2. Total Gadha's Complete Book of. NUMBER SYSTEM If n is an odd natural number, what is the highest number that always divides n × (n2 – 1)?. Answer: n . Totalgadha Number System Book - Download as PDF File .pdf), Text File .txt) or read online. Good book on number system. View Complete Book of Number System (Total Gadha) from BSC at University of South Africa. 1 http:/guegaucheekupme.tk Total Gadhas Complete Book of.

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guegaucheekupme.tk . In a number system the product of 44 and 11 is system, when converted to the decimal number system, becomes. 1. . definitely the 3 e books by total gadha number systems, is view test prep - complete book of geometry - total gadha ().pdf from maths. Total guegaucheekupme.tk Free Download Here The Complete Book of Number System - MBAtutes.

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Even DRM technology has failed to prevent Read more: Digital rights management - Wikipedia, the free encyclopedia. How I persevered for six years to succeed…. Related Groups. The highest indices of 2, 3, x and y are 3, 2, 4 and 2 respectively. Division Method: To find the LCM of 72, and , we use the division method in the following way: Note- This formula is applicable only for two numbers.

Hence both the sum and differences of the two numbers are divisible by the HCF. Find the highest four-digit number that is divisible by each of the numbers 24, 36, 45 and The highest four-digit number is Find the highest number less than that is divisible by each of the numbers 2, 3, 4, 5, 6 and 7. The LCM of 2, 3, 4, 5, 6 and 7 is Hence , and every multiple of , is divisible by each of these numbers. Hence, the number , , , and are all divisible by each of these numbers.

We can see that is the highest number less than which is multiple of Hence, the highest number divisible by each one of 2, 3, 4, 5, 6 and 7, and less than is Find the lowest number which gives a remainder of 5 when divided by any of the numbers 6, 7, and 8. The LCM of 6, 7 and 8 is Hence, is divisible by 6, 7 and 8. What is the smallest number which when divided by 9, 18, 24 leaves a remainder of 5, 14 and 20 respectively? Now the LCM of 9, 18, and 24 is Therefore, if we subtract 4 from 72, the resulting number will give remainders of 5, 14, and 20 with 9, 18, and A number when divided by 3, 4, 5, and 6 always leaves a remainder of 2, but leaves no remainder when divided by 7.

What is the lowest such number possible? We can see that is divisible by 7. For how many pairs a, b of natural numbers is the LCM of a and b is 2 3 5 7 11 13? Let's solve for the powers of 2. One of the number will have 2 3 in it, as the LCM has 2 3. Now the other number can have the powers of 2 as 2 0 , 2 1 , 2 2 , and 2 3. Therefore, number of pairs will be 4: All the digits of N 2 are added to obtain a number N 3 , and so on, till we obtain a single digit number N.

This single digit number N is called the digit sum of the original number N 1. Hence, the digit sum of the number is 9. In finding the digit-Sum of a number we can ignore the digit 9 or the digits that add up to 9. For example, in finding the digit-sum of the number , we can ignore the digits 2, 6, 1, and 9.

Digit-Sum Rule of Multiplication: The digit-sum of the product of two numbers is equal to the digit sum of the product of the digit sums of the two numbers!

The product of and 35 is A quick check will show that the digit-sum of the product is 3. The digit-sums of the individual numbers , and are 1, 9, and 5. Hence, the answer obtained by multiplication is not correct. Although the answer of multiplication will not be correct if the digit-sum of the product of the digit-sums is not equal to digit-sum of the product, but the reverse is not true i. What is that number? Digit sums on both sides will be the same.

If one of the multiplicand is 9, the digit sum is always 9. As one of the multiplicands is 9, the digit sum will be 9. Determining if a number is a perfect square or not S. Numbe r Squar e Digit- Sum of the S. Numbe r Squar e Digit-Sum of the square http: A number will NOT be a perfect square if its digit-sum is NOT 1, 4, 7, or 9, but it may or may not be a perfect square if its digit-sum is 1, 4, 7, or 9. Is the number a perfect square? Hence, the number cannot be a perfect square.

