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Re: If x and n are integers is the sum of x and n less than zero
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19 Feb 2012, 04:41
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Expert Reply
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.
Re: If x and n are integers is the sum of x and n less than zero
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13 Mar 2016, 08:11
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 _________________
Re: If x and n are integers is the sum of x and n less than zero
[#permalink]
21 May 2017, 18:44
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.
Re: If x and n are integers is the sum of x and n less than zero
[#permalink]
21 May 2017, 19:00
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.
Answer: B.
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.
Re: If x and n are integers is the sum of x and n less than zero
[#permalink]
21 May 2017, 19:05
Expert Reply
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.
Answer: B.
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.
Re: If x and n are integers is the sum of x and n less than zero
[#permalink]
21 May 2017, 19:08
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.
Answer: B.
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.
Re: If x and n are integers is the sum of x and n less than zero
[#permalink]
29 Mar 2018, 15:23
Expert Reply
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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