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Math Expert V
Joined: 02 Sep 2009
Posts: 56277
List A consists of five distinct integers. Is the range of the numbers  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 46% (02:01) correct 54% (01:48) wrong based on 144 sessions

### HideShow timer Statistics Fresh GMAT Club Challenge Question

List A consists of five distinct integers. Is the range of the numbers in list A greater than 8?

(1) List A does not contain a multiple of 5.
(2) No two numbers in list A are consecutive.

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Re: List A consists of five distinct integers. Is the range of the numbers  [#permalink]

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Bunuel wrote:

Fresh GMAT Club Challenge Question

List A consists of five distinct integers. Is the range of the numbers in list A greater than 8?

(1) List A does not contain a multiple of 5.
(2) No two numbers in list A are consecutive.

Question : Is the range of the numbers in list A greater than 8?

Statement 1: List A does not contain a multiple of 5.
Sets A could be {1, 2, 3, 4 ,6} range = 5 <8
Sets A could be {1, 2, 3, 4 ,11} range = 10 >8
NOT SUFFICIENT

Statement 2: No two numbers in list A are consecutive.
Sets A could be {1, 3, 5, 7 ,9} range = 8 =8 Answer to Question is NO
Sets A could be {1, 3, 5, 7 ,11} range = 10 >8 Answer to Question is YES
NOT SUFFICIENT

Combining statements
The closest elements of Sets A could be {1, 3, 7, 9, 11} range = 10 >8 Answer to Question is YES

SUFFICIENT

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Intern  B
Joined: 03 Nov 2017
Posts: 14
GMAT 1: 610 Q47 V28 Re: List A consists of five distinct integers. Is the range of the numbers  [#permalink]

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IMO E.

Statement 1 : Can')t be a multiple of 5, and has to be 5 distinct integers, no sure way to know if the range is going to be more than 8.

Statement 2 : No consecutive numbers, still no idea.

1+2 : Still not clear, so its E.

GMAT insight - want to know how you arrived at your answer? I think there is something wrong in mine.
Intern  B
Joined: 08 Feb 2015
Posts: 22
Re: List A consists of five distinct integers. Is the range of the numbers  [#permalink]

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C. As it cannot be multiple of 5 and no 2 consecutive numbers. So example will be 1 3 6 8 11.
Manager  G
Joined: 24 Nov 2016
Posts: 223
Location: United States
Re: List A consists of five distinct integers. Is the range of the numbers  [#permalink]

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GMATinsight wrote:
Bunuel wrote:

Fresh GMAT Club Challenge Question

List A consists of five distinct integers. Is the range of the numbers in list A greater than 8?

(1) List A does not contain a multiple of 5.
(2) No two numbers in list A are consecutive.

Question : Is the range of the numbers in list A greater than 8?

Statement 1: List A does not contain a multiple of 5.
Sets A could be {1, 2, 3, 4 ,6} range = 5 <8
Sets A could be {1, 2, 3, 4 ,11} range = 10 >8
NOT SUFFICIENT

Statement 2: No two numbers in list A are consecutive.
Sets A could be {1, 3, 5, 7 ,9} range = 8 =8 Answer to Question is NO
Sets A could be {1, 3, 5, 7 ,11} range = 10 >8 Answer to Question is YES
NOT SUFFICIENT

Combining statements
The closest elements of Sets A could be {1, 3, 7, 9, 11} range = 10 >8 Answer to Question is YES

SUFFICIENT

Does distinct integers mean they are positive integers?
Retired Moderator D
Joined: 25 Feb 2013
Posts: 1197
Location: India
GPA: 3.82
List A consists of five distinct integers. Is the range of the numbers  [#permalink]

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2
Bunuel wrote:

Fresh GMAT Club Challenge Question

List A consists of five distinct integers. Is the range of the numbers in list A greater than 8?

(1) List A does not contain a multiple of 5.
(2) No two numbers in list A are consecutive.

