Number System
- A number being divided by 52 gives remainder 45. If the number is divided by 13, the remainder will be
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Here, 52 is a multiple of 13.
Hence, the required remainder is obtained on dividing 45 by 13.Correct Option: B
Here, 52 is a multiple of 13.
Hence, the required remainder is obtained on dividing 45 by 13.
Required remainder = 6.
- The smallest number to be added to 1000, so that 45 divides the sum exactly, is :
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1000 = (45 × 22) + 10
∴ 45 – 10Correct Option: A
1000 = (45 × 22) + 10
∴ 45 – 10 = 35 to be added.
So, the smallest number to be added to 1000 to make the sum exactly divisible by 45 is 35.
- When a number is divided by 56, the remainder obtained is 29. What will be the remainder when the number is divided by 8 ?
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As we know that when the second divisor is factor of first divisor, the second remainder is obtained by dividing the first remainder by the second divisor.
Correct Option: B
As we know that when the second divisor is factor of first divisor, the second remainder is obtained by dividing the first remainder by the second divisor.
Hence, on dividing 29 by 8, the remainder is 5.
- A student was asked to multiply a number by 3/2 but he divided that number by 3/2. His result was 10 less than the correct answer. The number was :
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Let assume the given number be P. Then,
P × 3 − P ÷ 3 = 10 2 2
Correct Option: B
Let assume the given number be P. Then,
P × 3 − P ÷ 3 = 10 2 2 ⇒ 3P − 2P = 10 2 3 ⇒ 9P − 4P = 10 6
⇒ 5P = 60
⇒ P = 12
Hence , required number is 12.
- The sum of three consecutive integers is 51. The middle one is :
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Let us assume the 3 consecutive numbers are x, x + 1 and x + 2.
According to question,
∴ x + x + 1 + x + 2 = 51Correct Option: D
Let us assume the 3 consecutive numbers are x, x + 1 and x + 2.
According to question,
∴ x + x + 1 + x + 2 = 51
⇒ 3x + 3 = 51
⇒ 3x = 51 – 3 = 48⇒ x = 48 = 16 3
⇒ Middle number = 16 + 1= 17