LCM and HCF concept

[goyalsau]

Earnest Has posted some questions, I was not able to answer this answer so i thought its always better to post a single question in a forum

Hope you Like it guys,
And share your answer and explanation.

[diebeatsthegmat]

Earnest Has posted some questions, I was not able to answer this answer so i thought its always better to post a single question in a forum

Hope you Like it guys,
And share your answer and explanation.

this helps a lot... take a look at the following link and the other link in it too
https://www.manhattangmat.com/forums/if- ... -t282.html

[mk101]

IMO THE answer should be "C" ... is that the official answer?


s1 - GCF OF (x,y ) =10 - implies we can write the numbers x and y as 10p and 10q
But this information is not enough to provide the answer

S1 - The LCM (x,y) =180
but this is not enough to answer the question either

but when we combine the two statements then we get the answer based on the formula given below

we know THAT FOR given two numbers only HCF X LCM = Product of the two numbers..

therefore 10 x 180 = x X y

[nubu]

From statement 1 we have:
x = 10m
y = 10n
(m and n are positive integers and # 0; m and n do not have a common factor as 10 are the largest common factor of x and y)
xy= 100mn
=> not sufficient

From statement 2 we have:
180 = xp
180 = yq
(p and q are positive integers and #0)
=>Not sufficient

Statement 1 and Statement 2:
180 = xp = 10mp
180 = yq = 10nq
=> 18 = mp = nq
=>We have 2 cases
1) (m,p) = (2,9) and (n,q) = (3,6) OR (m,p) = (3,6) and (n,q) = (2,9)
2) (m,p) = (2,9) and (n,q) = (9,2) OR (m,p) = (9,2) and (n,q) = (2,9)
(We do not have a case like (2,9) and (6,3) as m and n must not have common factor)
In case 1: x = 20 & y = 30 => LCM = 60. Rejected
In case 2: x=20 & y = 90 => LCM = 180. So xy = 1800. Accepted

PICK C

[goyalsau]

Statement 1 and Statement 2:
180 = xp = 10mp
180 = yq = 10nq
=> 18 = mp = nq

=>We have 2 cases
1) (m,p) = (2,9) and (n,q) = (3,6) OR (m,p) = (3,6) and (n,q) = (2,9)
2) (m,p) = (2,9) and (n,q) = (9,2) OR (m,p) = (9,2) and (n,q) = (2,9)
(We do not have a case like (2,9) and (6,3) as m and n must not have common factor)
In case 1: x = 20 & y = 30 => LCM = 60. Rejected
In case 2: x=20 & y = 90 => LCM = 180. So xy = 1800. Accepted

PICK C

According to there can two pair of numbers
( 90, 20 ) and (180 , 10 ) If there are any other pairs then please let me know ..

[nubu]

That's right.I realized this pair (10,180) too and xy is still equal 1800. I dont think there is another pair