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# How many integers are there between, but not including

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Senior Manager
Joined: 17 Mar 2014
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Re: How many integers are there between, but not including  [#permalink]

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15 May 2018, 09:16
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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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Re: How many integers are there between, but not including  [#permalink]

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15 May 2018, 09:49
ammuseeru wrote:
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.

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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Re: How many integers are there between, but not including  [#permalink]

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06 Feb 2019, 22:29
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dzodzo85 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.

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.
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- Stne
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Re: How many integers are there between, but not including  [#permalink]

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06 Feb 2019, 22:53
stne wrote:
dzodzo85 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.

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.

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Merged. Thank you.
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Re: How many integers are there between, but not including  [#permalink]

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10 Feb 2020, 07:57
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Top Contributor
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 s
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
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Joined: 23 Feb 2015
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Re: How many integers are there between, but not including  [#permalink]

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21 Feb 2020, 12:38
longhaul123 wrote:
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

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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Re: How many integers are there between, but not including  [#permalink]

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21 Feb 2020, 12:58
ammuseeru wrote:
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.

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.

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

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.
Re: How many integers are there between, but not including   [#permalink] 21 Feb 2020, 12:58

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