A quick lesson on remainders:
When x is divided by 5, the remainder is 3.
In other words, x is 3 more than a multiple of 5:
x = 5a + 3.
When x is divided by 7, the remainder is 4.
In other words, x is 4 more than a multiple of 7:
x = 7b + 4.
Combined, the statements above imply that when x is divided by both 5 and 7 -- in other words, when x is divided by 35 -- there will be a constant remainder R.
Put another way, x is R more than a multiple of 35:
x = 35c + R.
To determine the value of R:
Make a list of values that satisfy the first statement:
When x is divided by 5, the remainder is 3.
x = 5a + 3 = 3, 8, 13, 18...
Make a list of values that satisfy the second statement:
When x is divided by 7, the remainder is 4.
x = 7b + 4 = 4, 11, 18...
The value of R is the SMALLEST VALUE COMMON TO BOTH LISTS:
R = 18.
Putting it all together:
x = 35c + 18.
Another example:
When x is divided by 3, the remainder is 1.
x = 3a + 1 = 1, 4, 7, 10, 13...
When x is divided by 11, the remainder is 2.
x = 11b + 2 = 2, 13...
Thus, when x is divided by both 3 and 11 -- in other words, when x is divided by 33 -- the remainder will be 13 (the smallest value common to both lists).
x = 33c + 13 = 13, 46, 79...
Onto the problem at hand:
j_shreyans wrote:Hi Guys ,
Pls help me out with the below .
Positive integer n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5. If n is greater than 30, what is the remainder that n leaves after division by 30?
(A) 3
(B) 12
(C) 18
(D) 22
(E) 28
Make a list of values that satisfy the first condition:
Positive integer n leaves a remainder of 4 after division by 6.
n = 6a + 4 = 4, 10, 16, 22,
28...
Make a list of values that satisfy the second condition:
Positive integer n leaves a remainder of 3 after division by 5.
n = 5b + 3 = 3, 8, 13, 18, 23,
28...
Thus, when n is divided by both 6 and 5 -- in other words, when n is divided by 30 -- the remainder will be 28 (the smallest value common to both lists).
n = 30c + 28 = 28, 58, 88...
When any of the values in this list are divided by 30, the remainder is 28.
The correct answer is
E.
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