If neither x nor y is equal to 0, is 3x &minu...
If neither x nor y is equal to 0, is 3x − 2y = 0?

(1) 27x3 − 8y3 = 0

(2) 9x2 − 4y2 = 0

• a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;

• b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;

• c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;

• d)

• e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

If neither x nor y is equal to 0, is 3x − 2y = 0?(1) 27x3 &minus...
We have to find out whether 3x − 2y = 0.
Alternatively, we can write 3x − 2y = 0 as x = 2 / 3y.
Thus, we have to determine whether x = 2 / 3y.
Statement 1:
We are given that 27x3 − 8y3 = 0.
⇒ 27x3 = 8y3
⇒ x3 = 8 / 27y3
⇒ x = 2 / 3y; taking the cube root of both the sides. (Remember that the real number x3 has only one real cube root.)
The answer is Yes. - Sufficient!
Statement 2:
We are given that 9x2 − 4y2 = 0
⇒ 9x2 = 4y2
⇒ x2 = 4 / 9y2
⇒ x = ±2 / 3y; taking the square root of both the sides. (Remember that the positive number x2 has two square roots, one positive and the other negative.)
If x = 2 / 3y, the answer is Yes; however, if x = −2 / 3y, the answer is No.
No unique value of x. - Insufficient!
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