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Are all elements of an increasing infinite sequence of positive integers odd? (1) All elements of the sequence are divisible by the same odd integer larger than 1 (2) The difference between any consecutive elements of the sequence is even
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16 Sep 2014, 01:04
Official Solution: Statement (1) by itself is insufficient. For example, if "the same odd integer" is 5, the sequence can contain no odd integers (10, 20, 30, ...) or only odd integers (5, 15, 25, ...). Statements (1) and (2) combined are insufficient. The same example shows that adding S2 to S1 does not help to answer the question. Answer: E
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Re: M1822
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24 Oct 2015, 08:41
Point 1: Insufficient bcz odd number greater than 1 can be a factor of even and odd positive numbers. For eg: 5 can be factor of 5,15,25 as well as 10,20 and 30.
Point 2: Insufficient bcz neither the statement nor the argument says the sequence starts with a positive odd number. Hence, the first number can either be positive odd or positive even. If so, the sequence can be off positive even or positive odd numbers. For eg: The sequence can be 2,4,6,8..... or 5,15,25,35 .....
Point 1 and 2 : Insufficient bcz there are different possible sequences 14,28,42 .. or 7,21,35 ...



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Re: M1822
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02 Sep 2016, 15:13
combining both
5, 15, 25, 35......
or 3, 9, 15, 21 .... so n dont understand why C is wrong



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Re: M1822
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02 Sep 2016, 17:17
vijaisingh2001 wrote: combining both
5, 15, 25, 35......
or 3, 9, 15, 21 .... so n dont understand why C is wrong Statement 1 : This says that the numbers in the sequence are nothing but the multiples of a particular odd integer say 3, 5, 7 etc. These multiples can be odd or even. So, INSUFFICIENT. Statement 2: This statement says, the difference between two numbers in the sequence is even. So, all the numbers in the sequence are either odd or even. So INSUFFICIENT. Combining 1 & 2, still the sequence can have all the multiplies of an odd number that are either even or odd. Still INSUFFICIENT. Hence E.



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Re: M1822
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19 Feb 2018, 05:04
Why is C wrong?
If you combine both statements, sequence is something like, 3,9,15,21. All odd.



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anchitahuja wrote: Why is C wrong?
If you combine both statements, sequence is something like, 3,9,15,21. All odd. what about other series do look at series other than the one you have mentioned



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Re: M1822
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02 Feb 2019, 13:22
Hi
In general, whenever a "sequence" is mentioned in the question stem on the GMAT, are we to assume a reference is being made specifically to an arithmetic progression? Although, for this question in particular, even if the reference were made to a GP, it would still not change the answer, but since the explanation offered exclusively refers to an AP, I thought it would be best to clarify.
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Re: M1822
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03 Feb 2019, 02:23
shubhajit wrote: Hi
In general, whenever a "sequence" is mentioned in the question stem on the GMAT, are we to assume a reference is being made specifically to an arithmetic progression? Although, for this question in particular, even if the reference were made to a GP, it would still not change the answer, but since the explanation offered exclusively refers to an AP, I thought it would be best to clarify.
Thanks SN A sequence of numbers is not necessarily an arithmetic or geometric progression. A sequence, by definition, is an ordered list of terms. While, a set, by definition, is a collection of elements without any order.
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Re: M1822
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03 Feb 2019, 06:05
Bunuel wrote: Are all elements of an increasing infinite sequence of positive integers odd?
(1) All elements of the sequence are divisible by the same odd integer larger than 1
(2) The difference between any consecutive elements of the sequence is even #1: all elements of sequence divisible by same odd integer >1 sequence of such a no wont be possible 3,5,7,9,11,.. all terms but if 5,15,25,35 then yes so in sufficient #2 its true for all set of even or odd consective integers.. in sufficient from 1&2 in sufficient as we can have varied set of consective integers imo e



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Re: M1822
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23 Nov 2019, 07:54
Hello, I didn't understand why C is not correct, could someone help? Here is my reasoning:
Are all elements of an increasing infinite sequence of positive integers odd?
(1) All elements of the sequence are divisible by the same odd integer larger than 1 > could be 3,6,9. 5,10,15. > ok we have options with odd and even numbers => insufficient
(2) The difference between any consecutive elements of the sequence is even > To have a difference resulting in even, we can have odd  odd (eg. 3 1) or even  even (eg. 4 2) = > insufficient.
(1) and (2) All elements are divisible by the same odd. Difference of any consecutive is even.
To be divisible by the same odd and also be even with the difference of any consecutive we have: can't be 3,6,9 since difference consecutive is odd. Then we should have something like 3,9,15 as a sequence, i.e. it would be all odds.
I'm not understanding the flaw in this reasoning, could someone help?
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Re: M1822
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23 Nov 2019, 08:15
mvmarcus7 wrote: Hello, I didn't understand why C is not correct, could someone help? Here is my reasoning:
Are all elements of an increasing infinite sequence of positive integers odd?
(1) All elements of the sequence are divisible by the same odd integer larger than 1 > could be 3,6,9. 5,10,15. > ok we have options with odd and even numbers => insufficient
(2) The difference between any consecutive elements of the sequence is even > To have a difference resulting in even, we can have odd  odd (eg. 3 1) or even  even (eg. 4 2) = > insufficient.
(1) and (2) All elements are divisible by the same odd. Difference of any consecutive is even.
To be divisible by the same odd and also be even with the difference of any consecutive we have: can't be 3,6,9 since difference consecutive is odd. Then we should have something like 3,9,15 as a sequence, i.e. it would be all odds.
I'm not understanding the flaw in this reasoning, could someone help?
Regards It's not clear why you eliminate other possible cases. For example, 10, 20, 30, ... All are divisible by 5 and the difference is even.
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