Data Sufficiency

ela07mjt wrote:When the positive integer n is divided by 25, the remainder is 13. What is the value of n ?

(1) n < 100
(2) When n is divided by 20, the remainder is 3.

Anurag@Gurome wrote:

hemant_rajput wrote:n will be of form 25k -13
...
so now there are 4 possible values of n - 12,37,62,87
NOT Sufficient.

Hi Hemant!

Although you have achieved the "correct answer" that too using the proper algebraic method, I'd chip in to point out a mistake which may be a silly mistake or a basic misconception.

If a positive integer n leaves a remainder of 13 when divided by 25, n will either of the form (25k + 13) or (25j - 12), where k is some non-negative integer and j is some positive integer.

You could've clearly checked this with the possible values of n you've got.
12, 37, 62, and 87 - all of them leaves a remainder of 12 (not 13) when divided by 25.

Hope this helps.

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...

ela07mjt wrote:When the positive integer n is divided by 25, the remainder is 13. What is the value of n ?

(1) n < 100
(2) When n is divided by 20, the remainder is 3.