum of natural numbers up to 100 that are divisible by both 2 and 3. a) 816 b) 1024 10. c) 1280 d) 2036 How many natural numbers up to 200 are not divisible by either 2 or 5? a) 60 b) 70 c) 140 d) 80 What is the minimum number that can be added to ‘12345’, to make it a perfect square? a) 142 b) 199 c) 182 d) 162
stops. a) 100 c) 128 11.
When a number is divided by 34, the remainder is 13. If thrice the same number is divided by 17, the remainder is a) 5 b) 3 13. c) 7 d) 2 Find the least possible number which when divided by 7 and 5, leaves a remainder of 2 and 1 respectively. a) 16 b) 9 c) 23 d) 37
7.
When two numbers are divided by 21, they 14. leave a remainder of 4 and 3. What will be the remainder, when the product of these two numbers is divided by 7? a) 5 b) 7 c) 12 d) 1
9.
th
Find the 130 term in the given series A, B, B, C, C, C, D, D, D, D,….
A bus started with a full capacity of passengers. At every stop 50% of the passengers got down. The number of passengers boarding the bus is 50% of the number of passengers who alighted at every stop. If the number of passengers in the bus rd
Ajay purchased a box of sweets and gave half the number of sweets to his wife, three sweets to his first son, one-third of the remaining to his second son and two to his third son. Find the number of sweets he purchased, if he is finally left with 4 sweets. a) 12 b) 14 12. c) 16 d) 24
How many three digit numbers, have the digits in numerical order and are in Arithmetic Progression? Progression? a) 16 b) 32 c) 20 d) 36
b) T d) Q
after the 3 stop was 54, find the total number of passengers who got down in all the three
6.
8.
a) R c) P
b) 64 d) 256
What is the relation between Arithmetic Mean (AM), Geometric Mean (GM) & Harmonic Mean (HM) for ‘n’ different non-zero non -zero integers?
a) AM = GM = HM b) AM => GM => HM c) HM => AM => GM d) Cannot be determined Find the approximate value of the sum of the first 15 terms in t he given series. -729, -243, -81, -27, -9, -9, …. a) 0 b) -729 c) -1093.5 d) -8748 A ball is dropped from the top of a building. Each time it hits the ground it bounces back th to 3/4 of its previous height. If it bounces th back to a height of 486 inches after the 5 bounce, find the height of the building. a) 972 inches b) 1024 inches c) 729 inches d) 2048 inches The speed of a train is 80 kmph and for every bogie added, the speed decreases by 10%. How many minimum number of bogies should be added to reduce the speed of the train to less than 50 kmph? a) 3 b) 4 c) 5 d) 6 n
15.
If 100! is divisible by 12 , what is the maximum value of n? a) 97 b) 24 c) 48 d) 12
16.
If n! is divisible by 15 , the minimum value of n is
32
a) 134 c) 140
b) 130 d) 144
17.
If a, b and c are in Geometric Progression, then log a, a, log b, b, log c, c, are in a) Arithmetic Progression b) Harmonic Progression c) Geometric Progression d) None None of these
18.
Find the sum of 8+88+888+…..up 8+88+888+…..up to n terms.
a) 8 10
8 10
n
9n
n 1
10 9n
b) c) 8 10 ‘ d) 8 10
19.
n1
81 10
n1
10
Find the approximate value of
2
2
2 .......
a) -1 b) 2 c) 1 d) Cannot Cannot be determined 20.
If x and y are integers, for how many pairs of (x, y), the value of |x| + |y| = 4? a) 16 b) 20 c) 12 d) 8
2. LCM & HCF
EXERCISE
Multiples If a = b x c, then b and c are called the factors of a, and a is called the multiple of b and c, where a, b and c are positive integers. Factor / Divisor
1.
Find the greatest number that divides 43, 91 and 183 leaveing the same remainder. a) 4 b) 7 c) 9 d) 13
2.
If the H.C.F. of two numbers is 23, and their L.C.M is 4186, one of the two numbers is a) 276 b) 300 c) 322 d) 345
3.
If ‘N’ is the greatest number that divides 1305, 4665 and 6905, leaving the same remainder the sum of the digits in ‘N’ is a) 4 b) 5 c) 6 d) 8
4.
