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Number System: Level 3 Test -1

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Question 1
A player rolls a die and receives the same number of rupees as the number of dots on the face that turns up. What should the player pay for each roll if he wants to make a profit of one rupee per throw of the die in the long run?
Rs. 2.50
Rs. 2
Rs. 4
Question 1 Explanation: 
By analysing the above information, we feel it is a probability question but it is not. Since in the long run the probability of each number appearing is the same, let us assume at first that in ‘x ’ throws one can get 1, 2, 3, 4, 5 and 6, that is n/6 times each. Hence, the earning could be (1+2+3+4+5+6)x/6 = Rs.7x/2.  Now the task is to determine what should the player pay so that he has aprofit of one rupee. For this, each throw he plays has to make a profit for x rupee. Hence the formula for his cost should be (7n/2– x ). So his cost per throw should be (7/2 – 1) = 5/2 = Rs.2.50.
Question 2
What is the greatest power of 5 which can divide 80! exactly
None of these
Question 2 Explanation: 
We have to obtain the highest power of 5 so that the 80! can be exactly divided by 5 , so in the first step we use factorisation method without checking for any remainder ,and then we will divide it till the lowest term . When we start dividing 80 by 5, in the first step 80 is divisible by 5 so there is no remainder. But we have to further divide 16 with five this time we have a remainder i.e. 1 without carrying it we come know the number of fives in the 80! Is 19 i.e. 16+3=19. So the highest power which will divide the 80! exactly is 19. So the correct answer is option C
Question 3
If x is a positive integer such that 2x +12 is perfectly divisible by x, then the number of possible values of x is
Question 3 Explanation: 
In these type of questions, we are given one thing i.e. (2x + 12) is perfectly divisible by x,
and using this we can make out that when we divide (2x + 12)/x
then the result will come in terms of x or it will be an integer as x is an integer.
So on dividing the given expression by x the resultant expression will be in the form of 2+12/x.
Now if we have to make the expression an integer, there is only two ways for doing
so ,one is that 12/x should be a integer and thus 12 is perfectly divisible by x.
The possible values for the term x that remain: 1,2, 3, 4, 6, 12
. Hence, the answer is 6 values. Here we can use the value 6 only
because we not only have to see the 12/x to be an integer but as long as the whole condition
which is given in the initial stage of the question.
So, the right answer is option is C.
Question 4
If 8 + 12 = 2, 7 + 14 = 3 then 10 + 18 = ?
Question 4 Explanation: 
This is another tricky question. In this type of questions you can only find the answer
if you have practiced a lot of questions of this type.
In this question when we look at the statements
which states that 8+12=2 ,
we all know that the result would come 20
but they has given is as 2 ,
and in the second case the statement given is 7+14 =3,
so result given is 3 instead of 21.
By observing both these statements,
the logic strikes that examiner has added the digits of one
and tens place the first statement is 8+12 =2+0=2
and the other one is 7+14=2+1=3,
and thus we arrive at our correct answer: 10+18=2+8+10.
Question 5
A five digit number is formed using digits 1, 3, 5, 7 and 9 without repeating any one of them. What is the sum of all such possible numbers?
Question 5 Explanation: 
This is a logical question.
We have been given a set of numbers and we have to arrange it in an order without any repetition so if we do it in a simple way then it will take more time and will be difficult to solve. Here is an another method: Fix any of the digits and fill all the numbers you will see as you fill in the next boxes, the number is filled in four ways by keeping one fixed at one position and the number of ways by which the other can be filled are 4! i.e. 24 ways. So it is clear that each of the five digits will appear 24 times so the sum for each position will be
24(1+3+5+7+9) = 600 Now this is only for positions where one may be at a fixed position and the all other sums will be
600(1 + 10 + 100 + 1000 + 10000) = 6666600.
Thus, we arrive at the total in using a simplified approach rather than using the process of counting.
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