Bunuel wrote:
How many integers are there between, but not including, integers r and s ?
(1) s - r = 10
(2) There are 9 integers between, but not including, r + 1 and s + 1.
Target question: How many integers are there between, but not including, integers r and s ? Statement 1: s - r = 10 First of all, this tells us that s is greater than r
So, on the number line, we have: ------r------------s----
Also notice that, if we take the given equation and add r to both sides, we get s = r+10
So, we can replace s with r+10 to get: ------r------------(r+10)----
Since r is an integer, we know that r+1 is an integer, and r+2 is an integer, and r+3 is an integer, etc.
If we add all of these values to our number line we get: ------r--
(r+1)--(r+2)--(r+3)--(r+4)--(r+5)--(r+6)--(r+7)--(r+8)--(r+9)--(r+10)----
We can see that there are
9 integers between r and s Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: There are 9 integers between, but not including, r + 1 and s + 1.The key here is to recognize that the number of integers between r + 1 and s + 1 IS THE SAME AS the number of integers between r and s
For example, we know that there are three integers between 5 and 9 (the integers are 6, 7 and 8)
If we add one to 5 and 9, we get 6 and 10
Notice that there are also three integers between 6 and 10 (the integers are 7, 8 and 9)
So, if there are 9 integers between r + 1 and s + 1, then we can also conclude that
there are 9 integers between r and sSince we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
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