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If n is an integer, is n positive?
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Updated on: 09 Nov 2015, 17:49
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If n is an integer, is n positive? 1) (2n+1)/(n+1) is an integer 2) n=−n
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Originally posted by jcmsolis2015 on 09 Nov 2015, 17:38.
Last edited by ENGRTOMBA2018 on 09 Nov 2015, 17:49, edited 2 times in total.
Formatted the question and updated the topic.




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Re: If n is an integer, is n positive?
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09 Nov 2015, 20:38
jcmsolis2015 wrote: If n is an integer, is n positive?
1) (2n+1)/(n+1) is an integer
2) n=−n Target question: Is n positive? Given: In is an integer Statement 1:(2n+1)/(n+1) is an integer Rewrite as: (n+1+ n)/(n+1) is an integer Rewrite as: (n+1)/(n+1) + n/(n+1) is an integer Or... 1 + n/(n+1) is an integer This means that n/(n+1) is an integer How can this be? How can some number divided by a number that's 1 greater be an integer? This ONLY WORKS if n = 0, so statement 1 is really telling us that n = 0 In other words, n is NOT positiveSince we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: n=−n Add n to both sides to get: 2n = 0 Divide both sides by 2 to get: n = 0 So, n is NOT positiveSince we can answer the target question with certainty, statement 2 is SUFFICIENT Answer = D Cheers, Brent
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Re: If n is an integer, is n positive?
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09 Nov 2015, 17:48
jcmsolis2015 wrote: If n is an integer, is n positive?
1) (2n+1)/(n+1) is an integer
2) n=−n Follow posting guidelines (link in my signatures). Given that n is an integer, is n > 0? Per statement 2, n=n > 2n=0 > n=0. Answer to "is n > 0" = NO. Sufficient. Per statement 1, (2n+1)/(n+1) = integer > n =0 and n =2 satisfy the conditions (out of some other negative values, no need to check any more). No positive integer values of n will satisfy this given condition. Thus you get a "no" for "is n > 0" for both n =0 and n = 2 , making this statement sufficient as well. D is thus the correct answer.




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If n is an integer, is n positive?
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10 Nov 2015, 01:18
Engr2012 wrote: jcmsolis2015 wrote: If n is an integer, is n positive?
1) (2n+1)/(n+1) is an integer
2) n=−n Follow posting guidelines (link in my signatures). Given that n is an integer, is n > 0? Per statement 2, n=n > 2n=0 > n=0. Answer to "is n > 0" = NO. Sufficient. Per statement 1, (2n+1)/(n+1) = integer > n =0 and n =2 satisfy the conditions (out of some other negative values, no need to check any more). No positive integer values of n will satisfy this given condition. Thus you get a "no" for "is n > 0" for both n =0 and n = 2 , making this statement sufficient as well. D is thus the correct answer. I must disagree with the reasoning on statement 1. Just because you gave 2 examples in which the statement holds true, that does not mean the statement does not hold true for any positive values of N. The message from this is: the only scenario in which you can use two examples to prove that a statement is sufficient or not, is when you (relating to this question) have a value of N for which the answer is YES and a value for N for which the answer is NO. Proving that the statement is insufficient. I guessed B on this question. update On statement 1 I reasoned that the only way for it to be true would be 2n=n meaning that n should equal 0.



