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If m and n are consecutive positive integers, is m greater t
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12 Feb 2014, 02:04
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The Official Guide For GMAT® Quantitative Review, 2ND EditionIf m and n are consecutive positive integers, is m greater than n ? (1) m1 and n+1 are consecutive positive integers. (2) m is an even integer. Data Sufficiency Question: 86 Category: Arithmetic Properties of numbers Page: 158 Difficulty: 650 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
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Re: If m and n are consecutive positive integers, is m greater t
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12 Feb 2014, 02:04
SOLUTIONIf m and n are consecutive positive integers, is m greater than n?(1) m1 and n+1 are consecutive positive integers > m>n, if m were less than n than m1 (integer less than m) and n+1 (integer more than n) wouldn't be consecutive. Sufficient. Or look at this in another way: stem says that the distance between m and n is 1. Now, if m<n then the distance between m1 and n+1 would be 3 and they couldn't be consecutive as (1) states. Thus it must be true that m>n. (2) m is an even integer. Clearly insufficient. Answer: A.
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Re: If m and n are consecutive positive integers, is m greater t
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12 Feb 2014, 11:36
The question states that \(m\) &\(n\) are consecutive positive integers. The question can then be boiled down to whether the order is \(m,n\) or \(n,m\).
(1) m1 and n+1 are consecutive positive integers.
We know that \(m1\) and \(n+1\)are consecutive positive integers. If the order is \(m,n\) then this statement clearly fails. If the order is \(n,m\) then this statement is true, hence \(A\) is sufficient.
(2) m is an even integer.
If \(m\) is an even integer, \(n\) must be odd. \(n\) can still fall to the left or right of \(m\), and therefore statement (2) is insufficient.
Answer: A




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Re: If m and n are consecutive positive integers, is m greater t
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12 Feb 2014, 05:12
St1: m1 and n+1 are consecutive positive integers.
Case 1: m is even, n is odd and m < n Let m = 2, n = 3 m1 = 1, n+1 = 4 > not consecutive positive integers.
Case 2: m is even, n is odd and m > n Let m = 2, n = 1 m1 = 1, n+1 = 2 > consecutive positive integers.
Case 3: m is odd, n is even and m < n Let m = 3, n = 4 m1 = 2, n+1 = 5 > not consecutive positive integers.
Case 4: m is odd, n is even and m > n Let m = 3, n = 2 m1 = 2, n+1 = 3 > consecutive positive integers.
Not sufficient. Dow to B, C or E.
St2: m is an even integer. Not sufficient. If m = 2 and n = 1 > m > n but if m = 2 and n = 3 > m < n.
St 1 + St2: Not sufficient as illustrated by case 1 and case 2.
Answer (E).



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Re: If m and n are consecutive positive integers, is m greater t
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12 Feb 2014, 08:56
Donnie84 wrote: St1: m1 and n+1 are consecutive positive integers.
Case 1: m is even, n is odd and m < n Let m = 2, n = 3 m1 = 1, n+1 = 4 > not consecutive positive integers.
Case 2: m is even, n is odd and m > n Let m = 2, n = 1 m1 = 1, n+1 = 2 > consecutive positive integers.
Case 3: m is odd, n is even and m < n Let m = 3, n = 4 m1 = 2, n+1 = 5 > not consecutive positive integers.
Case 4: m is odd, n is even and m > n Let m = 3, n = 2 m1 = 2, n+1 = 3 > consecutive positive integers.
Not sufficient. Dow to B, C or E.
St2: m is an even integer. Not sufficient. If m = 2 and n = 1 > m > n but if m = 2 and n = 3 > m < n.
St 1 + St2: Not sufficient as illustrated by case 1 and case 2.
Answer (E). I think you are making a mistake somewhere !! Well from the different cases you have illustrated it is clear that "A" is sufficient !! Because both cases where m1,n+1 were consecutive you had m>n therefore statement "1" is clearly sufficient. Hope that helped