Statement 1: {2,4,6,8,11} $$range=9>8$$

{1,2,3,4,6} $$range=5<8$$. Insufficient

Statement 2: {2,4,6,8,11} $$range=9>8$$

{-2,0,2,4,6} $$range=8$$ hence not greater than 8. Insufficient

Combining 1 & 2 we know that none of the number are consecutive so the minimum difference between any two numbers will be $$2$$. So moving from the least to the maximum value, the minimum difference will be $$2+2+2+2=8$$

We also know that none of the number can be multiple of $$5$$, so $$5$$ and a number prior and/or after it will also be excluded. This will further increase the difference by at least $$1$$ (depending upon the elements) e.g (1,3,7,9,11) or {-7,-4,-2,1,3}

Hence the minimum range will be $$8+1=9$$. Sufficient

Option C

Originally posted by niks18 on 03 Dec 2017, 10:24.
Last edited by niks18 on 04 Dec 2017, 11:07, edited 1 time in total.
Retired Moderator P
Joined: 22 Aug 2013
Posts: 1435
Location: India
Re: List A consists of five distinct integers. Is the range of the numbers  [#permalink]

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exc4libur wrote:
GMATinsight wrote:
Bunuel wrote:

Fresh GMAT Club Challenge Question

List A consists of five distinct integers. Is the range of the numbers in list A greater than 8?

(1) List A does not contain a multiple of 5.
(2) No two numbers in list A are consecutive.

Question : Is the range of the numbers in list A greater than 8?

Statement 1: List A does not contain a multiple of 5.
Sets A could be {1, 2, 3, 4 ,6} range = 5 <8
Sets A could be {1, 2, 3, 4 ,11} range = 10 >8
NOT SUFFICIENT

Statement 2: No two numbers in list A are consecutive.
Sets A could be {1, 3, 5, 7 ,9} range = 8 =8 Answer to Question is NO
Sets A could be {1, 3, 5, 7 ,11} range = 10 >8 Answer to Question is YES
NOT SUFFICIENT

Combining statements
The closest elements of Sets A could be {1, 3, 7, 9, 11} range = 10 >8 Answer to Question is YES

SUFFICIENT

Does distinct integers mean they are positive integers?

Hi
No, it doesnt mean that the integers have to be positive. They could be 0 or negative as well.
Retired Moderator P
Joined: 22 Aug 2013
Posts: 1435
Location: India
Re: List A consists of five distinct integers. Is the range of the numbers  [#permalink]

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IMO E.

Statement 1 : Can')t be a multiple of 5, and has to be 5 distinct integers, no sure way to know if the range is going to be more than 8.

Statement 2 : No consecutive numbers, still no idea.

1+2 : Still not clear, so its E.

GMAT insight - want to know how you arrived at your answer? I think there is something wrong in mine.

Hi

You are right, each statement alone is not sufficient. But when you combine the two statements, you see that they have to be distinct integers, and no two integers should be consecutive. So if you arrange all five distinct integers in ascending order (smallest to largest), the least difference between any two consecutive terms should be 2. Lets try to make such a set: I will start with least integer as 1, then next integer will have a minimum value of 3 (because they cannot be consecutive), now next integer can take a minimum value of 5, but since multiples of 5 are not allowed, next minimum value will be 6, next minimum value 8, and next 11. So we have:

1, 3, 6, 8, 11.. as you can see range is (11-1) = 10, which is > 8 .

Now if you start with 2, next number will take minimum value of 4, then 6, then 8, then 11 (since 10 is not allowed)
So 2, 4, 6, 8, 11.. here range is 11-2 = 9, which is again > 8.

In any case no matter which smallest integer you start with, range will always be greater than 8, if you go by data of both statements.
Manager  G
Joined: 24 Nov 2016
Posts: 223
Location: United States
List A consists of five distinct integers. Is the range of the numbers  [#permalink]

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amanvermagmat wrote:

List A consists of five distinct integers. Is the range of the numbers in list A greater than 8?

(1) List A does not contain a multiple of 5.
(2) No two numbers in list A are consecutive.

Does distinct integers mean they are positive integers?

Hi
No, it doesnt mean that the integers have to be positive. They could be 0 or negative as well.

