Number System
- 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 }
- 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.
- When two numbers are separately divided by 33, the remainders are 21 and 28 respectively. If the sum of the two numbers is divided by 33, the remainder will be
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Here , d = 33
If two numbers are separately divided by a certain divisor (d) leaving remainders r1 and r2, then remainder after their sum is divided by the same divisor.Correct Option: D
Here , d = 33
If two numbers are separately divided by a certain divisor (d) leaving remainders r1 and r2, then remainder after their sum is divided by the same divisor.
Required Remainder = r1 + r2 – d
Required Remainder = 21 + 28 – 33 = 16
- When a number is divided by 24, the remainder is 16. The remainder when the same number is divided by 12 is
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According to question ,
∴Number , remainder = 16 24
Correct Option: B
According to question ,
∴Number , remainder = 16 24
Required remainder = 16 – 12 = 4 (because 24 is a multiple of 12.)
- In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 46, then the dividend is
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Given , Remainder = 46
As per the given question ,
Divisor = 5 × Remainder
Divisor = 5 × 46 = 230
And Divisor = 10 × Quotient
Quotient =230 = 23 10
Correct Option: D
Given , Remainder = 46
As per the given question ,
Divisor = 5 × Remainder
Divisor = 5 × 46 = 230
And Divisor = 10 × Quotient
Quotient =230 = 23 10
∴ Dividend = Divisor ×
Quotient + Remainder
Dividend = 230 × 23 + 46
Required dividend = 5290 + 46 = 5336
