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# How many integers n are there such that a > n > b ?

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Math Expert
Joined: 02 Sep 2009
Posts: 52971
How many integers n are there such that a > n > b ?  [#permalink]

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25 Nov 2014, 07:27
1
4
00:00

Difficulty:

55% (hard)

Question Stats:

55% (01:27) correct 45% (01:44) wrong based on 149 sessions

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Tough and Tricky questions: Number Properties.

How many integers n are there such that a > n > b ?

(1) a − b = 4
(2) a and b are not integers.

Kudos for a correct solution.

Source: Chili Hot GMAT

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Joined: 25 May 2014
Posts: 46
Re: How many integers n are there such that a > n > b ?  [#permalink]

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25 Nov 2014, 07:47
1
1
(1)->a-b=4
if a=5 and b=1 then 5-1=4, there will be 3 integers such that a > n > b. i.e {2,3,4}
if a=-1 and b=-5 then (-1)-(-5) = 4 thus there will be 3 integers such that a > n > b. i.e {-2,-3,-4}
but if a= 4.5 and b=0.5 then there will be 4 integer values on the number line between 0.5 and 4.5 i.e. {1,2,3,4}
we get 2 different answers so NOT SUFFICIENT.

(2)--> a and b are not integers.
clearly not SUFFICIENT as there can be any number of integer values between a and b depending upon the values of a and b
if a=2.5 and b = 1.5 then there will be only one integer {2} such that a > n > b.
if a= 4.5 and b=0.5 then there will be 4 integer values on the number line between 0.5 and 4.5 i.e. {1,2,3,4}

Combining both statements
For any non integral values of a and b such that a-b=4 , there will always be 4 integers such that a > n > b.
Thus [C].
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Re: How many integers n are there such that a > n > b ?  [#permalink]

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25 Nov 2014, 08:33
1

By testing cases

test cases: +ve integers, +ve & -ve integers and -ve integers - all give n=3
test cases: +ve fractions, +ve & -ve fractions and -ve fractions - all give n=4

1. Not sufficient as n can be 3 or 4
2. Not sufficient as n can be anything

Combining 1 & 2 we arrive at n=4
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Posts: 143
GMAT 1: 740 Q49 V41
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Re: How many integers n are there such that a > n > b ?  [#permalink]

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25 Nov 2014, 17:00
1
Per the premise, we basically must determine whether a and b are integers or non-integers.
Statement 1 only tells us the difference (4) between them. n could be 3 or 4--Insufficient.
Statement 2 only tells us that a and b are non-integers... Insufficient.

Combining them yields n=4. Sufficient. C
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Re: How many integers n are there such that a > n > b ?  [#permalink]

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25 Nov 2014, 20:21
1
Qs: How many integers n are there such that a > n > b ?

(1) a − b = 4

Case 1 : If a = 1, b = 5 , we have 3 integers (2,3,4) in between .
Case 2 :If a = 1.1, b = 5.1 , we have 4 integers (2,3,4,5) in between.
Clearly insufficient

(2) a and b are not integers.
Clearly insufficient.

Combining 1 and 2, only the Case 2 remains. Hence C) should be the answer
Manager
Joined: 22 Sep 2012
Posts: 129
Concentration: Strategy, Technology
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Re: How many integers n are there such that a > n > b ?  [#permalink]

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25 Nov 2014, 20:22
Qs: How many integers n are there such that a > n > b ?

(1) a − b = 4

Case 1 : If a = 1, b = 5 , we have 3 integers (2,3,4) in between .
Case 2 :If a = 1.1, b = 5.1 , we have 4 integers (2,3,4,5) in between.
Clearly insufficient

(2) a and b are not integers.
Clearly insufficient.

Combining 1 and 2, only the Case 2 remains. Hence C) should be the answer
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GMAT 1: 770 Q50 V44
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Re: How many integers n are there such that a > n > b ?  [#permalink]

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25 Nov 2014, 23:42
Bunuel wrote:

Tough and Tricky questions: Number Properties.

How many integers n are there such that a > n > b ?

(1) a − b = 4
(2) a and b are not integers.

Kudos for a correct solution.

Source: Chili Hot GMAT

1) a-b = 4. If a=1, b=5, then n has 3 values. If a=1.5, b=5.5, n has 4 values. NOT SUFFICIENT.
2) a, b are not integers, not sufficient.

Combining them, if a and b are not integers, n will always have 4 values. SUFFICIENT.

Math Expert
Joined: 02 Sep 2009
Posts: 52971
Re: How many integers n are there such that a > n > b ?  [#permalink]

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26 Nov 2014, 06:29
Bunuel wrote:

Tough and Tricky questions: Number Properties.

How many integers n are there such that a > n > b ?

(1) a − b = 4
(2) a and b are not integers.

Kudos for a correct solution.

Source: Chili Hot GMAT

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Re: How many integers n are there such that a > n > b ?  [#permalink]

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18 Oct 2018, 04:46
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Re: How many integers n are there such that a > n > b ?   [#permalink] 18 Oct 2018, 04:46
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