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Re: If n is an integer, is n positive?
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10 Nov 2015, 09:33
Martijn wrote: I must disagree with the reasoning on statement 1. Just because you gave 2 examples in which the statement holds true, that does not mean the statement does not hold true for any positive values of N. The message from this is: the only scenario in which you can use two examples to prove that a statement is sufficient or not, is when you (relating to this question) have a value of N for which the answer is YES and a value for N for which the answer is NO. Proving that the statement is insufficient. I guessed B on this question. . Martijn is correct; plugging in numbers typically works best when you suspect that the statement is NOT SUFFICIENT. In these cases, all you need to do is find values that yield different (conflicting) answers to the target question. Conversely, if the statement is SUFFICIENT, then plugging in values will only HINT at whether or not the statement is sufficient, but you won't be able to make any definitive conclusions. For example, let's say we have the following target question: If n is a positive integer, is (2^n)  1 prime? Let's say statement 1 says: n is a prime number: Now let's plug in some prime values of n: If n = 2, then (2^n)  1 = 2²  1 = 3, and 3 IS prime If n = 3, then case (2^n)  1 = 2³  1 = 7, and 7 IS prime If n = 5, then (2^n)  1 = 2⁵  1 = 31, and 31 IS prime At this point, it certainly APPEARS that statement guarantees that (2^n)  1 is prime? Let’s try one more prime value of n. If n = 7, then (2^n)  1 = 2⁷  1 = 127, and 127 IS prime So, can we be 100% certain that statement 1 is sufficient? No. The truth of the matter is that statement 1 is NOT SUFFICIENT. To see why, let’s examine the possibility that n = 11 If n = 11, then (2^n)  1 = (2^11)  1 = 2047, and 2047 is NOT prime Here’s a different example: Target question: Is x > 0? Let's say statement 1 says: 5x > 4x Now let's plug in some values of x that satisfy the condition that 5x > 4x. x = 3, in which case x > 0 x = 0.5, in which case x > 0 x = 15, in which case x > 0 x = 1000, in which case x > 0 Once again, it APPEARS that statement 1 provides sufficient information to answer the target question. Can we be 100% certain? No. Perhaps we didn't plug in the right numbers (as was the case in the first example). Perhaps there's a number that we could have plugged in such that x < 0If we want to be 100% certain that a statement is SUFFICIENT, we'll need to use a technique other than plugging in. Here, we can take 5x > 4x, and subtract 4x from both sides to get x > 0 VOILA  we can now answer the target question with absolute certainty. So, statement 1 is SUFFICIENT. TAKEAWAY: Plugging in numbers is best suited for situations in which you suspect that the statement is not sufficient. In these situations, plugging in values can yield results that are 100% conclusive. Conversely, in situations in which the statement is sufficient, plugging in values can STRONGLY HINT at sufficiency, but the results are not 100% conclusive. For more on this, you can watch our free video titled “Choosing Good Numbers: http://www.gmatprepnow.com/module/gmatdatasufficiency?id=1102 or you can read an article I wrote: http://www.gmatprepnow.com/articles/dat ... lugvalues Cheers, Brent
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Re: If n is an integer, is n positive?
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11 Nov 2015, 01:23
GMATPrepNow wrote: Martijn wrote: I must disagree with the reasoning on statement 1. Just because you gave 2 examples in which the statement holds true, that does not mean the statement does not hold true for any positive values of N. The message from this is: the only scenario in which you can use two examples to prove that a statement is sufficient or not, is when you (relating to this question) have a value of N for which the answer is YES and a value for N for which the answer is NO. Proving that the statement is insufficient. I guessed B on this question. . Martijn is correct; plugging in numbers typically works best when you suspect that the statement is NOT SUFFICIENT. In these cases, all you need to do is find values that yield different (conflicting) answers to the target question. Conversely, if the statement is SUFFICIENT, then plugging in values will only HINT at whether or not the statement is sufficient, but you won't be able to make any definitive conclusions. For example, let's say we have the following target question: If n is a positive integer, is (2^n)  1 prime? Let's say statement 1 says: n is a prime number: Now let's plug in some prime values of n: If n = 2, then (2^n)  1 = 2²  1 = 3, and 3 IS prime If n = 3, then case (2^n)  1 = 2³  1 = 7, and 7 IS prime If n = 5, then (2^n)  1 = 2⁵  1 = 31, and 31 IS prime At this point, it certainly APPEARS that statement guarantees that (2^n)  1 is prime? Let’s try one more prime value of n. If n = 7, then (2^n)  1 = 2⁷  1 = 127, and 127 IS prime So, can we be 100% certain that statement 1 is sufficient? No. The truth of the matter is that statement 1 is NOT SUFFICIENT. To see why, let’s examine the possibility that n = 11 If n = 11, then (2^n)  1 = (2^11)  1 = 2047, and 2047 is NOT prime Here’s a different example: Target question: Is x > 0? Let's say statement 1 says: 5x > 4x Now let's plug in some values of x that satisfy the condition that 5x > 4x. x = 3, in which case x > 0 x = 0.5, in which case x > 0 x = 15, in which case x > 0 x = 1000, in which case x > 0 Once again, it APPEARS that statement 1 provides sufficient information to answer the target question. Can we be 100% certain? No. Perhaps we didn't plug in the right numbers (as was the case in the first example). Perhaps there's a number that we could have plugged in such that x < 0If we want to be 100% certain that a statement is SUFFICIENT, we'll need to use a technique other than plugging in. Here, we can take 5x > 4x, and subtract 4x from both sides to get x > 0 VOILA  we can now answer the target question with absolute certainty. So, statement 1 is SUFFICIENT. TAKEAWAY: Plugging in numbers is best suited for situations in which you suspect that the statement is not sufficient. In these situations, plugging in values can yield results that are 100% conclusive. Conversely, in situations in which the statement is sufficient, plugging in values can STRONGLY HINT at sufficiency, but the results are not 100% conclusive. For more on this, you can watch our free video titled “Choosing Good Numbers: http://www.gmatprepnow.com/module/gmatdatasufficiency?id=1102 or you can read an article I wrote: http://www.gmatprepnow.com/articles/dat ... lugvalues Cheers, Brent Hi Brent, I have quick question regarding your example is x>0. If I use x=2 in the statement 5x>4x, so 10<8 so X won't be smaller than zero. it should be insufficient. However, through simple algebra you proved that X>0. I'm confused. what did I miss? Thanks



