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# If x and n are integers is the sum of x and n less than zero

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Re: If x and n are integers is the sum of x and n less than zero [#permalink]
Thanks Bunel for the solution.
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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 can be rejected here as there is no way we can get a +ve relation from a -ve one..
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Re: If x and n are integers is the sum of x and n less than zero [#permalink]
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]
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.
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Re: If x and n are integers is the sum of x and n less than zero [#permalink]
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
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Re: If x and n are integers is the sum of x and n less than zero [#permalink]
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]
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]
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
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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

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

x + n < 0?

(1) x + 3 < n – 1

x - n < -4

We can't do anything further. INSUFFICIENT.

(2) -10x > 10n
10n + 10x < 0
10(n + x) < 0
(n+x) < 0

SUFFICIENT.

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Re: If x and n are integers is the sum of x and n less than zero [#permalink]
BrentGMATPrepNow Bunuel Why can't we multiply statement 1 by -1? We have x-n < -4. If we multiply both sides by -1 and flip the inequality, the answer becomes x+n>4 which would be sufficient. It seems to be wrong here but I don't understand why? Are we not allowed to multiply the expression by -1?
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