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• 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

Congratulations - you have completed Number System Basics: Test 3.You scored %%SCORE%% out of %%TOTAL%%.You correct answer percentage: %%PERCENTAGE%% .Your performance has been rated as %%RATING%%
 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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