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Re: The integers r, s and t all have the same remainder when div
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13 Sep 2019, 18:36
Hi All,
We're told that The R, S and T are all INTEGERS and that all have the SAME remainder when divided by 5. We're asked for the value of T. This question can be solved in a couple of different ways - and it's built around a math pattern that you might not realize is there (unless you TEST VALUES to prove it).
To start, for 3 numbers to have the SAME remainder when divided by 5, they will fit a particular pattern:
IF....
the remainder is 0, then the numbers will be evenly divisibly by 5 --> such as 0, 5, 10, 15, 20, 25, etc
the remainder is 1, then the numbers will all be "1 more" than a multiple of 5 --> such as 1, 6, 11, 16, 21, 26, etc
the remainder is 2, then the numbers will all be "2 more" than a multiple of 5 --> such as 2, 7, 12, 17, 22, 27, etc
Etc.
(1) R + S = T
Using the above patterns, if we add two numbers with the SAME remainder, then we'll end up with the sum of their two remainders. For example, if R= 6 and S= 11, then we'll have a sum of 17... but 17 has a remainder of TWO (re: the sum of the two individual remainders of 1) when it's divided by 5. We're told that all 3 integers must have the SAME remainder though, so R and S clearly CANNOT have remainders of 1.
This issue occurs with all of the other options EXCEPT for remainders of 0.... for example, if R=5 and S=10, then we'll have a sum of 15... and 15 ALSO has a remainder of 0. This ultimately means that R, S and T MUST each be a multiple of 5, but we don't know exactly which multiple of 5 T is.
Fact 1 is INSUFFICIENT
(2) 20 <= T <= 24
Fact 2 gives us 5 possible values for T: 20, 21, 22, 23 and 24.... but we don't know which one it is (and we have no additional information that relates the values of R and S to the value of T, so there's no way to define the exact value of T.
Fact 2 is INSUFFICIENT
Combined, we know...
T must be a multiple of 5.
T is one of the numbers from 20 to 24, inclusive.
The only value that 'fits' both pieces of information is 20.
Combined, SUFFICIENT
Final Answer: [spoiler]C[/spoiler]
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