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# Is x and y are positive integers, what is the value of xy?

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Manager
Joined: 24 Apr 2008
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Is x and y are positive integers, what is the value of xy?  [#permalink]

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Updated on: 29 Apr 2017, 17:20
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Difficulty:

15% (low)

Question Stats:

77% (00:40) correct 23% (00:48) wrong based on 145 sessions

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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

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.
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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
2
3
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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26 Apr 2008, 08:55
1
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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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
1
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 co-prime after division by 10.
NOT SUFFICIENT

Statement 2: LCM = 180 , (x,y)= (2,180), (10, 180), (90, 4).... and others
NOT SUFFICIENT

Combined : GCF * LCM = x*y .. Its a formula..
SUFFICIENT

Longer 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 co-prime after division by 10.
NOT SUFFICIENT

Statement 2: LCM = 180 , (x,y)= (2,180), (10, 180), (90, 4).... and others
NOT SUFFICIENT

Combined : x, y = (10,180), (20,90)
xy = 1800
SUFFICIENT

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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
Top Contributor
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=100
case b: x=10 and y=20. Here, xy=200
Since 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 & 2
There'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) = 1800
Since we can now answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
Brent
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Re: Is x and y are positive integers, what is the value of xy? &nbs [#permalink] 20 Apr 2018, 07:49
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