if x and y are the integers most nearly equal to and x < < y, what is the value of xy ? gre

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If ten and y are positive integers, what is the value of xy? [#permalink]   Updated on: xxx Jun 2012, 04:29

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

(i) The greatest common cistron of x and y is x
(2) The least common multiple of x and y is 180

Originally posted by ctgmat123 on 14 Jun 2010, 16:50.
Last edited by Bunuel on thirty Jun 2012, 04:29, edited 2 times in full.

Edited the question and added the OA

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Re: Information Sufficiency trouble [#permalink]   14 Jun 2010, 17:12

ctgmat123 wrote:

Can someone walk me through this one?

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

1) The greatest common factor of x and y is 10
ii) the least mutual multiple of ten and y is 180

Thank you

Welcome to the Gmat Lodge. Beneath is a solution for your problem:

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

(ane) The greatest common cistron of x and y is ten. Clearly insufficient as multiple values are possible for \(xy\): for instance if \(x=y=10\), \(GCF(x,y)=10\) and \(xy=100\) Merely if \(x=ten\) and \(y=xx\), \(GCF(x,y)=10\) and \(xy=200\).

(two) the least common multiple of x and y is 180. Also insufficient as once again multiple values are possible for \(xy\): for instance if \(x=10\) and \(y=180\), \(LCM(ten,y)=180\) and \(xy=1800\) BUT if \(ten=1\) and \(y=180\), \(LCM(x,y)=180\) and \(xy=180\).

(1)+(ii) The about of import property of LCM and GCF is: for whatever positive integers \(x\) and \(y\), \(xy=GCF(x,y)*LCM(ten,y)\), hence \(xy=GCF(x,y)*LCM(x,y)=10*180=1800\). Sufficient.

Answer: C.

Hope information technology helps.
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Re: ds question [#permalink]   19 Oct 2010, 02:41

satishreddy wrote:

if Ten and Y are positive integers, what is the value of xy

1) the greatest mutual cistron of X and Y is 10
ii) the to the lowest degree mutual multiple of X and Y is 180

This is just a formula based.

( GCFof 10 and y )* (LCM of 10 and y)= x * y

This is valid for all the numbers.Hope this will do.

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Re: Data Sufficiency problem [#permalink]   20 October 2010, 11:27

Squeamish, I didn't know GCF(10&Y)*LCM(X&Y)=X*Y

Kudos!!

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lcm [#permalink]   24 Feb 2012, 13:14

Some solutions above rely on the "property" that GCFxLCM is xy, which is nice when you lot know the holding. Unfortunately, it is virtually impossible to learn all such properties for the GMAT. Here'due south a away to (effort) to derive the property for this and similar problems:

GCF = 10 = 2x5
LCM = 180 = 3x3x2x2x5

The solution centers on the definition of LCM. Call back how nosotros find LCM for two numbers? Nosotros accept all the prime number factors the two numbers share and multiply them by prime number factors that the numbers don't share.

ie, LCM of (2x2x5x7) and (2x7x11) would be: (2x2x5x7x11)

Since we are looking for the actual product of ten and y, the result will exist the LCM times the factors they share (since nosotros didn't double count them in the original LCM calculation), namely the GCF, since that's what the GCF encapsulates.

Hence, xy = LCM x GCF.

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Re: If x and y are positive integers, what is the value of xy? [#permalink]   19 December 2012, 15:32

This is tough.

whenever you meet such question break downwardly into factors the numbers.