Is N be a perfect square? We can see that the digit sum of a perfect square is always 1, 4, 7, or 9. As the digit sum of the number is 3, it cannot be a perfect square. If a five-digit number N is such that the sum of the digits is 29, can N be the square of an integer? To put it simply, if the given number is an integer, then the greatest integer gives the number itself, otherwise it gives the first integer towards the left of the number of x on the number line.

For example, [1. We can see that [1. Note that the red dot indicates that integer value on the number line is not included while the green dot indicates that the integer value is included.

The product of three consecutive odd numbers is What is the sum of the three numbers? Then, the number of divisors of N is A.

In the value of the number 30! Then, the unit digit of the number that is left is A. How many different values of N are possible? In , my age was equal to the last two digits of my birth year. My grandfather said that it was true for him also. N is the sum of the squares of three consecutive odd numbers such that all the digits of N are the same.

If N is a four-digit number, then the value of N is http: While driving on a straight road, Jason passed a milestone with a two-digit number. After exactly an hour, he passed a second milestone with the same two digits written in reverse order. Exactly one more hour after that, he passed a third milestone with the same two digits reversed and separated by a zero. What is the sum of the two digits? The squares of the natural numbers are written in a straight line … to form a digits number.

What is the th digit from the left? Then the sum of the digits of S is A. Swadesh threw five standard dice simultaneously. He found that the product of the numbers on the top faces was Which of the following could not be the sum of the numbers on the top five faces? The last two digits of S are A. How many natural numbers between 1 and are NOT multiples of any of the numbers 2, 3, or 5? The last two digits of 4 are A. The numbers and are multiplied.

All the divisors of 72 are multiplied. The number AB, where A and B are single-digit numbers, is divisible by N is the smallest natural number which when multiplied by 7 gives a product P. Every digit of P is one. The product when N is multiplied by 8 is A. The remainder when 7 77 is divided by 9 is A. In the nineteenth century a person was X years old in the year X 2. How old was he in ? The average of the nine numbers 9, 99, ,…, is A.

Then A does not contain the digit A. How many natural numbers less than 65 have odd number of divisors including 1 and those numbers themselves? The person who says 'five' is taken out of the line. Those remaining repeat this procedure until only four people remain in the line. What was the original position in the line of the last person to leave? What is the sum of the sum of the sum of the digits of 55!?

An Indian king was born in a year that was a square number, lived a square number of years and died in a year that was also a square number. Then the year he could have been born in was A. To number the pages of a book, exactly digits were used. How many pages did the book have? The highest power of 12 that can divide 5 36 — 1 is A. What is the largest prime whose cube divides 1!

The number 2n! I and II only B. I and III only D. Baghira, the oldest inmate of Tihar Jail is learning mathematics. He notices the following facts about his prisoner number: It is a three digit number not bigger than If you sum the cube of the digits of the number, you get the number itself.

The number is the sum of consecutive factorials. The number in base 10 is written as b. Then, the base b is equal to A. His Mercedes registration number is a four-digit perfect square formed by repeating the rightmost digit of his nightclub number. The teacher of Confusius, the confused soul, told him: If you reverse the digits of my age and subtract the number from my age you again have a perfect square.

The remainder when 2 is divided by 13 is A. How many positive integers less than or equal to are relatively prime to ? The difference between the cubes of two consecutive positive integers is Then the product of these integers is A. How many integers between 1 and , both inclusive, can be expressed as the difference of the squares of two non negative integers? The product P of three positive integers is 9 times their sum, and one of the integers is the sum of the other two.

The sum of all possible values of P is A.

Let M be the greatest number divisible by 8, such that no digit from 0 to 9 is repeated in M. What is the remainder when M is divided by ? Let q and r be the quotient and remainder when M, a five digit number, is divided by Then I. A, B and C can be equal for some value of x. A, B and C can all take different values for some value of x. I is true but II is false B.

II is true but I is false C. Both I and II are true D. Both I and II are false How many perfect squares are the divisors of the product 1! The number ! How many zeroes are there at the end? The unit digit of 7 7 7 is A.

In how many ways can the number be written as a sum of two or more consecutive positive integers? It is given that m and n are two smallest natural numbers satisfying following conditions I.

