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Mathematical Skills | Number System

Q. No. 7:	What is the value of M and N respectively if M39048458N is divisible by 8 and 11, where M and N are single digit integers?
A :	7,8
B :	8,6
C :	6,4
D :	5,4

Solution Answer: C A number is divisible by 8 , if the number formed by the last three digits is divisible by 8. i.e 58N is divisible by 8 => N=4 Again a number is divisible by 11, if the difference between the sum of digits at even places and sum of digits at the odd places is either 0 or divisible by 11. i.e, (M+9+4+4+8) - (3+0+8+5+N) = M-N+9 = M+5 It cannot be zero hence, M+5 =11 => M=6.

Q. No. 8:	The LCM of two numbers is 280 and their ratio is 7:8. The two numbers are
A :	70,80
B :	35,40
C :	42,48
D :	28,32

Solution Answer: B Let the number be 7x and 8x HCF = x Hence, HCFLCM = 7x 8x => 280x = 56 x*x => x= 5 Thus numbers are 35 and 40.

Q. No. 9:	The numbers 1 to 29 are written side by side as follows 1234567891011......2829. If the number is divided by 9, then what is the remainder?
A :	3
B :	1
C :	0
D :	2

Solution Answer: A Sum of digits from 1 to 10 = 46 sum of digits from 11 to 20 =56 sum of digits from 21 to 29 =63 sum of the digits from numbers = 46+56+63 =165 Sum of digits in the number 165 =12 which gives a remainder of 3 when divided by 9.

Q. No. 10:	*If N=2³3⁴ , M= 2²3⁵, then find the number of factors of N that are common with the factors of M.*
A :	8
B :	15
C :	18
D :	20

Solution Answer: B The factors that are common must also be the factors of HCF(N,M) HCF(N,M) = 2²3⁴ Number of factors of 2²3⁴ = (2+1)(4+1) = 15 so there are 15 factors that are common to both.

Q. No. 11:	A and B are playing mathematical puzzles. A asks B "which whole numbers, greater than one, can divide all the nine three digit numbers 111, 222, 333, 444, 555, 666, 777, 888 and 999?" B immediately gave the desired answer. It was
A :	3, 37 and 119
B :	3, 37 and 111
C :	9, 37 and 111
D :	3, 9 and 37

Solution Answer: B Each of the number can be written as a multiple of 111. The factors of 111 are 3 and 37 Thus the desired answer is 3,37 and 111.

Q. No. 12:	It is given that 2³²+1 is exactly divisible by a certain number. Which one of the following is also divisible by the same number?
A :	2⁹⁶+1
B :	2¹⁶-1
C :	2¹⁶+1
D :	2⁶⁴+1

Solution Answer: A If 2³²+1 = a+b Since a³+ b³ = (a+b)³ -3ab(a+b) = (a+b)[(a+b)² -3ab] So, a³+ b³ is always divisible by (a+b)

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Number System