LEVEL WISE QUESTIONS

Level 1 - Easy

Questions 1

If one-third of one-fourth of a number is 15, then three-tenth of that number is:

1. 35       B. 36          C. 46       D. 54 

Questions 2

Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:

1. 9        B. 11      C. 13      D. 15

Questions 3

What is the place value of 7 in the numeral 2734?

1. 70      B. 7         C. 700       D. 7000

Question 4

1. 13      B. 12     C. 14      D. 11

Question 5

In a question on division with zero remainder, a candidate took 12 as divisor instead of 21.

The quotient obtained by him was 35. The correct quotient is:

1. 26     B. 25     C. 0      D. 20

Question 6

How many numbers from 29 to 79 are exactly divisible by 11.

1. 5      B. 6       C. 7      D. 4

Question 7

If 123x4 is divisible by 4, then the digit in place of x is :

1. 1        B. 3        C. 0       D. 7

Question 8

Find the unit digit in the product (243 × 397 × 2497 × 3913)?

1. 4      B. 2      C. 1      D. 3

Question 9

A girl wrote all the numbers from 100 to 200. Then she started counting the number of one's that has been used while writing all these numbers. What is the number that she got?

1. 111        B. 119       C. 120      D. 121

Question 10

The LCM of two numbers is 280 and their ratio is 7:8. The two numbers are

1. 70,80        B. 35,40      C. 42,48       D. 28,32

Question 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:

1. 18       B. 24          C. 42       D. 81

Question 12

The sum of two number is 25 and their difference is 13. Find their product.

1. 104        B. 114        C. 315       D. 325

Question 13

The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:

1. 20          B. 23      C. 169        D. None of these

Question 14

How many five digit multiples of 11 are there, if the five digits are 3,4,5,6 and 7 in the same order?

1. 10     B. 11      C. 12      D. 13

Question 15

When a number is divided by 36, it leaves a remainder of 19. What will be the remainder when the number is divided by 12?

1. 10        B. 7        C. 19       D. None of these

Question 16

The sum of the first 100 natural numbers, 1 to 100 is divisible by 

1. 2,4 and 8      B. 2 and 4     C. 2       D. 100

Question 17

How many different factors does 48 have, excluding 1 and 48?

1. 12      B. 4     C. 8      D. 10

Question  18

Find the G.C.D of 12x²y³z², 18x³y²z⁴, and 24xy⁴z³

A.6xy²z²        B. 6x³y⁴z³      C. 24xy²z²       D. 24xy³z²

Question 19

48 students have to be seated such that each row has the same number of students as the others. If at least 3 students are to be seated per row and at least 2 rows have to be there, how many arrangements are possible?

A.4       B. 10       C. 8        D. 7

Question 20

How many divisors does 7200 have?

A.20      B. 4      C. 54      D. None of these

Question 21

If ( 0.004 * 10^a )( 0.32 * 10^b ) = 128 * 10³, a + b = ?

A.3     B. 5       C. 6       D. 8

Question 22

Which one of the following is not a prime number?

A.31        B. 61       C. 71       D. 91

Question 23

What least number must be added to 1056, so that the sum is completely divisible by 23 ?

A.2       B. 3       D. 18       D. 21

Question 24

1397 x 1397 = ?

A.1951609          B. 1981709          C. 18362619         D. None of these

Question 25

How many of the following numbers are divisible by 132 ?
264, 396, 462, 792, 968, 2178, 5184, 6336

A.4       B. 5      C. 6       D. 7

Question 26

397 x 397 + 104 x 104 + 2 x 397 x 104 = ?

A.250001       B. 251001       C. 260101      D. 261001

Question 27

(35423 + 7164 + 41720) - (317 x 89) = ?

A.28213         B. 84307        C. 50674      D. 56094

Question 28

Which one of the following numbers is completely divisible by 45?

A.181560       B. 331145         C. 202860      D. None of these

Question 29

A number when divide by 6 leaves a remainder 3. When the square of the number is divided by 6, the remainder is:

A.0         B. 1        C. 2         D. 3

Question 30

The sum of even numbers between 1 and 31 is:

A.6         B. 28         C. 240         D. 512

Level 2 - Moderate

Questions 1

The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?

1. 3      B. 4      C. 9     D. Cannot be determined

Questions 2

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:

1. 18     B. 24     C. 42    D. 81

Question 3

If a worker in a factory receives one rupee on the first day from the second days onwards his wage is

increased by one rupee every day. What is the total amount of wage he receives after 40 days?

