If the least common multiple of integers x and y is 840, what is the value of x?
(1) The greatest common factor of x and y is 28.
(2) y = 168
OA : C
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LCM and GCF
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GMATGuruNY
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RULE:
For any positive integers x and y, xy = (LCM of x and y)(GCF of x and y).
Statement 1:
Thus:
xy = (840)(28).
It's possible that x=1 and y=840*28.
It's possible that x=840*28 and y=1.
Since x can be different values, INSUFFICIENT.
Statement 2:
840=168*5.
It's possible that x=5 and y=168, with the result that the LCM of x and y is 840.
It's possible that x=168*5 and y=168, with the result that the LCM of x and y is 840.
Since x can be different values, INSUFFICIENT.
Statements combined:
Since xy = (840)(28) and y=168, x=(840/168)(28) = 5*28 =140.
SUFFICIENT.
The correct answer is C.
For any positive integers x and y, xy = (LCM of x and y)(GCF of x and y).
Statement 1:
Thus:
xy = (840)(28).
It's possible that x=1 and y=840*28.
It's possible that x=840*28 and y=1.
Since x can be different values, INSUFFICIENT.
Statement 2:
840=168*5.
It's possible that x=5 and y=168, with the result that the LCM of x and y is 840.
It's possible that x=168*5 and y=168, with the result that the LCM of x and y is 840.
Since x can be different values, INSUFFICIENT.
Statements combined:
Since xy = (840)(28) and y=168, x=(840/168)(28) = 5*28 =140.
SUFFICIENT.
The correct answer is C.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
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OptimusPrep
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Always remember x*y = LCM (x, y) * GCF (x, y)manik11 wrote:If the least common multiple of integers x and y is 840, what is the value of x?
(1) The greatest common factor of x and y is 28.
(2) y = 168
OA : C
Statement 1: GCF = 28
x*y = 840*28
We cannot say anything about x
INSUFFICIENT
Statement 2: y = 168
Clearly we cannot tell anything about x
INSUFFICIENT
Combining both the statements:
LCM = 840, GCF = 28 and y = 168
Hence we can find the value of x
SUFFICIENT
Correct Option: C