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Re: If m and n are consecutive positive integers, is m greater t
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12 Feb 2014, 10:09
Zatmah wrote: Donnie84 wrote: St1: m1 and n+1 are consecutive positive integers.
Case 1: m is even, n is odd and m < n Let m = 2, n = 3 m1 = 1, n+1 = 4 > not consecutive positive integers.
Case 2: m is even, n is odd and m > n Let m = 2, n = 1 m1 = 1, n+1 = 2 > consecutive positive integers.
Case 3: m is odd, n is even and m < n Let m = 3, n = 4 m1 = 2, n+1 = 5 > not consecutive positive integers.
Case 4: m is odd, n is even and m > n Let m = 3, n = 2 m1 = 2, n+1 = 3 > consecutive positive integers.
Not sufficient. Dow to B, C or E.
St2: m is an even integer. Not sufficient. If m = 2 and n = 1 > m > n but if m = 2 and n = 3 > m < n.
St 1 + St2: Not sufficient as illustrated by case 1 and case 2.
Answer (E). I think you are making a mistake somewhere !! Well from the different cases you have illustrated it is clear that "A" is sufficient !! Because both cases where m1,n+1 were consecutive you had m>n therefore statement "1" is clearly sufficient. Hope that helped Thanks Zatmah! Great catch! Using both the statements, we are down to case 2 only in which m > n. Answer is (C).



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Re: If m and n are consecutive positive integers, is m greater t
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12 Feb 2014, 11:41
Donnie84 wrote: St1: m1 and n+1 are consecutive positive integers.
Case 1: m is even, n is odd and m < n Let m = 2, n = 3 m1 = 1, n+1 = 4 > not consecutive positive integers.
Case 2: m is even, n is odd and m > n Let m = 2, n = 1 m1 = 1, n+1 = 2 > consecutive positive integers.
Case 3: m is odd, n is even and m < n Let m = 3, n = 4 m1 = 2, n+1 = 5 > not consecutive positive integers.
Case 4: m is odd, n is even and m > n Let m = 3, n = 2 m1 = 2, n+1 = 3 > consecutive positive integers.
Not sufficient. Dow to B, C or E.
St2: m is an even integer. Not sufficient. If m = 2 and n = 1 > m > n but if m = 2 and n = 3 > m < n.
St 1 + St2: Not sufficient as illustrated by case 1 and case 2.
Answer (E). You're almost correct; look at your statement 1 possibilities. Both of the possibilities that show m, n as consecutive integers also have m>n. Therefore statement A is sufficient.



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Re: If m and n are consecutive positive integers, is m greater t
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12 Feb 2014, 12:12
speedilly wrote: Donnie84 wrote: St1: m1 and n+1 are consecutive positive integers.
Case 1: m is even, n is odd and m < n Let m = 2, n = 3 m1 = 1, n+1 = 4 > not consecutive positive integers.
Case 2: m is even, n is odd and m > n Let m = 2, n = 1 m1 = 1, n+1 = 2 > consecutive positive integers.
Case 3: m is odd, n is even and m < n Let m = 3, n = 4 m1 = 2, n+1 = 5 > not consecutive positive integers.
Case 4: m is odd, n is even and m > n Let m = 3, n = 2 m1 = 2, n+1 = 3 > consecutive positive integers.
Not sufficient. Dow to B, C or E.
St2: m is an even integer. Not sufficient. If m = 2 and n = 1 > m > n but if m = 2 and n = 3 > m < n.
St 1 + St2: Not sufficient as illustrated by case 1 and case 2.
Answer (E). You're almost correct; look at your statement 1 possibilities. Both of the possibilities that show m, n as consecutive integers also have m>n. Therefore statement A is sufficient. Thanks speedilly! Got it finally. Gosh, this question was really challenging



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Re: If m and n are consecutive positive integers, is m greater t
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12 Feb 2014, 23:46
Zatmah wrote: Donnie84 wrote: St1: m1 and n+1 are consecutive positive integers.
Case 1: m is even, n is odd and m < n Let m = 2, n = 3 m1 = 1, n+1 = 4 > not consecutive positive integers.
Case 2: m is even, n is odd and m > n Let m = 2, n = 1 m1 = 1, n+1 = 2 > consecutive positive integers.
Case 3: m is odd, n is even and m < n Let m = 3, n = 4 m1 = 2, n+1 = 5 > not consecutive positive integers.
Case 4: m is odd, n is even and m > n Let m = 3, n = 2 m1 = 2, n+1 = 3 > consecutive positive integers.
Not sufficient. Dow to B, C or E.
St2: m is an even integer. Not sufficient. If m = 2 and n = 1 > m > n but if m = 2 and n = 3 > m < n.
St 1 + St2: Not sufficient as illustrated by case 1 and case 2.
Answer (E). I think you are making a mistake somewhere !! Well from the different cases you have illustrated it is clear that "A" is sufficient !! Because both cases where m1,n+1 were consecutive you had m>n therefore statement "1" is clearly sufficient. Hope that helped Indeed, A is sufficient ,:)



