Number System
- A number when divided by 192 gives a remainder of 54. What remainder would be obtained on dividing the same number by 16 ?
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Here, the first divisor 192 is a multiple of second divisor 16.
Correct Option: C
Here, the first divisor 192 is
a multiple of second divisor 16.
∴ Required remainder
= remainder obtained by dividing 54 by 16 = 6
Hence required remainder is 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 ?
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If the quotient in the first case be q.
Then, number = 5q + 3Correct Option: D
If the quotient in the first case be q.
Then, number = 5q + 3
On Squaring,
The number = (5q + 3)2
= 25q2 + 30q + 9
On dividing by 5, remainder = 9 – 5 = 4
Hence required answer is 4 .
- A 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
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Let the number be 10a + b .
After interchanging the digits, the number obtained = 10b + a.Correct Option: A
Let the number be 10a + b .
After interchanging the digits, the number obtained = 10b + a.
According to the question,
Resulting number = 10a + b + 10b + a
Resulting number = 11a + 11b
Resulting number = 11 (a + b)
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
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Let two numbers are a and b and the divisor is d .
According to question ,∴ R1 = a = 3 d ∴ R2 = b = 4 d
Correct Option: C
Let two numbers are a and b and the divisor is d .
According to question ,∴ R1 = a = 3 d ∴ R2 = b = 4 d Now , R = 3 + 4 = 3 + 4 = 2 d d
⇒ 7 - 2 = 5 is divisible by d .
Required divisor = 5 { ∴ d > 4 }
- 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
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Given , Remainder = 28
Let the quotient be Q and the remainder be R. Then
According to question ,
Divisor = 7 Q = 3 RCorrect Option: D
Given , Remainder = 28
Let the quotient be Q and the remainder be R. Then
According to question ,
Divisor = 7 Q = 3 R∴ Q = 3 R = 3 × 28 = 12 7 7
⇒ Quotient = 12
∴ Divisor = 7 Q = 7 × 12 = 84
∴ Dividend = Divisor × Quotient + Remainder = 84 × 12 + 28 = 1008 + 28 = 1036
Hence the dividend is 1036.
