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505-555 Level|   Number Properties|                  
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AliciaSierra
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How many integers are there between, but not including, integers r and 15 May 2018, 10:16
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Why did we assume that R to S is continuous series ?

can't it be 0, 1, 10

R=0, S=10 ..but number of integer between S and R will 1.
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How many integers are there between, but not including, integers r and 15 May 2018, 10:49
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ammuseeru
Why did we assume that R to S is continuous series ?

can't it be 0, 1, 10

R=0, S=10 ..but number of integer between S and R will 1.
Show more

Hello

What do you mean by continuous series - can you please make it clear?
Whichever values we assume for r/s, as far as those values satisfy the given constraint (that s - r = 10), there will always be 9 integers between them.

The values that you have taken: r=0, s=10 - here also there are 9 integers between r and s (1, 2, 3, 4, 5, 6, 7, 8, 9).
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How many integers are there between, but not including, integers r and 06 Feb 2019, 23:29
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dzodzo85
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.

I may have mistakenly chosen the wrong answer, but nevertheless some expert explanation will help me understand this better.
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Dear Moderator,
Found this DS question in the PS section, hope you will do the needful. Thank you.
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How many integers are there between, but not including, integers r and 06 Feb 2019, 23:53
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stne
dzodzo85
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.

I may have mistakenly chosen the wrong answer, but nevertheless some expert explanation will help me understand this better.

Dear Moderator,
Found this DS question in the PS section, hope you will do the needful. Thank you.
Show more
__________________
Merged. Thank you.
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How many integers are there between, but not including, integers r and 10 Feb 2020, 08:57
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Bunuel
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.
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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 s
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent
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How many integers are there between, but not including, integers r and 21 Feb 2020, 13:38
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longhaul123
one small doubt in the statement 1. Why shouldn't we consider s=-10 and r=20 in which case the sum is 10 but the number of integers between them is not 9. Kindly explain
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If s=-10 and r=-20 then it makes sense. s-r=10 and the integers between s and r is also 9.
Hope it helps.
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How many integers are there between, but not including, integers r and 21 Feb 2020, 13:58
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ammuseeru
Why did we assume that R to S is continuous series ?

can't it be 0, 1, 10

R=0, S=10 ..but number of integer between S and R will 1.
Show more
Hello ammuseeru
Quote:
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.
Show more
You can consider whatever you like in the highlighted part until you consider both statements. But, if you take statement 1 then you have to be specific in your thinking.
In statement 1, s-r=10 means s=r+10.

r--(r+1)---(r+2)---(r+3)----(r+4)---(r+5)---(r+6)---(r+7)---(r+8)--(r+9)----s (r+10)-->The are just 9 integers.
So, it has to be in ''continuous serious'' definitely.
If you're asked that how many integers between 97 and 100? can you skip any digit? definitely not. The series are continuous (97, 98, 99, 100).
Quote:
R=0, S=10 ..but number of integer between S and R will 1
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Here, the number of integers=(s-r)+1
=10+1 (in statement 1, s-r=10)
=11
=11-2(excluding s and r)
=9 integers
Hope it helps.
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How many integers are there between, but not including, integers r and 05 Aug 2025, 03:34
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