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Re: If m and n are consecutive positive integers, is m greater t
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17 Feb 2014, 01:48
SOLUTIONIf m and n are consecutive positive integers, is m greater than n?(1) m1 and n+1 are consecutive positive integers > m>n, if m were less than n than m1 (integer less than m) and n+1 (integer more than n) wouldn't be consecutive. Sufficient. Or look at this in another way: stem says that the distance between m and n is 1. Now, if m<n then the distance between m1 and n+1 would be 3 and they couldn't be consecutive as (1) states. Thus it must be true that m>n. (2) m is an even integer. Clearly insufficient. Answer: A.
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Re: If m and n are consecutive positive integers, is m greater t
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23 Feb 2014, 11:46
Hi  I have another (slightly different way) that works better and faster for me
If m and n are consecutive positive integers, is m greater than n?
(1) m1 and n+1 are consecutive positive integers. For M > N to be consecutive and true, M = N + 1 and N = M 1 stem (1) give us precisely the algebraic expression we require to prove M > N is true
(2) m is an even integer Insufficient. For example, if M = 4, N could be 3 or 5.
Hence A alone is sufficient.



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If m and n are consecutive positive integers, is m greater t
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14 Jun 2015, 02:52
Statement 1) Let's pick some consecutive numbers Case 1m=15 , n=14 m1=14, n+1=15 Case2m=14, n=15 M1=13 n+1=16 > not sonsecutive > m>n (see first case, m&n can be consecutive ONLY in case M>N ) Statement 2) clearly not sufficient
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If m and n are consecutive positive integers, is m greater than n ?
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24 Feb 2016, 02:52
If m and n are consecutive positive integers, is m greater than n ? (1) m 1 and n + 1 are consecutive positive integers. (2) m is an even integer. Arithmetic Properties of numbers For two integers x and y to be consecutive, it is both necessary and sufficient that I x  y I = 1. (1) Given that m1 and n + 1 are consecutive integers, it follows that ~ m  1) ( n + 1 ~ = 1, or lm  n  ~ = 1. Therefore, m  n  2 = 1 or m  n  2 = 1. The former equation implies that m n = 3, which contradicts the fact that m and n are consecutive integers. Therefore, m  n  2 = 1, or m = n + 1, and hence m > n; SUFFICIENT. (2) If m = 2 and n = 1, then m is greater than n. However, if m = 2 and n = 3, then m is not greater than n; NOT sufficient I know all of the topics of the question. But my confusion is that question describes m and n are consecutive positive integers, so why we need I x  y I = 1. Why we use absolute for positive integers. Would any one like to explain me please.