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Re: If n is an integer, is n positive?
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11 Nov 2015, 08:03
Mo2men wrote: Hi Brent, I have quick question regarding your example is x>0. If I use x=2 in the statement 5x>4x, so 10<8 so X won't be smaller than zero. it should be insufficient. However, through simple algebra you proved that X>0. I'm confused. what did I miss?
Thanks
Plugging in x = 2 does not satisfy the given inequality 5x > 4x We get: (5)(2) > (4)(2), which evaluates to 10 > 8, HOWEVER 10 is not greater than 8 Cheers, Brent
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Re: If n is an integer, is n positive?
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11 Nov 2015, 08:27
GMATPrepNow wrote: Mo2men wrote: Hi Brent, I have quick question regarding your example is x>0. If I use x=2 in the statement 5x>4x, so 10<8 so X won't be smaller than zero. it should be insufficient. However, through simple algebra you proved that X>0. I'm confused. what did I miss?
Thanks
Plugging in x = 2 does not satisfy the given inequality 5x > 4x We get: (5)(2) > (4)(2), which evaluates to 10 > 8, HOWEVER 10 is not greater than 8 Cheers, Brent Shouldn't I reverse the sign because of multiplication with negative number to be 10<8. I will happy if you spot my mistake in my understanding. Thanks in advance for support



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Re: If n is an integer, is n positive?
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15 Nov 2015, 01:58
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. If n is an integer, is n positive? 1) (2n+1)/(n+1) is an integer 2) n=−n There is one variable (n) in the original condition and 2 equations in the given conditions, so there is high chance (D) is the answer. For condition 1, n=0,2, so the answer is 'no' and is sufficient. For condition 2, 2n=0, n=0, so the answer is 'no' and is sufficient, making the answer (D). For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: If n is an integer, is n positive?
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08 Jan 2017, 22:21
GMATPrepNow wrote: jcmsolis2015 wrote: If n is an integer, is n positive?
1) (2n+1)/(n+1) is an integer
2) n=−n Target question: Is n positive? Given: In is an integer Statement 1:(2n+1)/(n+1) is an integer Rewrite as: (n+1+ n)/(n+1) is an integer Rewrite as: (n+1)/(n+1) + n/(n+1) is an integer Or... 1 + n/(n+1) is an integer This means that n/(n+1) is an integer How can this be? How can some number divided by a number that's 1 greater be an integer? This ONLY WORKS if n = 0, so statement 1 is really telling us that n = 0 In other words, n is NOT positiveSince we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: n=−n Add n to both sides to get: 2n = 0 Divide both sides by 2 to get: n = 0 So, n is NOT positiveSince we can answer the target question with certainty, statement 2 is SUFFICIENT Answer = D Cheers, Brent Hi Brent, We can plug 2 in statement 1 and get result as 3 which is an integer. We can plug 0 and get result as 1 which is also an integer. There are 2 values of n(2 and 0) that can give integer as result. Doesn't this imply that Statement 1 is insufficient to answer whether n is positive? Please help by correcting my understanding.



