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Number System: Remainders Test-4

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Question 1
When p is divided by the 15, 13 was the remainder then what will be the remainder when p is divided by 5
A
4
B
8
C
3
D
2
Question 1 Explanation: 
The number p is when divided by 15, 13 was the remainder ,
so p is in the form  = 15 k +13 and  the possible values for p would be 13 , 28 , 33…..
So when the various values of p i.e 13,28,33….
when divided by 5 then the remainder will be 3 each time
So the right answer is option (c)
Question 2
P when divided by 7 leaves the remainder 4 and q when divided by 7 leaves remainder 5 . then what will be the remainder when p +q is divided by 7
A
0
B
2
C
none
D
cannot be determined
Question 2 Explanation: 
We know that p/7 = 4 as the remainder ; hence p is in the form o f 7 k +4
q/7 = 5 as the remainder , so q is in the form  = 7J +5
Adding both i.e p+q and dividing by 7 ; the multiple of 7
will be cancelled and so the total of remainders are 9 which is greater than the 7
and can be further divided  by 7 , we will get 2 as remainder
so the right answer for the question is (b)
Question 3
When p is divided by 12, then 9 remains in the end so what will be at the end when, 4p are divided by 12
A
0
B
8
C
6
D
2
Question 3 Explanation: 
4p can be written as p + p + p + p
So when p is divided by 12, 9 was the remainder
So each time when 9 is divided by all p’s 9 will be the remainder
So the total of all 9’s would be 36 which is greater than the 12 and can be further divided by 12.
So we all know 36 is multiple of 12 so there will be no remainder when 4p is divided by the 12.
So the answer option (a) is the right answer
Question 4
p and q when divided by 17, we get remainder as 9 and 11, so what will be the remainder when (p-q)2  is divided by 17
A
4
B
8
C
6
D
2
Question 4 Explanation: 
Here we are given by the two remainders of two number p and q when divided by 17
P is the form of 17k + 9 ; whereas q is the form of 17y +11 ;
Possible values of p = 9 , 26 , 43 , 60 …… Possible value of q = 11 , 28 , 45
Considering any value of p & q and substituting the same the answer will be 4 i.e option a.
Question 5
What will be the minimum number which when divided by 5,6,7 leaves the remainder 2,3,4 respectively
A
417
B
210
C
207
D
none
Question 5 Explanation: 
From the question we can observe that a common number is decreased each time
That means 3 is subtracted from 5 ,6,7, to get the remainders 2,3,4
That means if a number which is completely divisible by 5 and if we subtract 2 from
the number then 3 will be the remainder This case is also applicable for rest of
the two cases. So the minimum number which will satisfy this criteria can be obtained by subtracting 3 from the LCM of 5 6 7
If we subtract 3 from 210, we are left with 207 and when this 207 is divided by 5, 6, 7
then, 2, 3,4will be the remainder respectively
We are asked by the minimum number so the right answer for the question is (c)
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