1. 720      B. 820      C. 810       D. 740

Question 4

A bell in a clock rings once at 1 O'clock, twice at 2 O'clock, thrice at 3 O'clock and so on..

Then how many times it rings in a day.

1. 150     B. 146     C. 156     D. 136

Question 5

What is the sum of natural numbers between 20 and 100.

1. 4860      B. 4840      C. 4880      D. None of these

Question 6

What is the sum of all two digit numbers?

1. 4900       B. 4895        C. 4905      D. None of these

Question 7

If 123xy is divisible by 40, then the value in place of x+y is :

1. 1      B. 7       C. 4        D. 3

Question 8

What is tha value of (x-a)(x-b)(x-c) - - - - - (x-z)

1. 1      B. 2      C. 3       D. 0

Question 9

What is the unit digit in 2⁹?

1. 3      B. 4      C. 1      D. 2

Question 10

What is the minimum number of square marbles required to tile a floor of length 5 metres 78 cm and width 3 metres 74 cm?

1. 176        B. 187         C. 540         D. 748

Question 11

What number should be subtracted from x3+4x2−7x+12 if it is to be perfectly divisible by x + 3?               

1. 42        B. 39          C. 13       D. None of these

Question 12

Find the remainder when 2⁸⁹ is divided by 89?

1. 1      B. 2     C. 87       D. 88

Question 13

Find the unit's digit in 264¹⁰²+264¹⁰³?

1. 0        B. 2      C. 4       D. 6

Question 14

In a meet, persons from five different places have assembled in Bangalore High School. From the five places the persons come to represent are 42,60,210,90 and84. What is the minimum number of rooms that would be required to accommodate so that each room has the same number of occupants and occupants are all from the same places?

1. 44           B. 62           C. 81           D. 96

Question 15

A set has exactly five consecutive positive integers starting with 1. What is the percentage decrease in the average of the numbers when the greatest one of the numbers is removed from the set?

1. 8.5       B. 12.5        C. 15.2       D. 16.66

Question 16

Which one of the following is the minimum value of the sum of two integers whose product is 36?

1. 37       B. 20      C. 15       D. 12

Question 17

What is the remainder when 91+92+93+....+98 is divided by 6?

1. 3        B. 2       C. 0       D. 5

Question 18

What is the unit's digit of the number 6²⁵⁶–4²⁵⁶?

1. 0           B. 1          C. 4        D. 7

Question 19

Four digits of the number 29138576 are omitted so that the result is as large as possible. The largest omitted digit is

1. 5         B. 6        C. 7        D. 8

Question 20

If a person makes a row of toys of 20 each, there would be 15 toys left. If they made to stand in rows of 25 each, there would be 20 toys left, if they made to stand in rows of 38 each, there would be 33 toys left and if they are made to stand in rows of 40 each, there would be 35 toys left. What is the minimum number of toys the person have?

1. 1255          B. 3805        C. 7595        D. 3795

Question 21

a, b, c, d, and e are five consecutive numbers in increasing order of size. Deleting one of the five numbers from the set decreased the sum of the remaining numbers in the set by 20%. Which one of the following numbers was deleted?

1.  A        B. B        C. C         D. D

Question 22

A chain smoker had spent all the money he had. He had no money to buy his cigarettes. Hence, he resorted to join the stubs and to smoke them. He needed 4 stubs to make a single cigarette. If he got a pack of 10 cigarettes as a gift, then how many cigarettes could he smoke in all?

1. 10       B. 11         C. 12         D. 13

Question 23

2ab5 is a four-digit number divisible by 25. If the number formed from the two digits ab is a multiple of 13, then ab =

1. 10       B. 25       C. 52         D. 65

Question 24

A number when divided by 342 gives a remainder 47. When the same number is
divided by 19, what would be the remainder?

1. 5       B. 9        C. 4      D. 0

Question 25

A bank issued credit card numbers and the corresponding PIN (Personal Identification Number). Both are 3-digit numbers up to 996. Pinaki was the last to get the credit card and so he had the last possible credit card number. He was afraid of forgetting his PIN. He wrote down the number 123 in his diary to remember his PIN. He also wrote out the way to calculate 123 : "Multiply the card number by PIN. Divide the product by 997. The remainder is 123". Once, Prafull saw his diary in which Pinaki wrote this number 123. Prafull did a lot of purchasing, as he now knows Pinaki's PIN. What is Pinaki's PIN?

