Number System: Quantitative Aptitude MCQ Question with Details Solution

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Number System MCQ Question

The number system or the numeral system is the system of naming or representing numbers. There are various types of number systems in Mathematics like integer, prime, binary, decimal, etc. In this chapter Examportal Discussed All type Number System MCQ Question with details Explanation.


Q10. 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?

(a) 9

(b) 3

(c) 0

(d) 4

Answer: (d)

Explanation:  Let the number be 5q + 3, where q is quotient

Now, (5q + 3)2 = 25q2 + 30q  + 9  = 25q2 + 30q + 5 + 4 = 5[5q2 + 6q + 1] + 4

Hence, remainder is 4

Q11. A number when successively divided by 7 and 8 leaves the remainders 3 and 5 respectively. What is the remainder when the same number is divided by 56?

(a) 38

(b) 31

(c) 37

(d) 26

Answer: (a)

Explanation:  56 = d1 × d2

∴ required remainder = d1 r2 + r1,

where d1 = 7 and r 1 = 3 and r2 = 5.

i.e. 7 × 5 + 3 = 38

Q12. The four integers next lower than a number, and the four next higher than that number, are written down and added together, this sum is divisible by,

(a) 4

(b) 5

(c) 7

(d) 9

Answer: (a)

Explanation: Let the number = x.

Four integers next lower than x are (x–1), (x–2), (x–3), (x–4) four integers next higher than x are (x+1), (x+2), (x+3), (x+4),

Sum = (x–1) + (x–2) + (x–3) + (x–4) + (x+1) + (x+2) + (x+3) + (x+4) = 8x

Sum is divisible by 8, 4

 

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