Fairly simple problem

knight247 wrote:If a≠0 is (1/a) > a/(b^4 + 3)?
1)a=b²
2)a²=b^4


OA is [spoiler]A[/spoiler]. Detailed explanations would be appreciated.
Thanks

I. If a ≠ 0 and a = b², then a > 0 and the stem “Is (1/a) > a/(b^4 + 3)?” can be rewritten as “Is (1/a) > a/( a²+ 3)?” or “Is 1 > a²/( a² + 3)?” and the answer is YES. Sufficient

II. If a ≠ 0 and b^4 = a², then b² = a if a > 0, and b² = -a if a < 0. The two possibilities for a won’t take us to a concrete decision to answer. [spoiler]Insufficient


Hence A[/spoiler]

is the answer D, i.e both statements are sufficient.

knight247 wrote:If a≠0 is (1/a) > a/(b^4 + 3)?
1)a=b²
2)a²=b^4


OA is [spoiler]A[/spoiler]. Detailed explanations would be appreciated.
Thanks

aditi.ahlawat wrote:is the answer D, i.e both statements are sufficient.

knight247 wrote:If a≠0 is (1/a) > a/(b^4 + 3)?
1)a=b²
2)a²=b^4


OA is [spoiler]A[/spoiler]. Detailed explanations would be appreciated.
Thanks

(1/a) > a/(b^4 + 3)
=> b^4 + 3 > a^2 (cross multiplication)
=> b^4 - a^2 + 3 >0 ?? --- (1)

Statement 1 : a=b2 . So, substituting in (1) 3>0 ... sufficient
Statement 2: b^4 - b^16 + 3 >0.. No information about b. So, INSUFFICIENT

So, Ans is A

goelmaya wrote:

aditi.ahlawat wrote:is the answer D, i.e both statements are sufficient.

knight247 wrote:If a≠0 is (1/a) > a/(b^4 + 3)?
1)a=b²
2)a²=b^4


OA is [spoiler]A[/spoiler]. Detailed explanations would be appreciated.
Thanks

(1/a) > a/(b^4 + 3)
=> b^4 + 3 > a^2 (cross multiplication)
=> b^4 - a^2 + 3 >0 ?? --- (1)

Statement 1 : a=b2 . So, substituting in (1) 3>0 ... sufficient
Statement 2: b^4 - b^16 + 3 >0.. No information about b. So, INSUFFICIENT

So, Ans is A

how did U b^16 in Statement 2?
the equation is b^4 - a^2 + 3 >0 ?? and the option is a^2 = b^4
so when the value is plugged in, it should become
b^4 - b^4 + 3 >0
=>3>0
=> True.
So the answer should be D.
Experts please reply.

As with most sufficiency problems involving an inequality, determining the answer often hinges upon the SIGN of any denominator expressions.

In this case, b^4 + 3 is always positive, regardless of the value of b. a, on the other hand, can be either positive or negative, based on the initial formula alone.

In (A), we are told that a = b^2, which tells us that a MUST be positive. This allows the cross-multiplication to occur without creating more than one possible inequality:

b^4 + 3 > b^4, which of course is always true. SUFFICIENT

In (B), we are given a^2 = b^4. This looks similar to part (A) but is different:

a = +/- b^2, which leads to the following TWO POTENTIAL INEQUALITIES:

b^4 + 3 > b^4 OR b^4 + 3 < b^4, each of which gives a different answer. INSUFFICIENT

Therefore, (A) is the answer.

As with most sufficiency problems involving an inequality, determining the answer often hinges upon the SIGN of any denominator expressions.

In this case, b^4 + 3 is always positive, regardless of the value of b. a, on the other hand, can be either positive or negative, based on the initial formula alone.

In (A), we are told that a = b^2, which tells us that a MUST be positive. This allows the cross-multiplication to occur without creating more than one possible inequality:

b^4 + 3 > b^4, which of course is always true. SUFFICIENT

In (B), we are given a^2 = b^4. This looks similar to part (A) but is different:

a = +/- b^2, which leads to the following TWO POTENTIAL INEQUALITIES:

b^4 + 3 > b^4 OR b^4 + 3 < b^4, each of which gives a different answer. INSUFFICIENT

Therefore, (A) is the answer.