1. 874        B. 875        C. 876        D. 877

Question 26

The least common multiple of two natural numbers a and b, is 399. What is the minimum possible sum of the digits of the number a(given a > b)?

1. 1      B. 3       C. 5       D. 7

Question 27

When writing numbers from 1 to 10,000, how many times is the digit 9 written?

1. 3200      B. 3600       C. 4000      D. 4200

Question 28

How many keystrokes are needed to type numbers from 1 to 1000 on a standard keyboard?

1. 3001       B. 2893      C. 2704       D. 2890

Question 29

How many natural numbers below 660 are divisible by 5 and 11 but not by 3?

1. 8      B. 9      C. 10       D. 11

Question 30

The positive integers m and n leave remainders of 2 and 3, respectively, when divided by 6. m>n. What is the remainder when m–n is divided by 6?

1. 2        B. 3       C. 5        D. 6 

Level  3- Difficult

Question 1

The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is:

1. 380       B. 395       C. 400      D. 425

Question 2

The LCM of two numbers x and y is z. What is the LCM of 3x and 3y?

A.      3z       B. z       C. 9z      D. 27z

Question 3

If a and b are even integers while c and d are odd integers, then which of the following

Is true?

A.(a +b+ c)(b+c+d) is odd         B. (a+c)(b+d) is even

C.(a+d)(b-c) is odd                       D.a+b+c-d is odd

Question 4

What is the remainder when 123……..10 is divided by 32?

1. 22         B. 14       C. 9        D. 0

Question 5

If a seven digit number 7495x2y is divisible by 36, the number of ordered pairs of x and y are

A.      4        B. 1       C. 2          D.5

Question 6

H.C.F of two numbers is 2 and the product of the two numbers is 64. How many such pairs are possible?

A. 1        B. 2       C. 3       D. 4

Question 7

What is the product of all the factors of 1728?

A.      1728^14      B. 1728^28       C. 1728^15       D.1728^30

Question 8

Find the number of zeroes in 100! ?

A.      11         B. 12          C. 24         D. 25

Question 9

How many times a typist uses keys in a type writer for printing numbers in a book of 300 pages.

1. 180      B. 603      C. 792       D. None of these

Question 10

What is the unit digit in 7⁴²?

1. 3      B. 5     C. 7      D. 9

Question 11

A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?

1. 13       B. 59       C. 35      D. 37

Question 12

The product of 4 consecutive even numbers is always divisible by

1. 600      B. 768      C. 864      D. 384

Question 13

What is the minimum number of square marbles required to tile a floor of length 5 metres 78 cm and width 3 metres 74 cm?

1. 176      B. 187     C. 540       D. 748

Question 14

The largest number amongst the following that will perfectly divide 101¹⁰⁰–1 is:

1. 100        B. 10000       C. 100¹⁰⁰          D. 100000

Question 15

P =1234567891011.............9989991000

Find the remainder when first 1000 digits of the number P are divided by 16?

1. 7       B. 9       C. 11      D. 13

Question 16

Each of X alarm tolls at regular intervals. All of them tolls together twelve times a day. No two alarm at equal intervals of time. If each alarm tolls after a whole number of minutes, what is the maximum possible value of X?

1. 14      B. 16       C. 18       D. 20

Question 17

Three gold coins of weight 780gm, 840gm and 960gm are cut into small pieces, all of which have the equal weight. Each piece must be heavy as possible. If one such piece is shared by two persons, then how many persons are needed to give all the pieces of gold coins?

1. 86         B. 70        C. 43        D.  35

Question 18

N is the smallest number that has 5 factors. How many factors does (N - 1) have?

1. 2      B. 3       C. 4       D. 5

Question 19

Let X be a four-digit number with exactly three consecutive digits being same and is a multiple of 9. How many such X’s are possible?

1. 12         B. 16         C. 19           D. 20

Question 20

The remainder when m + n is divided by 12 is 8, and the remainder when m – n is divided by 12 is 6. If m > n, then what is the remainder when mn divided by 6?

1. 1        B. 2       C. 3        D. 4

Question 21

a, b, c, d, and e are five consecutive integers in increasing order of size. Which one of the following expressions is not odd?