The greatest four digit number divisible by 15, 25, 40 and 75 is a) 9000 b) 9400 c) 9600 d) 9800
A factor or a divisor of an integer ‘n’ is an integer which divides ‘n’ leaving a remainder ‘0’. Common Factors A common factor of two or more numbers is a number which divides each of the numbers leaving a remainder ‘0’. e.g: 3 is a common factor of 6 and 15. H.C.F (Highest Common factor)
The highest common factor also called the greatest common divisor of two or more numbers is the greatest number that divides each of the numbers leaving a remainder ‘0’. This is symbolically written 5. as G. C.D, GCD, G.C.D. or H.C.F
e.g: 3, 4, 6, 12 are the factors of 12 & 36. Among them the greatest is 12 and hence the H. C. F of 12 and 36 is 12. L.C.M (Least common multiple)
6.
The least common multiple of two or more given numbers is the ‘least or lowest number’ which is exactly divisible by each of the numbers leaving a 7. remainder ‘0’. e.g: The L.C.M of 36 and 60 is 180. Finding the L.C.M and the H.C.F of Fractions
8.
The product of two numbers is 4107. If the H.C.F. of these numbers is 37, the t he greater number is a) 101 b) 107 c) 111 d) 185 Three numbers are in the ratio 3: 4: 5 and their L.C.M. is 2400. Their H.C.F. is a) 40 b) 80 c) 120 d) 200 The G.C.D. of 1.08, 0.36 and 0.9 is a) 0.03 b) 0.9 c) 0.18 d) 0.108 The product of two numbers is 2028 and their
H.C.F. is 13. The number of such pairs is a) 1 b) 2 c) 3 d) 4 9.
Note: The Product of two numbers = The Product of their L.C.M and H.C.F Co-Prime / Relative Prime Two numbers m and n are said to be co-prime or relative prime if the G.C.D or H.C.F of m and n is equal to 1.
The least multiple of 7, which leaves a remainder 4, when divided by 6, 9, 15 and 18 is a) 74 b) 94 c) 184 d) 364
10.
11.
12.
The least number which should be added to 18. 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is a) 3 b) 13 c) 23 d) 33 Find the least number which is divisible by 9, and leaves a remainder of 3 when divided by 5, 6, 7 and 8. a) 1677 b) 1683 c) 2523 d) 3363 A, B and C go around a circular stadium stadium starting from the same point, at the same time and in the same direction. A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds. How long will it take for A, B and C to meet again at the starting point? a) 24 minutes and 18 seconds b) 26 minutes and 18 seconds c) 45 minutes d) 46 minutes and 12 seconds
13.
The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, the other number is a) 279 b) 283 c) 308 d) 318
14.
Find the least number that will be exactly divisible by 12, 18, 21 and 30 when doubled. a) 196 b) 630 c) 1260 d) 2520
15.
Find the smallest number that will be exactly divisible by 12, 16,18, 21 and 28 when decreased by 7. a) 1008 b) 1015 c) 1022 d) 1032
16.
252 can be expressed as a product of primes as: a) 2 x 2 x 3 x 3 x 7 b) 2 x 2 x 2 x 3 x 7 c) 3 x 3 x 3 x 3 x 7 d) 2 x 3 x 3 x 3 x 7
17.
The greatest possible length which can be used to measure the exact lengths of 7 m, 3 m 85 cm and 12 m 95 cm is
Three numbers are co-prime to each other. The product of the first two numbers is 551 and the product of the last two t wo numbers is 1073. The sum of the three numbers is a) 75 b) 81 c) 85 d) 89
19.
The length, breadth and height of the room are 12 m, 9 m & 6 m respectively. r espectively. If the room is filled with cubical boxes, find the minimum number of the maximum size cubical boxes, that can be filled in the room. a) 20 b) 22 c) 24 d) 36
20.
Find the smallest number that leaves a remainder of 8 when divided by 12, 15,20 and 54. a) 504 b) 536 c) 544 d) 548
EXERCISE
a) 15cm c) 35cm
b) 25cm d) 42cm
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