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# How many integers are there between integers i and k, inclusive?

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How many integers are there between integers i and k, inclusive?  [#permalink]

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29 Aug 2019, 23:39
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Competition Mode Question

How many integers are there between integers i and k, inclusive?

(1) k - i = 22

(2) There are 21 integers between, but not including, i + 1 and k + 1.

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Re: How many integers are there between integers i and k, inclusive?  [#permalink]

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30 Aug 2019, 00:18
1
How many integers are there between integers i and k, inclusive?

(1) k - i = 22
Let k=32 and i=10
32-10+1=23

SO k-i+1=22+1=23............. SUFFICIENT

(2) There are 21 integers between, but not including, i + 1 and k + 1.

k+1-i-1=21 -> k-i=21
without inclusion of k and i, it is 21 so add 2 to get inclusive number.
SUFFICIENT

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Re: How many integers are there between integers i and k, inclusive?  [#permalink]

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30 Aug 2019, 01:01
1
Statement 1 is sufficient because knowing that k-i =22 implies that there are 22+1 =23 integers between k and i both k and i inclusive.

Statement 2 is also sufficient. It is basically saying that k-(i+1)=21. This means that i+1 was not counted and I was also not counted. Therefore total integers between k and i with both k and i inclusive =21+2=23.

The answer is therefore D imo

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Re: How many integers are there between integers i and k, inclusive?  [#permalink]

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30 Aug 2019, 03:21
+ 1 and – 1 will affect result and it needs to be checked if the integers are inclusive or exclusive.

(1) $$k - i = 22$$

Snce nothing s gven about inclusivity or exclusivity the statement is INSUFFICIENT.

(2) There are 21 integers between, but not including, $$i + 1$$ and $$k + 1$$

$$k + 1 – (i + 1) – 1$$ would give the required answer since $$i +1$$ and $$k + 1$$ are not included.

SUFFICIENT.

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Re: How many integers are there between integers i and k, inclusive?  [#permalink]

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30 Aug 2019, 04:27
Asked: How many integers are there between integers i and k, inclusive?

(1) k - i = 22
Number of integers between integers i and k, inclusive = k-i + 1 = 22 + 1 = 23
SUFFICIENT

(2) There are 21 integers between, but not including, i + 1 and k + 1.
21 = k - (i+2) +1 = k - i -2 + 1
k - i + 1 = 23
Number of integers between integers i and k, inclusive = 23
SUFFICIENT

IMO D
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Re: How many integers are there between integers i and k, inclusive?  [#permalink]

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30 Aug 2019, 05:09
IMO it's D. Each says the number of integers in between.
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Re: How many integers are there between integers i and k, inclusive?  [#permalink]

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30 Aug 2019, 08:20
How many integers are there between integers i and k, inclusive?

(1) k - i = 22

(2) There are 21 integers between, but not including, i + 1 and k + 1.

#1
k=i+22
integers inclusive k& i
k-i +1 ; i+22-i+1 ; 23 sufficient
#2
There are 21 integers between, but not including, i + 1 and k + 1
so b/w i & k there will be 21+2 ; 23 integers
IMO D
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Re: How many integers are there between integers i and k, inclusive?  [#permalink]

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30 Aug 2019, 13:48
How many integers are there between integers i and k, inclusive?

we are asked how many no's are in between two integers.

(1) k - i = 22

If I = 23 and k = 1 satisfying condition k-I = 22, there are total 23 integers.
If I = 25 and k = 3 satisfying condition k-I = 22, there are total 23 integers.
Sufficient

(2) There are 21 integers between, but not including, i + 1 and k + 1.
there are total 21 integers between I, and K but excluding (1) integer that is I+1. We don't care about k+1 because we don't have to count that based on our question. so, there are 22 integers total.
Sufficient

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Re: How many integers are there between integers i and k, inclusive?  [#permalink]

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30 Aug 2019, 16:58
I think D?

Statement 1) just add one to the subtraction to get number of integers between; should not matter if negative?
statement 2) Same as above?
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Re: How many integers are there between integers i and k, inclusive?  [#permalink]

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30 Aug 2019, 19:34
Statement (1) is sufficient.
Let k,23 and I, 1
So,K-I=22.with out considering I,22-1=21.
There are 21 integers between them.
Option A

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Re: How many integers are there between integers i and k, inclusive?  [#permalink]

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31 Aug 2019, 07:24
Bunuel wrote:

Competition Mode Question

How many integers are there between integers i and k, inclusive?

(1) k - i = 22

(2) There are 21 integers between, but not including, i + 1 and k + 1.

Similar question: https://gmatclub.com/forum/how-many-int ... 40737.html
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Re: How many integers are there between integers i and k, inclusive?   [#permalink] 31 Aug 2019, 07:24
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