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Is x and y are positive integers, what is the value of xy? [#permalink]
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Is x and y are positive integers, what is the value of xy? (i) The greatest common factor of x and y is 10 (ii) The least common multiple of x and y is 180
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Originally posted by quiet888 on 26 Apr 2008, 08:24.
Last edited by stonecold on 29 Apr 2017, 17:20, edited 1 time in total.
Added the OA.



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Re: Is x and y are positive integers, what is the value of xy? [#permalink]
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26 Apr 2008, 08:55
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quiet888 wrote: Is x and y are positive integers, what is the value of xy?
(i) The greatest common factor of x and y is 10 (ii) The least common multiple of x and y is 180 these question ans choice is always either C or E.. lets see.. xy? 1) gcd is 10 x=10 y=20 GCD =10 xy=200 x=10 y=60 GCD=10, xy=600 2) LCM x=180 y=2 LCM=180 xy=360 x=180 y=180 LCM=180 xy=180^2 Insuf together suppose x=180 y=10 suppse x=90 y=20 xy= is the same..Sufficient C it is.



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Re: Is x and y are positive integers, what is the value of xy? [#permalink]
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26 Apr 2008, 11:50
another thing..with these type of question where we have the GCD and LCM..usually we can tell something like an XY but we cant really tell what X is or what y is...



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Re: Is x and y are positive integers, what is the value of xy? [#permalink]
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27 Apr 2008, 14:27
anyway to solve this in under 2mins? fresh?



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Re: Is x and y are positive integers, what is the value of xy? [#permalink]
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27 Apr 2008, 19:17
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jimmyjamesdonkey wrote: anyway to solve this in under 2mins? fresh? Yes, even under 20 seconds if you remember that xy = GCD*LCM. Sure!
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Re: Is x and y are positive integers, what is the value of xy? [#permalink]
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28 Apr 2008, 07:25
Woah can you elaborate that a little bit...I always have such problems with GCF & LCM..



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Re: Is x and y are positive integers, what is the value of xy? [#permalink]
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19 Jul 2011, 00:30
FN wrote: quiet888 wrote: Is x and y are positive integers, what is the value of xy?
(i) The greatest common factor of x and y is 10 (ii) The least common multiple of x and y is 180 these question ans choice is always either C or E.. lets see.. xy? 1) gcd is 10 x=10 y=20 GCD =10 xy=200 x=10 y=60 GCD=10, xy=600 2) LCM x=180 y=2 LCM=180 xy=360 x=180 y=180 LCM=180 xy=180^2 Insuf together suppose x=180 y=10 suppse x=90 y=20 xy= is the same..Sufficient C it is. hi, For (ii) The least common multiple of x and y is 180 isn't x*y = 5400? my rational... if 180 is the Lowest Common Multiple, meaning that both x and y have 3, 3, 5, 2, 2 at least appeared twice for x y. So if x = 2, ?, 3, 5 y = 2, ?, 3, 5  x & y's LCM which is 180 = 2* 3* 5* ?* ?* So after pulling 5 & 3 & 2, we still need one 2 and one 3 to fulfil the 3, 3, 5, 2, 2 = (180) requirement. Having said that, the ? in each x & y should be 2 and 3. So multiple all 8 digits, it should x*y = 2* 2* 3* 5* 2* 3*3* 5* = 5400?



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Re: Is x and y are positive integers, what is the value of xy? [#permalink]
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01 Aug 2011, 08:31
Could some body help me to understand this a little better.
here is where I am getting stuck
GCF = 10, There for X = 10A nd Y = 10B where A and B are separate constants
for example 20 and 30, here the GDF is 10 and a = 2 and b = 3
sice we dont have a and b from this equation. this is insufficient
statement 2:
LCM is 180 so X*N1 = 180 and Y * N2 = 180
since we do not know the values of N1 and N2 this statement is not sufficient.
even if we combine, we dont have information to solve.
I see come body explaining the answer are LCM*GCD. Could you please tell me how you arrived at that equation