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Re: If n is an integer, is n positive?
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06 Jun 2017, 22:02
getisb wrote: GMATPrepNow wrote: jcmsolis2015 wrote: If n is an integer, is n positive?
1) (2n+1)/(n+1) is an integer
2) n=−n Target question: Is n positive? Given: In is an integer Statement 1:(2n+1)/(n+1) is an integer Rewrite as: (n+1+ n)/(n+1) is an integer Rewrite as: (n+1)/(n+1) + n/(n+1) is an integer Or... 1 + n/(n+1) is an integer This means that n/(n+1) is an integer How can this be? How can some number divided by a number that's 1 greater be an integer? This ONLY WORKS if n = 0, so statement 1 is really telling us that n = 0 In other words, n is NOT positiveSince we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: n=−n Add n to both sides to get: 2n = 0 Divide both sides by 2 to get: n = 0 So, n is NOT positiveSince we can answer the target question with certainty, statement 2 is SUFFICIENT Answer = D Cheers, Brent Hi Brent, We can plug 2 in statement 1 and get result as 3 which is an integer. We can plug 0 and get result as 1 which is also an integer. There are 2 values of n(2 and 0) that can give integer as result. Doesn't this imply that Statement 1 is insufficient to answer whether n is positive? Please help by correcting my understanding. Even I am arriving at the same conclusion. Brent, can you please help here ? Are we missing something in our understanding ?
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If n is an integer, is n positive?
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06 Jun 2017, 22:07
Ah, I got it now. In both the cases (with values of n as 0 or 2), we are able to get an integer value as an output and thus, are able to answer the main question (is N positive ?) definitively as in both the cases, we are getting a NO (n is NOT positive with values of 0 and 2) and thus, statement 1 is sufficient.
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Re: If n is an integer, is n positive?
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01 Nov 2017, 10:39
Statement 1: (2n + 1)/(n+1) is integer Let (2n + 1)/(n+1) = k rearranging gives => n = (k1)/(k2) Now note that k1 and k2 are coprimes, for n to be integer, (k1)/(k2) must be integer For that, k  1 = k 2 , which is definitely not possible, or k  1 = 0 (to make n as integer) => k =1 => n = 0
so n must be zero and not positive, sufficient to answer the question
Statement 2: n = n, only n = 0, this is valid , sufficient
Answer (D)



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Re: If n is an integer, is n positive?
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01 Nov 2017, 19:41
(1) (2n+1)/(n+1) is an integer. We have (2n+1)/ (n+1) = (n+1 +n)/(n+1) = 1 + n/ (n+1) is an integer => n/(n+1) is an integer <=> n = 0 => n isn't positive => sufficient (2): n=−n <=> 2n = 0 <=> n =0 => n isn't positive => sufficient Hence, the answer is D.  Kindly press +1 Kudos if the explanation is clear. Thank you



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Re: If n is an integer, is n positive?
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25 Sep 2018, 10:25
GMATPrepNow wrote: jcmsolis2015 wrote: If n is an integer, is n positive?
1) (2n+1)/(n+1) is an integer
2) n=−n Target question: Is n positive? Given: In is an integer Statement 1:(2n+1)/(n+1) is an integer Rewrite as: (n+1+ n)/(n+1) is an integer Rewrite as: (n+1)/(n+1) + n/(n+1) is an integer Or... 1 + n/(n+1) is an integer This means that n/(n+1) is an integer How can this be? How can some number divided by a number that's 1 greater be an integer? This ONLY WORKS if n = 0, so statement 1 is really telling us that n = 0 In other words, n is NOT positiveSince we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: n=−n Add n to both sides to get: 2n = 0 Divide both sides by 2 to get: n = 0 So, n is NOT positiveSince we can answer the target question with certainty, statement 2 is SUFFICIENT Answer = D Cheers, Brent Hi Brent, In the above statement 1, can n be 2? Because in the 3rd step above in which 1+ n/(n+1), if we replace n with 2, the answer will be 2. So technically n can be 0 or 2? However, the statement still prove to be sufficient.




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