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If x and y are positive integers, what is the greatest [#permalink]
 04 Mar 2012, 07:21
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If x and y are positive integers, what is the greatest common divisor of x and y? (1) 2x + y = 73 (2) 5x – 3y = 1 MMMMMMmm Here I'm not sure that the answer is C because is true that we need of both statement to find possible values for X and Y. Infact statement 1 and 2 we do not have values for the variables (can be everything). But it seems to be a trap answer......
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Last edited by Bunuel on 04 Mar 2012, 07:44, edited 1 time in total.
Edited the question and the OA
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Re: If x and y are positive integers, what is the greatest commo [#permalink]
04 Mar 2012, 07:41
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carcass wrote: If x and y are positive integers, what is the greatest common divisor of x and y?
1) 2x + y = 73
2) 5x – 3y = 1
MMMMMMmm
Here I'm not sure that the answer is C because is true that we need of both statement to find possible values for X and Y. Infact statement 1 and 2 we do not have values for the variables (can be everything).
But it seems to be a trap answer...... If x and y are positive integers, what is the greatest common divisor of x and y?This is a classic "C trap" question: "C trap" is a problem which is VERY OBVIOUSLY sufficient if both statements are taken together. When you see such question you should be extremely cautious when choosing C for an answer. (1) 2x+y=73. Suppose GCD(x, y) is some integer d, then x=md and y=nd, for some positive integers m and n. So, we'll have 2(md)+(nd)=d(2m+n)=73. Now, since 73 is a prime number (73=1*73) then d=1 and 2m+n=73 (vice versa is not possible because m and n are positve integers and therefore 2m+n can not equal to 1). Hence we have that GCD(x, y)=d=1. Sufficient. (2) 5x-3y=1 --> 5x=3y+1 --> 5x and 3y are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1 (for example 20 and 21 are consecutive integers, thus only common factor they share is 1). So, 5x and 3y don't share any common factor but 1, thus x and y also don't share any common factor but 1. Hence, GCD(x, y) is 1. Sufficient. Answer: D. Hope it's clear.
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Re: If x and y are positive integers, what is the greatest [#permalink]
04 Mar 2012, 09:22
Thanks bunuel. From your explanation can we suppose to apply the reasoning from statement two to the first one or is not possible ?? would be a big mistake because 1 is NOT prime??'
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Re: If x and y are positive integers, what is the greatest [#permalink]
05 Mar 2012, 02:28
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Re: If x and y are positive integers, what is the greatest commo [#permalink]
07 Apr 2012, 15:55
Hi Bunuel, Can I hire your mind for my exam...? Well if I get a good grade, a large part of it would be due to you....Thanks. Bunuel wrote: carcass wrote: If x and y are positive integers, what is the greatest common divisor of x and y?
1) 2x + y = 73
2) 5x – 3y = 1
MMMMMMmm
Here I'm not sure that the answer is C because is true that we need of both statement to find possible values for X and Y. Infact statement 1 and 2 we do not have values for the variables (can be everything).
But it seems to be a trap answer...... If x and y are positive integers, what is the greatest common divisor of x and y?This is a classic "C trap" question: "C trap" is a problem which is VERY OBVIOUSLY sufficient if both statements are taken together. When you see such question you should be extremely cautious when choosing C for an answer. (1) 2x+y=73. Suppose GCD(x, y) is some integer d, then x=md and y=nd, for some positive integers m and n. So, we'll have 2(md)+(nd)=d(2m+n)=73. Now, since 73 is a prime number (73=1*73) then d=1 and 2m+n=73 (vice versa is not possible because m and n are positve integers and therefore 2m+n can not equal to 1). Hence we have that GCD(x, y)=d=1. Sufficient. (2) 5x-3y=1 --> 5x=3y+1 --> 5x and 3y are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1 (for example 20 and 21 are consecutive integers, thus only common factor they share is 1). So, 5x and 3y don't share any common factor but 1, thus x and y also don't share any common factor but 1. Hence, GCD(x, y) is 1. Sufficient. Answer: D. Hope it's clear. |
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Re: If x and y are positive integers, what is the greatest commo [#permalink]
05 Sep 2012, 08:24
Bunuel wrote: carcass wrote: If x and y are positive integers, what is the greatest common divisor of x and y?
1) 2x + y = 73
2) 5x – 3y = 1
MMMMMMmm
Here I'm not sure that the answer is C because is true that we need of both statement to find possible values for X and Y. Infact statement 1 and 2 we do not have values for the variables (can be everything).
