• The test assesses your understanding of No. System.
  • Questions belong to the very easy to easy difficulty range.
  • Low scores point to a flaw in basic understanding of the concepts.

Number System Basics: Test 3

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Question 1
In a mess, there are number of students having fun with their meal. The total number of students in the Mess is a two digit number and that number is a prime number. Keeping this in mind, which of the following could be the ratio of boys vs number of girls
A
7: 8
B
14: 15
C
25: 26
D
None of these
Question 1 Explanation: 
Given that the total number of students is a prime number,
the given ratio will be the exact number of boys and girl students,
so using the answer options, we can easily
find the ratio by adding and checking:
Option A: 7+8 = 15 not a prime number
Option C: 25+26 = 51, not a prime number
Option B: 14+15= 29 is a prime number,  so option b is the right answer.
Question 2
How many fractions in the form of the (p/q) (q not equal to zero) are there between 3/4  and 4/5?
A
1
B
56
C
Infinite
D
None of these
Question 2 Explanation: 
The right answer is infinite because between two
rational numbers there exist infinite number of rational numbers
Question 3
If we have two numbers r and r + 1 (both are prime numbers), then what can be said about r - 1?
A
It is a perfect number
B
It is a composite number
C
Its square is a composite number.
D
It has only 1 factor
Question 3 Explanation: 
It is given that r and r+1 are prime numbers.
This means r has to be 2, otherwise this is not possible.
r-1=1, and it is neither prime nor composite,
and it has only one factor.
Question 4
If p is prime number greater than 7 then what can we say about the divisibility of p2 -1?
A
Number divisible by 5
B
Number is not divisible by 5
C
Number must be divisible by 6
D
None
Question 4 Explanation: 
Since it is given that the prime number which is greater than the 7, let us consider one such number: 11 So if p = 11 then p2 -1=120
which is divisible by 5,6
P=13, 169-1=168 not divisible by 5 but divisible by 6
P=17, 289-1=288 not divisible by 5 but divisible by 6
So the right answer is option 3.
Question 5
If s is the summation of a two digit number and the number formed by reversing its digits, then  which of the following is correct about S?(i) S may be divisible by 11 (ii) S must be divisible by 11 (iii) S is an odd number
A
Only (i) and (ii)
B
Only (ii)
C
Only (ii) & (iii)
D
None of these
Question 5 Explanation: 
Let a two digit number be 'ab' = 10a + b (here a is not equal to 0)
S = (10a + b) + (10b + a) =11(a+b)
From this we can infer that S will always be divisible by 11, making statement (ii) correct.
And S is odd or even depends on (a+b),
because if it is even then S would be even and if it is odd then S would be odd as odd*odd=odd and odd*even=even.
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