1. ab + c           B. ab + d       C. ac + d      D. ac + e

Question 22

How many three digit numbers can be formed using the digits 1,2,3,4,5,6,7 and 8without repeating the digits and such that the tens digit is greater than the hundreds digit and less than the units digit?

1. 48       B. 56          C. 64        D. 72

Question 23

Find the sun of the digits of the least natural number P, such that the sum of the cubes of the four smallest distinct divisors of P equals 2P.

1. 7        B. 8        C. 9        D. 10

Question 24

How many ordered pairs of integer (x,y) are there such that their product is a positive integer less than 100.

1. 546       B. 636       C. 1090       D. 946

Question 25

N is the smallest number that has 5 factors. How many factors does (N - 1) have?

1. 2        B. 3       C. 4       D. 5

Question 26

Ram and Shyam take a vacation at their grandparents' house. During the vacation, they do any activity together. They either played tennis in the evening or practiced Yoga in the morning, ensuring that they do not undertake both the activities on any single day. There were some days when they did nothing. Out of the days that they stayed at their grandparents' house, they involved in one of the two activities on 22 days. However, their grandmother while sending an end of vacation report to their parents stated that they did not do anything on 24 mornings and they did nothing on 12 evenings. How long was their vacation?

1. 36 days        B. 14 days       C. 29 days        D. Cannot be determined

Question 27

A set of S consists of 
i). All odd numbers from 1 to 55.
ii). All even numbers from 56 to 150.
What is the index of the highest power of 3 in the product of all the elements of the set S?

1. 35     B. 48      C. 6      D. 36

Question 28

A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:

A. 145          B. 253       C. 370          D. 352

Question 29

What is the sum of two consecutive even numbers, the difference of whose squares is 84?

1. 34       B. 38        C. 42        D. 46

Question 30

What is the sum of two consecutive even numbers, the difference of whose squares is 84?

1. 20        B. 30        C. 40       D. None of these

FINDING THE REMAINDER IN DIVISIONS INVOLVING POWERS OF NUMBERS

FINDING THE REMAINDER IN DIVISIONS INVOLVING POWERS OF NUMBERS

Q. Find the remainder when 2^58 is divided by 7?

Ans. Let us find the pattern that remainders follow when successive powers of 2 are dividedby 7.

Remainder of 2^1 /7 is 2

Remainder of 2^2 /7 is 4

Remainder of 2^3 /7 is 1

Remainder of 2^4 /7 is 2

We can see that remainders are repeating after 3 steps, so the cyclicity is 3

Divide the power i.e. 58 by cyclicity which is 3. Remainder obtained is 1 when 58/3

So we can say that remainder when 2^58 is divided by 7 is same as the remainder of 2^1/7 which is 2.

• Some Basic Formulae:

1.      1. Identities

1. (a + b)(a - b) = (a2 - b2)
2. (a + b)2 = (a2 + b2 + 2ab)
3. (a - b)2 = (a2 + b2 - 2ab)
4. (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
5. (a3 + b3) = (a + b)(a2 - ab + b2)
6. (a3 - b3) = (a - b)(a2 + ab + b2)
7. (a3 + b3 + c3 - 3abc) = (a + b + c)(a2 + b2 + c2 - ab - bc - ac)
8. When a + b + c = 0, then a3 + b3 + c3 = 3abc.

2.      The sum of first n natural numbers is = [n(n+1)]/2. 

Example: The sum first 49 natural number is = [49(49+1)]/2 = [49(50)]/2 = 49 * 25 = 1225

3.     The sum of the squares of the first n natural numbers is = [n(n+1)(2n+1)]/6.

Example: The sum of the squares of the first 10 natural numbers is = 10(11)(21)/6 = 385.

4.  The sum of the cubes of the first n natural numbers is = [n(n+1)/2]²

    Example: The sum of the cubes of the first 10 natural numbers is = [10(10+1)/2]²

= [(10*11)/2]² = 55² = 3025

5.       The sum of the first n odd natural numbers is = n²

Example: The sum of the first 24 odd natural numbers is = 24² = 576.

6.       The sum of the first n even natural numbers is = n(n+1)

Example: The sum of the first 10 even natural numbers is = 10(10 + 1) = 10 * 11 = 110

7.       The p/q form of any recurring number = The non-recurring and recurring part written once)-(the non-recurring part)/ As many 9’s as the number of digits in the recurring part followed by as many 0’s as digits in the non-recurring part.

Example: : Express 0.5858585….. as fraction

= (585- 5/(990)

=58/99