So we want information to exactly calculate \(X*Y\)

1) we have x and the factor are 2 and 5 a agglomeration of numbers could have two and 5 in the shaded region to summate the GCF (remembre that to obtain the GCF yous take between 2 numbers those have the least power). Insuff

2) the same equally higher up 180 equal \(two^2\) \(3^ii\) and \(5\) simply nothing more . insuff

1) and 2) for any two positive integers 10 and Y, \(X*Y\) \(=\) \((LCM of X and Y) ten (GCF of X and Y)\). So y'all accept: \(2*5\) from \(GCF\) and \(2^ii\) \(3^2\) and \(v\) from\(LCM\). So yous can calculate exactly the value of \(X*Y\)

I 'll wait from Bunuel if my caption is correct
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Re: If ten and y are positive integers, what is the value of xy? [#permalink]   19 Dec 2012, 16:07

I call up answer should exist C as the property is GCF (x,y) * LCM(x,y) = Product of the two numbers
Hence value of xyv= ten*180= 1800

To prove A as insufficient you tin plug numberssay X = ten , Y = 30 GCF =10 product = 300 Another case X = 10 Y = 10 Hence product = 100

To prove B as insufficient you can plug in numbers X= ninety Y = 180 , Another case X=ane Y = 180
Hence Insufficient

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If x and y are positive integers, what is the value of xy? [#permalink]   08 Nov 2014, 23:22

how-do-you-do
I've been trying to wrap my head around all that gcd and lcm would tell me about the numbers. When bodily numbers are given information technology is a little easier. Only when not, it gets difficult, for me (like this : If a and b are positive integers divisible by half-dozen, is 6 the greatest common divisor of a and b? (1) a = 2b + vi (2) a = 3b ------sorry about this.. i cant paste urls however)

Then I need some generalizations (so i can summarize finally )

-What do GCD and LCM tell us about the numbers?
-Is it always possible to know the numbers themselves when the LCM or GCD are given?
-We found the product of numbers here. Tin we notice the numbers themselves in whatever case?
Please help me, fifty-fifty if you know the answer to one of these questions. Besides permit me know if whatsoever of them don't make sense, and why.
Thank you loads

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Re: If ten and y are positive integers, what is the value of xy? [#permalink]   26 Oct 2015, 02:xx

X and Y are integers

\(XY= ?\)

Statement i

GCF( greatest Common gene) of x and y = \(10\)

x = 10 and y = 10
GCF = 10
hence xy = 100

ten = 10 and y = xxx
GCF = 10
hence xy = 300

Clearly Non Sufficient

Statement ii

LCM( least common multiple) of x and y = \(180\)

ten= 180 and y = 1
LCM = 180
hence xy= 180

x=180 and y = 2
LCM = 180
Hence xy = 360

Clearly non sufficient

Now Combining Argument 1 and 2

we Know that
HCF of ten and y * Lcm of x and y = x* y

Therefore \(x * 180 = 1800\)

Sufficient

So Reply = C

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Re: If x and y are positive integers, what is the value of xy? [#permalink]   28 Jan 2017, 03:52

Given data-> x and y are positive integers.
Nosotros need the value of 10*y

Statement 1->
GCD(x,y)=10
x=ten
y=10
GCD=10
xy=100

10=10
y=20
GCD=10
xy=200

Hence not sufficient.

Statement 2->
LCM(ten,y)=180
x=180
y=180
LCM=180
xy=180*180

10=1
y=180
LCM=180
xy=180

Hence not sufficient.

Combing the ii statements->

For ii positive integers => LCM(x,y)*GCD(x,y)=> xy
Hence xy=180*10=> 1800

Hence sufficient.

Hence C.

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Re: Is ten and y are positive integers, what is the value of xy? [#permalink]   19 Sep 2017, 21:46

quiet888 wrote:

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

(i) The greatest mutual factor of x and y is 10
(ii) The least mutual multiple of x and y is 180

We can solve this questions using 2 approach.
Shorter approach (ane min)

Statement 1: GCF = 10 , (10,y) = (x,20), (x, xxx), (20,30), (30,fifty)...... and so many numbers which are co-prime after division past x.
NOT SUFFICIENT

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

Combined : GCF * LCM = 10*y .. Its a formula..
SUFFICIENT

Longer approach (Time taking: 2 min )
Statement ane: GCF = ten , (10,y) = (10,20), (10, xxx), (xx,30), (30,50)...... and so many numbers which are co-prime number after segmentation by x.
NOT SUFFICIENT

Statement ii: LCM = 180 , (x,y)= (2,180), (ten, 180), (90, 4).... and others
Not SUFFICIENT

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

Answer C
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Re: Is x and y are positive integers, what is the value of xy? [#permalink]   twenty Apr 2018, 06:49

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 mutual multiple of ten and y is 180

Target question: What is the value of xy?

