GMATsid2016 wrote:Since a/b = integer/integer -- the definition of a rational number -- it is not possible that a/b is equal to an irrational value such as ³√2.
Thus, in order for (a/b)³ to be an integer, a/b must be an integer, implying that b is the CUBE OF AN INTEGER.
Thus, x = b^4 = (integer³)^4 = integer^12.
SUFFICIENT.
Hi GMATGuruNY ,
Everything is clear. can you please explain the above part?
Thanks,
Sid
Statement 2: x = b�, where b is an integer.
In my post above, the following was determined:
b = (
a/b)³
Since b is an integer, the second equation above implies that the value in blue must also be an integer, as follows:
b =
integer³.
Substituting b = integer³ into x = b�, we get:
x = (integer³)�.
Multiplying the exponents, we get:
x = integer¹².
Thus, x is equal to the 12th power of an integer.
SUFFICIENT.
Some test-takers might find the following approach more straightforward:
Test an EASY CASE.
Test POWERS OF 2.
Statement 1:
x =
2³, 2�, 2�, 2¹²...
If x = 2³, then x is NOT equal to the 12th power of an integer.
If x = 2¹², then x IS equal to the 12th power of an integer.
INSUFFICIENT.
Statement 2:
x =
2�, 2�, 2¹²...
If x = 2�, then x is NOT equal to the 12th power of an integer.
If x = 2¹², then x IS equal to the 12th power of an integer.
INSUFFICIENT.
Statements combined:
The smallest value common to both the red list and the blue list is 2¹², which is the 12th power of an integer.
If we extend the two lists, we get:
x =
2¹�, 2¹�, 2²¹, 2²�...
x =
2¹�, 2²�, 2²�...
The next value common to both lists is 2²� = 4¹², which is the 12th power of an integer.
Implication:
To satisfy both statements, x must be the 12th power of an integer.
SUFFICIENT.
The correct answer is
C.
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