Five consecutive integers are chosen. Let S denote their sum and let P denote their product. If the product of four positive integers is 10! What is the smallest possible value their sum can have? S is a six digit number beginning with 1. If the digit 1 is moved from the leftmost place to the rightmost place the number obtained is three times of S.

Which of the following numbers can be written as the sum of the squares of three odd natural numbers?

In a bag, some slips of paper are kept with the numbers thirteen or fourteen written on them. The slips with number thirteen written on them are five more than the slips with number fourteen written on them. Which of the following can be the sum of the numbers in the bag? Two natural numbers a and b are given in base How many two-digit positive integers are there which are one and a half times larger than the product of their digits?

A three-digit number abc is divisible by 7 if A. For how many values of k is 12 12 the least common multiple of 6 6 , 8 8 , and k? All the divisors of , including 1 and the number itself, are summed up.

The sum is What is the sum of the reciprocals of all the divisors of ? Then the set of intersection of all values of S and T is A.

What is the remainder when the number digits Yes B. Maybe D. Vinay has boxes with him. He has to put least oranges in one box and oranges at the most. Then the least number of boxes containing the same number of oranges is A. There were 90 questions in an exam. In a class, the teacher wrote a set of consecutive integers beginning with 1 on the blackboard.

Little Johnny came and erased one number. The average of the remaining numbers was 13 4 What was the number that little Johnny erased? What is the remainder when digits digits 10 If 11 sweets are distributed among four boys, then, which of the following is true? Two boys each received more than 1 sweet B. One of the boys received more than 3 sweets http: One of the boys received fewer than 3 sweets D.

One of the boys received exactly 2 sweets All possible pairs are formed from the divisors of How many such pairs have HCF of 45? How many natural numbers between 1 and have exactly four factors? S is a set of n natural numbers such that at least two numbers in S give the same remainder when divided by 3, and there exist at least two numbers in S whose sum is divisible by 3.

What is the minimum value of n which ensures that both the conditions for S are fulfilled? If four hens lay five eggs in six days, how many days will it take twenty-four hens to lay sixty eggs? For example, 4 and 12 are privileged numbers. What is the mean of all privileged numbers less than ?

What is the remainder when is divided by ? The digits of a three-digit number A are written in the reverse order to form another three-digit number B.

CAT A. The rightmost non-zero digit of the number 30 is A. What is the remainder when 4 96 is divided by 6? Let x and y be positive integers such that x is prime and y is composite. Then, A. None of the other statements is true.

He starts jumping from one lattice point to another. At each jump, Jumpy moves one unit to the right, or one unit to the left, or one unit up, or one unit down. If Jumpy takes 12 jumps in all, how many lattice points could he finally end up at? A faulty odometer of a car always jumps from digit 4 to digit 6, always skipping the digit 5, regardless of the position.

For example, after traveling for one kilometer the odometer reading changed from to If the odometer showed when the car was bought and now it shows , how many kilometers has the car traveled? In how many zeroes does ! A number N when divided by a divisor D gives a remainder of The number 5N when divided by D gives a remainder of 4.

How many values of D are possible? Which one of the following numbers is a perfect square? In how many ways can 7 13 be written as product of 3 natural numbers?

N has f factors, 2N has 2f factors, 6N has 4f factors, 15N has 3f factors. How many factors 30N has? How many zeroes are present at the end of 25! How many zeroes does 5 5! End in? S is a set of 10 consecutive two-digit integers such that the product of these 10 integers has the highest power of 2 contained in it.

How many such sets S are possible? N is a number such that the ratio of sum of its digit to product of its digits is 3: If N is divisible by 37 and N is the smallest such number, how many factors does N have? In a national hockey single elimination tournament, teams are participating. How many games will be played before a team becomes the national champion? A two-digit number is divided by the sum of its digits.

The answer is 6. What is the product of the digits? The sum of 20 distinct numbers is What is their minimum LCM possible? What is the smallest positive composite number generated by the expression p 2 — p — 1 where p is a prime number? N the least positive integer that is eleven times the sum of its digits. Then N is divisible by A. What can be the maximum value of K? The value of is A. How many arithmetic progressions can be formed from the elements of S that start with 1 and end with and have at least 3 elements?

