Q: When 40! is expressed in base 8 form, what is the last non–zero digit in the base 8 expansion?

Q: What least value should be given to * so that the number 145*603 is exactly divisible by 9?

Q: Let K be the largest number with exactly 3 factors that divide 25!. How many factors does (k – 1) have?

Q: The number of co-primes to the number 900 is ______.

Q: The traffic lights at three different road crossings change after every 36 sec; 72 sec; and 288 sec., respectively. If they all change simultaneously at 8:20:00 hrs, then they will again change simultaneously at _____?

Q: Find the smallest number that leaves a remainder of 4 on division by 5, 5 on division by 6, 6 on division by 7, 7 on division by 8 and 8 on division by 9.

Q: A class consists of 15 students and a teacher. The teacher writes a natural number on the board and asks students to tell something about the number. The first student says, “ This number is a multiple of 1”. The second student says, “This number is a multiple of 2” and so on till the 15th student. The teacher notices that all but two of them were correct in their statements and both of them spoke one after the other consecutively. Which two students were not correct?

Q: What is the unit digit for 123123!?

Q: Jaiswal plans a small business by starting a mini travels. So he purchased a 40-seater bus. He started his services on route number 2 (from Dwaraka Vilas to Nawab Palace of length 50 km). His profit (p) from the bus depends on the number of passengers, over a certain minimum number of passengers ‘n’ and the distance travelled by bus. His profit is Rs.3600 with 29 passengers in the bus for a journey of 42 km and Rs. 6300 with 36 passengers in the bus for a journey of 42 km.What is the minimum number of passengers that are required so that he will not suffer any loss?

Q: What is the rightmost non-zero digit in 15!?

Q: The average weight of 7 women is increased by 12 kg, when one of them whose weight is 95 kg is replaced by another woman. What is the weight of the new women (in kg)?

Q: One collective farm got an average harvest of 21 tons of wheat and another collective farm that had 12 acres of land given less to wheat, got 25 tons from a hectare. As a result, the second farm harvested 300 tons of wheat more than the first. How many tons of wheat did each farm harvest?

Q: What is the remainder when 120! is divided by 12024?

Q: Find the remainder obtained when 152010 +162011 is divided by 7.

Q: In how many ways possible ways can you write 1800 as a product of 3 positive integers a, b, c?

Q: A 5-digit number has a peculiar characteristic wherein the product of the first two digits with the last two digits minus the central digit results in a string that consists same numbers in all the digits. Which of the following option satisfies this condition?

Q: Lakshman needs to solve a riddle to make it to the next round of a puzzle test. The riddle he has got is " A 143 multiple can also be obtained by multiplying 'm' number of consecutive natural numbers. What is the minimum value 'm' can take ?

Q: Sum of two numbers x, y = 1050. What is the maximum value of the HCF between x and y?

Q: A bank issued credit card number and the corresponding PIN (Personal Identification number). Both are 3-digit numbers up to 996. Pinky was the last to get the card and so she had the last possible credit card number. She was afraid of forgetting her PIN. She wrote down the number 123 in her diary to remember her PIN, she 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 her diary in which Pinky wrote the number 123, Prafull did a lot of purchasing as he now knows Pinky’s PIN. What is Pinky’s PIN?

Q: The sum of two non co–prime numbers added to their HCF gives us 91. How many such pairs are possible?

Q: Find the HCF of 2/3, 4/9, 8/27.

Q: Find the remainder when (17)21 is divided by 16

Q: Raj who works in a neighbourhood metro city gets the same salary each month. He finds that whenever he adds up his six figure salary of two months, three months, four months, five months, or six months, each time the figures (or digits) of his salary remains the same, but not in a fixed order. Later, he told me that when he adds up his salary of 7 months his total salary becomes 999999. What is the salary of Raj?

Q: A number when divided by 5 leaves a remainder 3. What is the remainder when the square of the same number is divided by 5?

Q: The term (x13 + 1) is divided by (x – 1). The divisor, as well as the dividend, are polynomial terms, in this case what will be the remainder?

Q: What is the highest power of 12 that can divide 54!.

Q: Yash tries to divide a term that has got two numbers raised to a particular power value of 101, i.e., 43101 + 23101 by a number 66. What will be the remainder in this case?

Q: In a school, a particular set of students were chosen in which there were 576 boys and 448 girls who were to be divided into sections of an equal number of boys alone or girls alone. Find the total number of sections thus formed?

Q: A game was conducted in a typewriting class, where a candidate has to type/enter all the three-digit numbers without space. If made a mistake while typing, the candidate can use the backspace key once for one three-digit number. What is the least number of times a candidate has to press the keys to type all the three-digit numbers? (Assuming the candidate did not make any mistake)

Q: Hari takes a card from a deck which has got only two-digit numbers. The card he picked has got a number which can be obtained either by multiplying the digit sum by 8 and adding 1 to it or by multiplying the difference of digits by 13 and adding 2 to it. The number Hari got is ____.