Ok so if the integers can be positive negative or 0 then:
(1) No multiples of 5. Sets can be {-22,-21,-18,-16,-14} and range = last - first = -14 - (-22) = 8, which is not greater than 8. Or, {-11,-9,1,7,9} and range = 9 - (-11) = 20 > 8; not suf.
(2) No two numbers are consecutive. Sets can be {-22,-20,-18,-16,-14} range = 8. Or, {-11,-9,0,7,9} range = 20 > 8; not suf.
(3) Set can be {-3,-1,2,4,6} and the range = 6 - (-3) = 9 > 8. Or, {-11,-9,1,7,9} range = 20 > 8; sufficient.

Originally posted by exc4libur on 04 Dec 2017, 05:23.
Last edited by exc4libur on 04 Dec 2017, 06:49, edited 1 time in total.
Retired Moderator D
Joined: 25 Feb 2013
Posts: 1197
Location: India
GPA: 3.82
Re: List A consists of five distinct integers. Is the range of the numbers  [#permalink]

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1
exc4libur wrote:
amanvermagmat wrote:

List A consists of five distinct integers. Is the range of the numbers in list A greater than 8?

(1) List A does not contain a multiple of 5.
(2) No two numbers in list A are consecutive.

Does distinct integers mean they are positive integers?

Hi
No, it doesnt mean that the integers have to be positive. They could be 0 or negative as well.

Ok so if the integers can be positive negative or 0 then:
(1) No multiples of 5. Sets can be {-22,-21,-18,-16,-14} and range = last - first = -14 - (-22) = 8, which is not greater than 8. Or, {-11,-9,0,7,9} and range = 9 - (-11) = 20 > 8; not suf.
(2) No two numbers are consecutive. Sets can be {-22,-20,-18,-16,-14} range = 8. Or, {-11,-9,0,7,9} range = 20 > 8; not suf.
(3) Set can be {-2,0,2,4,6} and the range = 6 - (-2) = 8 not greater than 8. Or, {-11,-9,0,7,9} range = 20 > 8; not suf.

Im still not sure if my working is correct. If anyone can confirm that would be great thanks.

Hi exc4libur

0 is multiple of every number 0/5=0. So remove 0 from the set and then try to find out the range. See if it's greater or less than 8 Manager  G
Joined: 24 Nov 2016
Posts: 223
Location: United States
Re: List A consists of five distinct integers. Is the range of the numbers  [#permalink]

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niks18 wrote:
exc4libur wrote:
amanvermagmat wrote:

List A consists of five distinct integers. Is the range of the numbers in list A greater than 8?

(1) List A does not contain a multiple of 5.
(2) No two numbers in list A are consecutive.

Does distinct integers mean they are positive integers?

Hi
No, it doesnt mean that the integers have to be positive. They could be 0 or negative as well.

Ok so if the integers can be positive negative or 0 then:
(1) No multiples of 5. Sets can be {-22,-21,-18,-16,-14} and range = last - first = -14 - (-22) = 8, which is not greater than 8. Or, {-11,-9,0,7,9} and range = 9 - (-11) = 20 > 8; not suf.
(2) No two numbers are consecutive. Sets can be {-22,-20,-18,-16,-14} range = 8. Or, {-11,-9,0,7,9} range = 20 > 8; not suf.
(3) Set can be {-2,0,2,4,6} and the range = 6 - (-2) = 8 not greater than 8. Or, {-11,-9,0,7,9} range = 20 > 8; not suf.

Im still not sure if my working is correct. If anyone can confirm that would be great thanks.

Hi exc4libur

0 is multiple of every number 0/5=0. So remove 0 from the set and then try to find out the range. See if it's greater or less than 8 Thank you I'll make the changes. Awesome Math Expert V
Joined: 02 Sep 2009
Posts: 56277
Re: List A consists of five distinct integers. Is the range of the numbers  [#permalink]

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Bunuel wrote:

Fresh GMAT Club Challenge Question

List A consists of five distinct integers. Is the range of the numbers in list A greater than 8?

(1) List A does not contain a multiple of 5.
(2) No two numbers in list A are consecutive.

_________________ Re: List A consists of five distinct integers. Is the range of the numbers   [#permalink] 24 Dec 2018, 02:52
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