nahid078 wrote:after distributing the sweets equally among 25 children, 8 sweets remain. Had the number of children been 28, 22 sweets would have been left after equal distribution. What was the total number of sweets?
Rich is right - the answer choices make this question much easier. Let's have a go anyway...
When it comes to remainders, we have a nice rule that says:
If N divided by D, leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
Okay, onto the question..........
Let T = TOTAL # of sweets
After distributing the sweets equally among 25 children, 8 sweets remain.
In other words, when T is divided by 25, the remainder is 8.
By the above rule, the possible values of T are 8, 33, 58, 83, 108, ....
Had the number of children been 28, 22 sweets would have been left after equal distribution.
In other words, when T is divided by 28, the remainder is 22.
By the above rule, the possible values of T are 22, 50, 78, 106, 134, 162, 190, 218,....
Hmmm, we haven't found a number in common with each list yet.
So, let's use some logic.
In the first part, we can see that the possible values of T will have a UNITS DIGIT of either 8 or 3
In the second part, we can see that the possible values of T will have a UNITS DIGIT that's even.
So, we can see that the value of T that satisfies BOTH conditions will have 8 as its UNITS DIGIT
Let's take a look at our second list.
Once we're at 218, we can see that we won't get back to a units digit of 8 until we add FIVE 28's Since 5 x 28 = 140, and adding 140 to 218 will give us a UNITS DIGIT of 8 again.
So, let's keep adding 140 to the second list and see where we get a value that also satisfies the first condition.
218 + 140 = 358...PERFECT.
358 divided by 25 leaves remainder 8.
So, there were
358 sweets.