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? The number of employees in Obelix Menhir Co. The ratio of the number of employees who are graduate and above, to that of employees who are not, can possibly be A. When you reverse the digits of the number 13, the number increases by How many other two-digit numbers increase by 18 when their digits are reversed?

Then the sum of these four prime numbers is A. A three-digit number in base 10 is written in base 9 and base 11 to give two numbers N 1 and N 2 ,respectively.

What is the probability that N 1 and N 2 are also three-digit numbers? The single digits a and b are neither both nine nor both zero.

The repeating decimal 0. How many different denominators are possible? The last three digits of a number N are x For how many values of x can N be the square of an integer? What is the remainder when is divided by 13? What is the value of n such that n!

How many integers between and have the sum of their digits equal to 12? The digits 1, 2, 3, 4, and 5 are each used once to compose a five-digit number abcde such that the three-digit number abc is divisible by 4, bcd is divisble by 5, and cde is divisble by 3. Find the digit a. A gadha never lives up to years because its stupidity gets it killed. Dhondu and Bhondu are the cutest gadhas in Donkeyland. When you write Dhondu's age followed by Bhondu's age, you get a four-digit perfect square.

After 31 years, if you write their ages in the same order you again obtain a four-digit perfect square. How old is Dhondu? How many factors of N 2 are less than N but do not divide N completely? In how many ways can be written as a sum of two or more consecutive positive integers? The product of the ages of some teenagers is The sum of their ages is equal to A. In a village of inhabitants, at least x villagers have the same English initials for their first name and their surname.

The least possible value of x is http: What are the last two digits of 1 5? A Number N is divisible by 10, 90, 98 and but it is not divisible by 50 or or or It is also known that N is a factor of What is N? Every digit of a number n is equal to 1, i. My grandfather said he was 84 years old but he was not counting the Sundays. How old my grandfather really was?

What are the last two digits of? What is the sum of the digits of the denominator of the new fraction? As the unit digit of the product is 7, only the last triplet of units digits, i.

Therefore, we need to find three consecutive odd numbers ending in 9, 1 and 3 such that there product is Therefore, the numbers would be lying around The numbers are 79, 81 and 83 and the sum is D Finding the powers of all the prime factors in 30!

We obtain, 30! We need to find the units digit of this product to find the rightmost non- zero digit.

B The number which has 6 divisors will be of the form ab 2 or c 5 , where a, b and c are prime numbers. B The ages will be lying on either side of for us to have two solutions to same situation. Let the birth year of grandfather be 18ab. Similarly, the birth year for grandson is Since the number is greater than 10 12 and the sum of the digits is 2, one of the zeroes in 1 will be replaced by 1. Therefore, there will be 12 numbers generated this way. Apart from this, the number 2 also satisfies the criterion.

Hence, 13 numbers are possible. Therefore, subtracting 3 from these options we should get a multiple of 4. Only B and D fulfill the criterion. Out of three consecutive odd numbers, one will be a multiple of 3. Therefore, subtracting two from the options, we should get a multiple of 3. Out of B and D, only B satisfies the criterion. C The numbers are ab, ba and a0b and the difference is constant between two consecutive numbers.

Therefore, the numbers are 16, 61 and After , we will start writing four-digit squares — , … with every square we cover four digits.

Since we need to cover 19 digits, we will have to write 4 four-digit squares and then we will see the 3 rd digit of the fifth four-digit square. B Rule: Similarly, 12 — 1 is divisible by 11 and As 13 is the common factor, the whole expression is divisible by Similarly, 12 — 5 is divisible by 7 and As 17 is the common factor, the whole expression is divisible by As the expression is divisible by both 13 and 17, it is divisible by To get digits we will have to increase the power of 2 such that we get a four digit number followed by zeroes.

Simplify the rest similarly. Many terms will cancel out. B 4 integers- 0, 10, 16, and D The units digit is found by finding the remainder of the exponent with 4. Therefore, we need to find the remainder of 1! Therefore, 4 1 and 4 11 have the same last two digits, i. Therefore, 4 will have the same last two digits. A If a number is divisible by 72, it is divisible by 8 and 9. Normal Lewis Vocabulary book. Career Launcher RC 2 Flash cards would also do justice to your preparation.

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