But it seems to be a trap answer...... If x and y are positive integers, what is the greatest common divisor of x and y?This is a classic "C trap" question: "C trap" is a problem which is VERY OBVIOUSLY sufficient if both statements are taken together. When you see such question you should be extremely cautious when choosing C for an answer. (1) 2x+y=73. Suppose GCD(x, y) is some integer d, then x=md and y=nd, for some positive integers m and n. So, we'll have 2(md)+(nd)=d(2m+n)=73. Now, since 73 is a prime number (73=1*73) then d=1 and 2m+n=73 (vice versa is not possible because m and n are positve integers and therefore 2m+n can not equal to 1). Hence we have that GCD(x, y)=d=1. Sufficient. (2) 5x-3y=1 --> 5x=3y+1 --> 5x and 3y are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1 (for example 20 and 21 are consecutive integers, thus only common factor they share is 1). So, 5x and 3y don't share any common factor but 1, thus x and y also don't share any common factor but 1. Hence, GCD(x, y) is 1. Sufficient. Answer: D. Hope it's clear. Hi, Thanks for the explanation. I m not so good in reasoning so I put the values and check. For example in statement 1 I just entered the values of y as 1,3,5,7 and I get the values of X as 36,35,34,33 respect. After checking 4 - 5 values I got to know that the gcf is 1. Please let me know if my strategy is good or not. Thanks,
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Re: If x and y are positive integers, what is the greatest [#permalink]
05 Sep 2012, 14:04
Awesome explanation Brunnel.
Vivek, i tried to solve by plugging in numbers.
for (1) i plugged in 20,33 10,53 15, 43 and so on which satisfy the equation
and noticed that none of the pairs have any common prime factors.
So the GCF has to be 1.
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Re: If x and y are positive integers, what is the greatest commo [#permalink]
05 Sep 2012, 22:05
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vivekdixit07 wrote: Hi,
Thanks for the explanation.
I m not so good in reasoning so I put the values and check.
For example in statement 1 I just entered the values of y as 1,3,5,7 and I get the values of X as 36,35,34,33 respect. After checking 4 - 5 values I got to know that the gcf is 1.
Please let me know if my strategy is good or not.
Thanks, Try to understand this: If something generic is established, you can plug in specific examples and use them e.g. if I say, "All boys are crazy." I can say, "Tom, a boy, is crazy." But the other way around may not always work. From certain examples, you cannot establish something generic. e.g. I cannot say, "Tom is crazy. Alfred is crazy. Ross is crazy. We can conclude that all boys are crazy." Here, you have tried to do something like this which is not good. We cannot blindly plug in numbers and establish that GCD will be 1. We could have missed some pairs where GCD may not have been 1. What you can do is plug in some numbers and then think why you are getting GCD = 1 in each case and whether it will be true for all pair of values. Check out Bunuel's explanation above. It's very important and you can expect to be tested on such concepts in GMAT.
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Re: If x and y are positive integers, what is the greatest commo [#permalink]
15 Sep 2012, 17:38
VeritasPrepKarishma wrote: vivekdixit07 wrote: Hi,
Thanks for the explanation.
I m not so good in reasoning so I put the values and check.
For example in statement 1 I just entered the values of y as 1,3,5,7 and I get the values of X as 36,35,34,33 respect. After checking 4 - 5 values I got to know that the gcf is 1.
Please let me know if my strategy is good or not.
Thanks, Try to understand this: If something generic is established, you can plug in specific examples and use them e.g. if I say, "All boys are crazy." I can say, "Tom, a boy, is crazy." But the other way around may not always work. From certain examples, you cannot establish something generic. e.g. I cannot say, "Tom is crazy. Alfred is crazy. Ross is crazy. We can conclude that all boys are crazy." Here, you have tried to do something like this which is not good. We cannot blindly plug in numbers and establish that GCD will be 1. We could have missed some pairs where GCD may not have been 1. What you can do is plug in some numbers and then think why you are getting GCD = 1 in each case and whether it will be true for all pair of values. Check out Bunuel's explanation above. It's very important and you can expect to be tested on such concepts in GMAT. =============== Karishma, Bunuel, I solved the above problem in the following manner. Please let me know whether that is the right approach or not. 1) 2x+y=73=>y=73-2x As x & y are positive integers=> let x= 1 => y=71 x=2=> y=69 x=3=> y=67 => x & y have no common factors other than 1 in each cases. Sufficient 2) 5x-3y=1=> y=(5x-1)/3 As x& y are +ve integers for x= 2, y=3 x=5, y=8 x=8, y=13 => In each of the above cases, x & y have GCF=1. Sufficient ANS- D
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Re: If x and y are positive integers, what is the greatest commo [#permalink]
16 Sep 2012, 23:58
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monsoon1 wrote:
I solved the above problem in the following manner. Please let me know whether that is the right approach or not.
1) 2x+y=73=>y=73-2x
As x & y are positive integers=> let x= 1 => y=71
x=2=> y=69
x=3=> y=67
=> x & y have no common factors other than 1 in each cases. Sufficient
2) 5x-3y=1=> y=(5x-1)/3
As x& y are +ve integers for x= 2, y=3
x=5, y=8
x=8, y=13
=> In each of the above cases, x & y have GCF=1. Sufficient
ANS- D
Ok, let me give you an example to show you that this approach alone is not good. Say, I change the first statement a little: 1. 2x + y = 35 As x & y are positive integers=> let x= 1 => y=33 x=2=> y=31 x=3=> y=29 x &y have GCF = 1 in each case. Does it mean they will have GCF = 1 only? What if x = 10, y = 15? These values satisfy 2x + y = 35 but the GCF is not 1. Point is, after how many values do you say that for all values GCF will be 1? Plugging in numbers can help you think straight but it may not give you the correct answer. That is why understanding the theory is important.
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Re: If x and y are positive integers, what is the greatest commo
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