Statement 1: The greatest common factor of ten and y is ten
example a: ten=ten and y=10. Here, xy=100
case b: x=ten and y=twenty. Here, xy=200
Since we cannot respond the target question with certainty, statement 1 is NOT SUFFICIENT

Statement two: The to the lowest degree mutual multiple of x and y is 180
instance a: x=1 and y=180. Here, xy=180
case b: x=2 and y=180. Here, xy=360
Since nosotros cannot answer the target question with certainty, statement 2 is Non SUFFICIENT

Statements ane & 2
There'southward a dainty rule that says:
If x and y are positive integers, and 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 ane says the GCF of 10 and y is ten
Statement 2 says the LCM of x and y is 180
And so, from our handy rule, xy = (10)(180) = 1800
Since we can now answer the target question with certainty, the combined statements are SUFFICIENT

So, the respond is C

Cheers,
Brent
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Re: If 10 and y are positive integers, what is the value of xy? [#permalink]   fifteen Jul 2018, 11:56

Tin can someone explain to me why 20 & ninety don't piece of work?

Thank you.

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Re: If ten and y are positive integers, what is the value of xy? [#permalink]   fifteen Jul 2018, 19:45

krisbrown12 wrote:

Tin someone explain to me why 20 & 90 don't piece of work?

Cheers.

x and y could be 20 and xc. In this example too xy = xx*ninety = 1800. The same answer.
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Re: If x and y are positive integers, what is the value of xy? [#permalink]   xxx Sep 2019, 15:27

ctgmat123 wrote:

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

(1) The greatest common factor of ten and y is 10
x, y could = 10 in which instance xy = 100
or 10,y could = 10, 20 so xy = 200
Non sufficient because without knowing the remaining factors of 10 or y we can't say anything about the value of xy.

(2) The least common multiple of x and y is 180
180 = ii²*iii²*five, so it could exist that ten = 5 and y = 2²*3² in which case xy = 180
or x = 5*two, y = 3²*2² in which case xy = 360
Not sufficient because without knowing if they share whatsoever factors of 180 nosotros can't determine xy.

Together, we know 1) GCF = ten and LCM = 180, so x & y share 2*five every bit factors, and the other two*3² is split amongst them in some manner... product of xy = GCF*LCM = 1800, sufficient.

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Re: If x and y are positive integers, what is the value of xy? [#permalink]   05 Oct 2020, 06:38

ctgmat123 wrote:

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

(one) The greatest mutual gene of x and y is 10
(two) The least common multiple of x and y is 180

Solution:

Argument One Only:

The greatest common factor of x and y is 10.

If ten = 10 and y = 20, then xy = 200. However, if x = ten and y = thirty, and then xy = 300. Statement one lonely is not sufficient.

Statement Two Only:

The to the lowest degree common multiple of x and y is 180.

If x = 1 and y = 180, then xy = 180. However, if x = 60 and y = 90, and so xy = 5400. Statement two alone is not sufficient.

Statements One and Two Together:

Recall that the production of the LCM and GCF of two positive integers is the production of the ii integers. We have xy = x * 180 = 1800. The ii statements together are sufficient.

Reply: C
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Re: If x and y are positive integers, what is the value of xy? [#permalink]   05 Oct 2020, 09:44

Forget the conventional way to solve DS questions.

Nosotros will solve this DS question using the variable approach.

DS question with 2 variables: Let the original condition in a DS question contain ii variables. Now, 2 variables would by and large require two equation for us to be able to solve for the value of the variable.

