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Number System: Level 2 Test -3

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Question 1
9^6 + 7, when divided by 8, what would be the remainder by such operation
A
0
B
6
C
5
D
None of these
Question 1 Explanation: 
According to the remainder theorem, 
9^ 6 + 7/8 will have the same remainder  as 1^6 + 7/8 
and this will have the remainder as 0
Question 2
What is the least fraction number which must be added to 29/12+ 15/16, will make the result a whole number
A
21/38
B
31/38
C
31/48
D
17/48
Question 2 Explanation: 
Now 29/12 + 15/16 = 116+ 45/48 = clearly,
the least fraction among options given is 31/ 48 161/48 + 31/48 = 192/48=4
which is a whole number
Question 3
The highest power of 9 which completely divide 99!
A
20
B
24
C
22
D
12
Question 3 Explanation: 
99! = 99 x 98 x 97 x 96 x 95 x 94 x……………. x 1
To find the highest power of 9 that divides the
above product, it is required to find the sum of powers of all
9s in the expansion.  Sum of powers of 9 s
= 99/9^1  +  99/9^2  = 11 + 1 = 12 (ignoring the fractional part )
Question 4
In a community of 175 persons, 40 read the Times, 50 read the Samchar and 100 do not read any. How many persons read both the papers?
A
10
B
15
C
20
D
25
Question 4 Explanation: 
Number of persons, who read = 175-100 =75
Now, number of persons who read either and of the papers = (40 + 50) = 90
Hence, number of those who read both the papers  = (90 -75) = 15
Question 5
In a group of buffaloes and ducks, the number of legs of the group is 24 more than twice the number of heads of the group. Find the number of buffaloes in the group?
A
6
B
12
C
8
D
None of these
Question 5 Explanation: 
Let the number of buffaloes be x and number of ducks be y.
Then, number of legs = 4x + 2y,
number of heads = x + y given, 4x + 2y = 2(x + y) + 24
2x = 24
x =12
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