When a certain number is multiplied by 7, the product entirely comprises ones only (1111....). What is the smallest such number?
15873
Calculation:
Checking by division;
11 / 7 = 1.571...
111 / 7 = 15.857...
1111 / 7 = 158.714...
11111 / 7 = 1587.28...
111111 / 7 = 15873.
Alternate Method
Checking the options
The number obtained after multiplication by 7 has 1 as its digit only i.e. 11, 111, 1111, 11111, .. etc.
The units place digit is 1 and all options have 3 as the last digit so multiplying by 7 will result in 1 in units place.
_ _ _ _ 3
× 7
1 and 2 as carryover
The tens digit place is also 1 but 7 multiplied by 3 will have 2 as carryover and going through the numbers in option 7 multiplied by 7 has 9 as last digit but adding the carryover 2 makes it 1.
_ _ _ 73
× 7
11 and 5 as carryover
Hence, option 4 is correct.
Important Questions from Integers
Find the number of integers between $1$ and $150$ (inclusive) having $7$ as one of the digits but which are not divisible by $7$.
Integers are listed from 700 to 1000. In how many integers is the sum of the digits 10 ?
Using 2, 2, 3, 3, 3 as digits, how many distinct numbers greater than 30000 can be formed ?
Consider the following statements :
1. The sum of 5 consecutive integers can be 100.
2 The product of three consecutive natural numbers can be equal to their sum.
Which of the above statements is/are correct ?
The difference between a 2-digit number and the number obtained by interchanging the positions of the digits is 54.
Consider the following statements:
1. The sum of the two digits of the number can be determined only if the product of the two digits is known.
2. The difference between the two digits of the number can be determined.
Which of the above statements is/are correct?