We know that each condition would usually give us an equation, and Since we need 2 equations to match the numbers of variables and equations in the original condition, the logical answer is C.

To master the Variable Approach, visit

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and check our lessons and proven techniques to score high in DS questions.

Let's utilise the 3 steps suggested previously. [Watch lessons on our website to chief these 3 steps]

Step 1 of the Variable Arroyo: Modifying and rechecking the original condition and the question. We take to find the value of 'xy'.

=> Given that 'x' and 'y' are positive integers

Second and the tertiary step of Variable Arroyo: From the original condition, we have 2 variables (ten and y).To match the number of variables with the number of equations, we need 2 equations. Since conditions (i) and (ii) will provide ii equations, C would most likely be the answer.

Let'southward take await at both conditions together.

Status(one) tells united states of america that the greatest mutual factor of x and y is 10 .

Status(two) tells united states that The least mutual multiple of ten and y is 180 .

=> Production of numbers = product of their GCF and LCM

=> xy = 180 * 10 = 1800

Since the answer is unique, both conditions combined together are sufficient by CMT 2.

Both conditions combined together are sufficient.

And then, C is the correct answer.

Answer: C
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Re: If x and y are positive integers, what is the value of xy? [#permalink]   09 Oct 2020, 09:03

ctgmat123 wrote:

If ten and y are positive integers, what is the value of xy?

(1) The greatest mutual factor of ten and y is 10
(2) The least common multiple of x and y is 180

Solution:

Argument Ane Merely:

The greatest common gene of 10 and y is 10.

If x = 10 and y = 20, so xy = 200. Nonetheless, if ten = 10 and y = 30, then xy = 300. Statement 1 alone is not sufficient.

Argument Ii Only:

The least mutual multiple of x and y is 180.

If x = 1 and y = 180, then xy = 180. However, if x = 60 and y = 90, then xy = 5400. Statement ii lone is not sufficient.

Statements One and Two Together:

Recollect that the product of the LCM and GCF of two positive integers is the product of the two integers. We accept xy = 10 * 180 = 1800. The ii statements together are sufficient.

Respond: C
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Re: If x and y are positive integers, what is the value of xy? [#permalink]   04 Jun 2021, 03:32

This is a very simple question on the concepts of HCF and LCM. From the question data, we know that x and y are positive integers. We need to notice the value of xy.

From statement I alone, HCF(ten,y) = 10. This is bereft since 10 and y tin can have a host of values such that their HCF is 10.

For example, x = ten and y = x in which case their HCF is ten and their product is 100.
x = 10 and y = 20 in which example their HCF is still 10 only their product is 200.

Statement I lone is insufficient to requite us a unique value for xy. Answer options A and D tin be eliminated. Possible answer options are B, C or E.

From argument Ii alone, LCM(x,y) = 180. This is insufficient since x and y can have a host of values such that their LCM is 180.

For example, x = 36 and y = 5 in which example their LCM is 180 and their product is 180.
10 = 90 and y = 20 in which case their LCM is 180 but their product is 1800.

A common fault that some test takers make here is to remember the data from the beginning argument and therefore conclude that the beginning example is not possible. This is not right, note that yous are trying to solve the question using the second statement alone.

Statement II solitary is insufficient. Answer option B can exist eliminated. Possible answer options are C or E.

Combining statements I and II, nosotros have the following:
From argument I, HCF (x,y) = 10; from statement II lonely, LCM (ten,y) = 180.

Combining these two pieces of data should be done using a property rather than plugging in values. Remember, you are not trying to notice the values of ten and y individually; you are trying to calculate xy.

For whatever two numbers, Product of numbers = Product of their LCM and HCF.

Therefore, xy = 180 * 10 = 1800.
The combination of statements is sufficient to find a unique value of xy. Answer option E can be eliminated.

The correct answer option is C.

Hope that helps!
Aravind B T
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Re: If 10 and y are positive integers, what is the value of xy? [#permalink]

04 Jun 2021, 03:32

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