A number when divided by 192 gives a remainder of 54. What remainder would be obtained on dividing the same number by 16 ?
624 0650d458363078e50a2943253Here, the first divisor 192 is a multiple of second divisor 16.
∴ Required remainder
= remainder obtained by dividing 54 by 16 = 6
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 ?
566 0650d43a2cb11fc5036d68479A number consists of two digits. If the number formed by interchanging the digits is added to the original number, the resulting number (i.e. the sum) must be divisible by
523 0650d423410a18f5082eccafcLet the number be 10x + y
After interchanging the digits,
the number obtained = 10y + x
According to the question,
Resulting number
= 10x + y + 10y + x
= 11x + 11y
= 11 (x + y)
which is exactly divisible by 11.
If two numbers are each divided by the same divisor, the remainders are respectively 3 and 4. If the sum of the two numbers be divided by the same divisor, the remainder is 2. The divisor is
574 0650d401473357650645d2108Required divisor = 3 + 4 – 2 = 5
In a question on division, the divisor is 7 times the quotient and 3 times the remainder. If the remainder is 28, then the dividend is
477 0650d3f3f73357650645d20e3Let the quotient be Q and the remainder be R. Then
Divisor = 7 Q = 3 R
∴ Divisor = 7 Q = 7 × 12 = 84
Dividend = Divisor × Quotient + Remainder = 84 × 12 + 28 = 1008 + 28 = 1036
64329 is divided by a certain number, 175, 114 and 213 appear as three successive remainders. The devisor is
1751 05d91f524a01ffd5718894157Number at (i) = 643 – 175 = 468
Number at (ii) = 1752 – 114 = 1638
Number at (iii) = 1149 – 213 = 936
Clearly, 468, 1638 and 936 are multiples of 234 and 234 > 213.
Divisor = 234