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Manager  Joined: 19 Oct 2011
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Location: India
If x and n are integers is the sum of x and n less than zero  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 64% (01:39) correct 36% (02:00) wrong based on 237 sessions

### HideShow timer Statistics If x and n are integers, is the sum of x and n less than zero?

(1) x + 3 < n – 1
(2) -10x > 10n
Math Expert V
Joined: 02 Sep 2009
Posts: 56307
Re: If x and n are integers is the sum of x and n less than zero  [#permalink]

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4
2
If x and n are integers, is the sum of x and n less than zero?

Question: is x+n<0?

(1) x + 3 < n – 1 --> x-n<-4. Plugging numbers is probably the best way to prove that this statement is not sufficient: x=0 and n=5 then the answer is NO but if x=-5 and n=0 then the answer is YES. Not sufficient.

(2) -10x > 10n --> 10x+10n<0 --> reduce by 10: x+n<0, hence the answer to the question is YES. Sufficient.

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SVP  G
Joined: 24 Jul 2011
Posts: 1821
GMAT 1: 780 Q51 V48 GRE 1: Q800 V740 Re: If x and n are integers, is the sum of x and n less than  [#permalink]

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Using statement 1, x < n-4. x+n can thus be <0 if x and n are both <0 or it can be >0 if x and n are both >0. Insufficient.

Using statement 2, -2x>2n
=> x<-n
=> x+n<0. Sufficient.

B it is.
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Re: If x and n are integers is the sum of x and n less than zero  [#permalink]

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Thanks Bunel for the solution.
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Joined: 12 Aug 2015
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GRE 1: Q169 V154 Re: If x and n are integers is the sum of x and n less than zero  [#permalink]

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dvinoth86 wrote:
If x and n are integers, is the sum of x and n less than zero?

(1) x + 3 < n – 1
(2) -10x > 10n

Statement 1 can be rejected here as there is no way we can get a +ve relation from a -ve one..
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Current Student D
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Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: If x and n are integers is the sum of x and n less than zero  [#permalink]

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Clearly statement 1 is sufficient
As far as statement 1 goes => there is no way we can convert a - relation to a + one..
Hence B is sufficient
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Re: If x and n are integers is the sum of x and n less than zero  [#permalink]

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dvinoth86 wrote:
If x and n are integers, is the sum of x and n less than zero?

(1) x + 3 < n – 1
(2) -10x > 10n

Statement 1: We know here that x+3 < n-1. Via algebra, we can determine that x-n < -4. But we don't know if x+n is greater than or less than zero (or equal to zero).

X = 10
N = 14

X+N > 0

X-N = -4

Or
x = -4
n = 0

X+N < 0
X-N = -4

Statement 2: Here we know that -2x > 2n. The secret hidden trick here is to add one term to the other side. So we can quickly find that -x>n and then 0>n+x. The problem tried to hide it from us by making us first divide out the two and leading us to making a ratio. But addition is the ultimate step.
Manager  B
Joined: 21 Feb 2017
Posts: 71
Re: If x and n are integers is the sum of x and n less than zero  [#permalink]

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Bunuel wrote:
If x and n are integers, is the sum of x and n less than zero?

Question: is x+n<0?

(1) x + 3 < n – 1 --> x-n<-4. Plugging numbers is probably the best way to prove that this statement is not sufficient: x=0 and n=5 then the answer is NO but if x=-5 and n=0 then the answer is YES. Not sufficient.

(2) -10x > 10n --> 10x+10n<0 --> reduce by 10: x+n<0, hence the answer to the question is YES. Sufficient.

Why B alone is sufficient? Because if x and n are zero than it is equal to zero which is not less than zero. So B alone is not sufficient.

If we combine both than two statements contradict each other.

Please correct me where ever I am wrong.

Sent from my XT1663 using GMAT Club Forum mobile app
Math Expert V
Joined: 02 Sep 2009
Posts: 56307
Re: If x and n are integers is the sum of x and n less than zero  [#permalink]

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goalMBA1990 wrote:
Bunuel wrote:
If x and n are integers, is the sum of x and n less than zero?

Question: is x+n<0?

(1) x + 3 < n – 1 --> x-n<-4. Plugging numbers is probably the best way to prove that this statement is not sufficient: x=0 and n=5 then the answer is NO but if x=-5 and n=0 then the answer is YES. Not sufficient.

(2) -10x > 10n --> 10x+10n<0 --> reduce by 10: x+n<0, hence the answer to the question is YES. Sufficient.

Why B alone is sufficient? Because if x and n are zero than it is equal to zero which is not less than zero. So B alone is not sufficient.

If we combine both than two statements contradict each other.

Please correct me where ever I am wrong.

Sent from my XT1663 using GMAT Club Forum mobile app

(2) gives x+n<0. So, both x and n cannot be 0, otherwise x+n<0 won't be correct.
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Re: If x and n are integers is the sum of x and n less than zero  [#permalink]

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Bunuel wrote:
goalMBA1990 wrote:
Bunuel wrote:
If x and n are integers, is the sum of x and n less than zero?

Question: is x+n<0?

(1) x + 3 < n – 1 --> x-n<-4. Plugging numbers is probably the best way to prove that this statement is not sufficient: x=0 and n=5 then the answer is NO but if x=-5 and n=0 then the answer is YES. Not sufficient.

(2) -10x > 10n --> 10x+10n<0 --> reduce by 10: x+n<0, hence the answer to the question is YES. Sufficient.

Why B alone is sufficient? Because if x and n are zero than it is equal to zero which is not less than zero. So B alone is not sufficient.

If we combine both than two statements contradict each other.

Please correct me where ever I am wrong.

Sent from my XT1663 using GMAT Club Forum mobile app

(2) gives x+n<0. So, both x and n cannot be 0, otherwise x+n<0 won't be correct.

Understood. Thank you very much for explanation.

Sent from my XT1663 using GMAT Club Forum mobile app
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Re: If x and n are integers is the sum of x and n less than zero  [#permalink]

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dvinoth86 wrote:
If x and n are integers, is the sum of x and n less than zero?

(1) x + 3 < n – 1
(2) -10x > 10n

From statement 2, it is clear that n+x<0
From statement 1: x=5 8<n-1; if x=0 0<n-1; if x=-5 -5<n-1 So, not sufficient
CEO  V
Joined: 12 Sep 2015
Posts: 3855
Re: If x and n are integers is the sum of x and n less than zero  [#permalink]

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Top Contributor
dvinoth86 wrote:
If x and n are integers, is the sum of x and n less than zero?

(1) x + 3 < n – 1
(2) -10x > 10n

Target question: Is x + n < 0?

Given: x and n are integers

Statement 1: x + 3 < n – 1
Add 1 to both sides to get: x + 4 < n
In other words, n is GREATER than 4 more than x
There are several values of x and n that satisfy this condition. Here are two:
Case a: x = 1 and n = 6, in which case x + n = 7. In this case, x + n > 0
Case b: x = -10 and n = 0, in which case x + n = -10. In this case, x + n < 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: -10x > 10n
Add 10x to both sides to get: 0 > 10x + 10n
Divide both sides by 10 to get: 0 > x + n. PERFECT! This is precisely what the target question is asking.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

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Re: If x and n are integers is the sum of x and n less than zero  [#permalink]

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_________________ Re: If x and n are integers is the sum of x and n less than zero   [#permalink] 01 Jul 2019, 19:53
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