Practice No. System Questions and Answers

• Determine the value of 'a' such that the number 102a32 is divisible by 48.
• Aman is forming pairs of two natural numbers, A and B, such that their product equals 350. He wants to determine how many such pairs exist where A and B ar...
• If the sum of x , y , and z is 9, and the sum of their squares is 18, then determine the value of the expression xy + yz + zx .
• How many numbers between 340 and 1260 are divisible by both 18 and 24, but are not divisible by 5?
• What is the remainder when 7³⁵ is divided by 5?
• What is the largest three-digit number that leaves a remainder of 5 when divided by both 11 and 13? Call this number a. Additionally, what is the smallest ...
• Find the number of zeros at the end of 78!.
• If '502x62y' is a seven-digit number which is divisible by 72, then find the least possible value of (x - y).
• Let x = (726)245 – (437)458 + (333)335. What is the unit digit of x?
• On dividing (5757 + 57) by 58, the remainder obtained is ‘R’. Find the value of (R – 5).
• There are 120 candies, 120 chocolates, and 200 sweets to be distributed among groups A, B, and C, where each student in group A receives 5 candies, each st...
• Find the unit digit of (62375 - 7).
• There are two natural numbers such that the square of the smaller number exceeds five times the larger number by 4. Additionally, the sum of these two numb...
• Three numbers are in the ratio 5:9:12. The sum of the largest and smallest of these numbers is 8500. What is the difference between the largest and smalles...
• Find the unit digit of (62375 - 7)
• Aman and Rohan start running simultaneously on a circular track in opposite directions. Aman runs at a speed of 12 km/h while Rohan runs at 18 km/h. After ...
• A sum of ₹53,000 is divided among A, B, and C such that A gets 20% more than B, and B gets 25% less than C. What is the amount received by C?
• A shepherd owns two types of cattle: cows and sheep. After selling 40% of his cattle, he is left with a total of 90 cows and sheep. How many cattle did the...
• The average of 9 consecutive integers is 23. What is the sum of the smallest three integers?
• How many integers between 100 and 750 are divisible by both 18 and 24?
• How many two digits numbers are there which ends with 4 and completely divisible by '3'.
• 'x' varies directly as per 'y' and 'z'. When 'y' = 6 and 'z' = 8, then x = 16. Find the value of 'z', when 'y' = 8 and x = 24.
• A two-digit number is such that the sum of its digits is 10. If 36 is added to the number, the digits interchange their places. Find the number.
• The population of a town grows by 25% in the first year, declines by 20% in the second year, and rises by 30% in the third year. What is the total percenta...
• If the 6-digit number '5a1897' is divisible by '11', determine the value of 'a'.
• What is the total count of numbers between 165 and 2485 that are divisible by both 25 and 35?
• Find the largest 5-digit number that is divisible by 18, 24, and 36.
• A two-digit number is such that the sum of its digits is 12. If the number formed by reversing its digits is 18 less than the original number, find the ori...
• Find the smallest number that when divided by 6, 8, and 15 leaves a remainder of 5 in each case.
• If (2/3)rd of ‘x’ exceeds (2/5)th of (x + 5) by 6, then find the value of ‘x’.
• Find the value of ‘x’ if x = √729 + √1156
• Find the number of zeros in 58!.
• Find the unit digit of 351.
• When a number ‘N’ is divided by 40, the quotient is 70% more than the divisor and the remainder is 90% of the divisor. Find the value of ‘N’....
• If the sum of two positive numbers is 37 and the difference between these two numbers is 5, then what is the product of the two numbers?
• The sum of squares of two positive numbers is 185 while the product of these two numbers is 88. What is the square of the sum of the two numbers?
• The sum of two numbers is 30 while the difference between these two numbers is 6. What is 50% of the product of the two numbers?
• 25% of a number exceeds 1/6th of the same number by 7. What is the number?
• The difference between the squares of two positive numbers is 18 times the difference between the numbers. If the smaller number is 7, then what is the gre...
• Find the number of zeros at the end of the following expression: 12 × 16 × 25 × 40 × 45