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Re: Is x and y are positive integers, what is the value of xy? [#permalink]
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01 Aug 2011, 09:38
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GCF * LCM = X*Y it's a general rule 10*180 = 1800 so the the answer is C and u need less than 10 seconds
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Re: Is x and y are positive integers, what is the value of xy? [#permalink]
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01 Aug 2011, 10:04
Always; if we multiply two positive integers then the multiplication is same as the multiplication of their lcm and gcf. In this case lcm = 180 and gcf = 10 hence xy = (lcm)(gcf) = 180.10 = 1800
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Re: Is x and y are positive integers, what is the value of xy? [#permalink]
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02 Aug 2011, 10:44
manishgeorge wrote: Could some body help me to understand this a little better.
here is where I am getting stuck
GCF = 10, There for X = 10A nd Y = 10B where A and B are separate constants
for example 20 and 30, here the GDF is 10 and a = 2 and b = 3
sice we dont have a and b from this equation. this is insufficient
statement 2:
LCM is 180 so X*N1 = 180 and Y * N2 = 180
since we do not know the values of N1 and N2 this statement is not sufficient.
even if we combine, we dont have information to solve.
I see come body explaining the answer are LCM*GCD. Could you please tell me how you arrived at that equation it's a general rule and can always applied . if u want the details about how we arrived at that equation just let me know
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Re: Is x and y are positive integers, what is the value of xy? [#permalink]
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29 Apr 2017, 17:23
Directly we can say that since GCD*LCM=> Product of two integers.
Hence C must be the answer choice here.
Additionally to reject either options we can use the following test cases => Statement 1 => 10,10 10,100
Statement 2 => 1,180 180,180
Combing them > As LCM*GCD=product of the two numbers => xy=> 180*10=1800
Hence sufficient.
SMASH THAT C.
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Re: Is x and y are positive integers, what is the value of xy? [#permalink]
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19 Sep 2017, 22:46
quiet888 wrote: Is x and y are positive integers, what is the value of xy?
(i) The greatest common factor of x and y is 10 (ii) The least common multiple of x and y is 180 We can solve this questions using 2 approach. Shorter approach (1 min) Statement 1: GCF = 10 , (x,y) = (10,20), (10, 30), (20,30), (30,50)...... and so many numbers which are coprime after division by 10. NOT SUFFICIENTStatement 2: LCM = 180 , (x,y)= (2,180), (10, 180), (90, 4).... and others NOT SUFFICIENTCombined : GCF * LCM = x*y .. Its a formula.. SUFFICIENTLonger approach (Time taking: 2 min ) Statement 1: GCF = 10 , (x,y) = (10,20), (10, 30), (20,30), (30,50)...... and so many numbers which are coprime after division by 10. NOT SUFFICIENTStatement 2: LCM = 180 , (x,y)= (2,180), (10, 180), (90, 4).... and others NOT SUFFICIENTCombined : x, y = (10,180), (20,90) xy = 1800 SUFFICIENTAnswer C
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Re: Is x and y are positive integers, what is the value of xy? [#permalink]
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20 Apr 2018, 07:49
quiet888 wrote: Is x and y are positive integers, what is the value of xy?
(i) The greatest common factor of x and y is 10 (ii) The least common multiple of x and y is 180 Target question: What is the value of xy?Statement 1: The greatest common factor of x and y is 10 case a: x=10 and y=10. Here, xy=100case b: x=10 and y=20. Here, xy=200Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: The least common multiple of x and y is 180 case a: x=1 and y=180. Here, xy=180 case b: x=2 and y=180. Here, xy=360 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Statements 1 & 2There's a nice rule that says: If x and y are positive integers, then (GCF of x and y)(LCM of x and y)=xy(aside: whenever a question mentions the LCM and the GCF, be sure to consider the above rule)Statement 1 says the GCF of x and y is 10 Statement 2 says the LCM of x and y is 180 So, from our handy rule, xy = (10)(180) = 1800Since we can now answer the target question with certainty, the combined statements are SUFFICIENT So, the answer is C Cheers, Brent
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