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Re: If m and n are consecutive positive integers, is m greater than n ?
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24 Feb 2016, 02:58
Bahadur wrote: If m and n are consecutive positive integers, is m greater than n ? (1) m 1 and n + 1 are consecutive positive integers. (2) m is an even integer. Arithmetic Properties of numbers For two integers x and y to be consecutive, it is both necessary and sufficient that I x  y I = 1. (1) Given that m1 and n + 1 are consecutive integers, it follows that ~ m  1) ( n + 1 ~ = 1, or lm  n  ~ = 1. Therefore, m  n  2 = 1 or m  n  2 = 1. The former equation implies that m n = 3, which contradicts the fact that m and n are consecutive integers. Therefore, m  n  2 = 1, or m = n + 1, and hence m > n; SUFFICIENT. (2) If m = 2 and n = 1, then m is greater than n. However, if m = 2 and n = 3, then m is not greater than n; NOT sufficient I know all of the topics of the question. But my confusion is that question describes m and n are consecutive positive integers, so why we need I x  y I = 1. Why we use absolute for positive integers. Would any one like to explain me please. Hi, we take ABSOLUTE MOD because we are not aware whether x is big or y is big.. if x is bigger, xy=1.. if y is bigger, xy=1.. so xy=1..
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Re: If m and n are consecutive positive integers, is m greater than n ?
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24 Feb 2016, 03:07
chetan2u wrote: Bahadur wrote: If m and n are consecutive positive integers, is m greater than n ? (1) m 1 and n + 1 are consecutive positive integers. (2) m is an even integer. Arithmetic Properties of numbers For two integers x and y to be consecutive, it is both necessary and sufficient that I x  y I = 1. (1) Given that m1 and n + 1 are consecutive integers, it follows that ~ m  1) ( n + 1 ~ = 1, or lm  n  ~ = 1. Therefore, m  n  2 = 1 or m  n  2 = 1. The former equation implies that m n = 3, which contradicts the fact that m and n are consecutive integers. Therefore, m  n  2 = 1, or m = n + 1, and hence m > n; SUFFICIENT. (2) If m = 2 and n = 1, then m is greater than n. However, if m = 2 and n = 3, then m is not greater than n; NOT sufficient I know all of the topics of the question. But my confusion is that question describes m and n are consecutive positive integers, so why we need I x  y I = 1. Why we use absolute for positive integers. Would any one like to explain me please. Hi, we take ABSOLUTE MOD because we are not aware whether x is big or y is big.. if x is bigger, xy=1.. if y is bigger, xy=1.. so xy=1..
thank you I have overcome my confusion. thank you.



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Re: If m and n are consecutive positive integers, is m greater than n ?
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24 Feb 2016, 03:16
(1) m  1 and n + 1 are consecutive positive integers. (2) m is an even integer. Statement I : Sufficient Lets take the help of numbers here. m = 3 and n = 2 m1 = 2 and n + 1 = 3 ( m1 and n+1 are consecutive integers). m = 2 and n = 3 m1 = 1 and n + 1 = 4 ( m1 and n+1 are not consecutive integers). Generalize it, m = x n = x + 1 m  1 = x  1 n + 1 = x + 2 In this case, m1 and n+1 are not consecutive positive integers. Now, m = x + 1 n = x m  1 = x n + 1 = x + 1 In this case, m1 and n+1 are consecutive positive integers. Hence m > n Statement II: Not Sufficient. Answer A
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Re: If m and n are consecutive positive integers, is m greater than n ?
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29 Jun 2017, 14:42
If m and n are consecutive positive integers, is m greater than n ?(1) m1 and n+1 are consecutive positive integers.Lets check by substituting some values \(I  m > n\) \(m = 4 & n = 3\) \(m  1 = 4  1 = 3\) \(n + 1 = 3 + 1 = 4\) \(I  m > n\)  Satisfies the Equation as we are getting two consecutive integers 3 & 4 (Also you can check by plugging in other values like 7 & 8) \(II  m < n\) \(m = 3 & n = 4\) \(m  1 = 3  1 = 2\) \(n + 1 = 4 + 1 = 5\) \(II  m < n\)  This does not satisfy the Equation as we are not getting two consecutive equations. (Also you can check by plugging in other values like 8 & 7) Hence, we see that in order to satisfy the Eq. (1), m has to be greater than n. Hence (1) =====> is SUFFICIENT(2) m is an even integer.m is even, this does not give us any information about n, n can be consecutive integer which is higher than m or consecutive integer which is lower than m. Hence, (2) =====> is NOT SUFFICIENTHence, Answer is A
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Re: If m and n are consecutive positive integers, is m greater than n ?
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29 Jun 2017, 17:58
I have one small confusion. The question says that "if m and n are consecutive positive integers..." Doesn't this imply automatically that the order is m and then n? How are we unsure that its not m and n rather it could be n and m? Please help me.
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Re: If m and n are consecutive positive integers, is m greater than n ?
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29 Jun 2017, 23:52
csaluja wrote: I have one small confusion. The question says that "if m and n are consecutive positive integers..." Doesn't this imply automatically that the order is m and then n? How are we unsure that its not m and n rather it could be n and m? Please help me.
Thanks! If it were the way you are saying, we won't have this question. So, x and y are consecutive integers does NOT necessarily mean that y > x. P.S. Also, note that this is an official question.
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