Query on data sufficeincy! Help!!

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Hi all,

I have a query on the following question

Q) Is x^5 + 4x^3 + 8x^2 + 32 = 128

1) x^2 - 5x + 6 = 0
2) x^2 +5x +6 = 0

My query is:
When you solve the above equation with help of Statement 1 ie x = 2 or 3, both values satisfy the equation.
When you solve it with help of Statement 2, ie x = -2, -3, it does not satisfy the equation.

In such situations, what should be the answer..... I answered as option D ie either statement is suffecient to answer (either in negative or affirmative) if the equation equals 128.
However the answer in the mock test was A i.e. Statement 1 alone is suffiecinet???

Can some one please clarify if I am wrong and missing some important point?

Sagar

[Ian Stewart]

My query is:
When you solve the above equation with help of Statement 1 ie x = 2 or 3, both values satisfy the equation.
When you solve it with help of Statement 2, ie x = -2, -3, it does not satisfy the equation.

In such situations, what should be the answer..... I answered as option D ie either statement is suffecient to answer (either in negative or affirmative) if the equation equals 128.
However the answer in the mock test was A i.e. Statement 1 alone is suffiecinet???

A few issues here. From S1, you can certainly conclude that either x = 2 or x = 3. Plugging x = 2 into the equation in the question, we do find that the equation might be true. On the other hand, you can quickly see that x = 3 will not work in the equation:

x^5 + 4x^3 + 8x^2 + 32 = 128

Since 3^5 is already larger than 128, and the other terms on the left side of the equation are all positive, there's no way x = 3 can be a solution here. Or you could notice that if x is odd, the left side of the equation is odd (it's the sum of one odd number, x^5, and three even numbers), so can't possibly be equal to 128, an even number. So S1 is not sufficient, and neither A nor D can be correct here.

Then there's Statement 2. The second statement clearly contradicts the first; they have no solutions in common. This can *never* happen in a real GMAT question, since if it did, it would make no logical sense to consider both statements together. Of course, taken alone, S2 is sufficient to give a 'no' answer to the question, but the question is very poorly designed, and if the OA provided is A, something is very wrong with the source. Where is the question from?

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Thanks Ian for your help. Its from a mock test.

Sagar