Is x > sqrt(3)? (1) 3^(x) = sqrt(27) (2)x^3 + x^5 + x^7

We cannot be certain of the highlighted portion above. As i said, cosx actually expands into even powers of x, so more than one roots are certainly possible. Further, if you just put this expression in the spread sheet, you would see that at least three values of x (one very close to -2, one very close to 1 and one very close to 3.387) would make it valid.. there may be many others.

So, 2nd stem is fairly ambiguous

Great points, guys. There's really no reason for the problem to be outside the realm of the GMAT. It has been changed to address your thoughts.

That's not true at all. Even a simple equation like

\(x^3 = x\)

has three solutions for x, -1, 0 and 1. When you have an equation in which x is raised to various positive integer powers, you can have as many solutions as the highest power in the equation. It doesn't make any difference whether the powers are odd or even.

There are other situations besides the ones you describe where you can have multiple solutions. For example, the equation

\(1^x = 1\)

has an infinite number of solutions. And while it's beyond the scope of the GMAT, it's especially true of equations involving trigonometric functions (like the one in the example you first provided, then deleted) that you can have multiple solutions; the equation cos(x) = 0, for example, has an infinite number of solutions.

Excellent inputs from all. Thanks Ian and beyondgmatscore

On the GMAT, equations involving single-variables without even exponents or absolute values virtually always* solve to a single value. Knowing this saves time and can bail out a GMAT taker when the equation is beyond the know-how she or he possesses.

It is important to recognize that the GMAT is not a math test--it's a problem solving test. Limiting oneself to mathematical knowledge is limiting one's potential.

*An rare example from the Official Guide in which a single-variable-not-raised-to-an-even-exponent-or-absolute-valued equation has multiple solutions is PS #215, but even it has only one solution on the GMAT.

[quote="spacelandprep"]Q. Is x > sqrt(3)?

(1) 3^(x) = sqrt(27)

(2) x^3 + x^5 + x^7 = 3591/128


Statement 1: x=3/2=1.5 which is less than sqrt(3).Hence statement is sufficient.

Statement 2:x^3(1+x^2+x^4)=3591/128

3591/128 can be expressed as 3^3*7*19/2^7
comparing LHS and RHS x=3/2 which is less than sqrt(3).Hence 2 is also sufficient.

So Ans is D

If such examples are rare, it's because single-variable equations almost never appear in GMAT Data Sufficiency algebra questions. You can count on the fingers of two hands the number of such equations that appear in the DS section of the Official Guide and the Official Quant Review combined, which makes it debatable whether there's even any value to learning 'tricks' for guessing in such situations. And despite the minuscule number of such equations in the official guides, looking at Q30 in the DS section of the OG, Statement 1 has no absolute values or even powers, and yet gives two values for n, and Statement 2 does have an even power, yet gives only one value for n. If you were to apply the heuristic 'if there are no absolute values or even exponents, there's one solution', you're going to get this question wrong. It's early in the book as well, so it's not a difficult question.

The GMAT question designers are well aware of the overly simplistic 'tricks' that many prep companies encourage test takers to use, and they design questions to trap people who apply these tricks without understanding the underlying mathematics. For example, many books suggest counting equations and unknowns, and say that you need to have at least as many equations as unknowns to solve. Q123 (the infamous 'stamps question') in the DS section of the OG is one of dozens of examples I could give of official questions designed to trap the test taker who simply counts equations and unknowns.



What the GMAT certainly is *not* is a test of how many prep company tricks you can learn. It would defeat the entire purpose of the test if you could do well at it by learning a few 'tricks' from a prep book. It *is*, at least in part, a test of mathematical ability - not of computational ability, but rather of the ability to reason logically about mathematical concepts. You simply cannot do well on the Quant section of the GMAT without learning some math.

Absolutely. Learn the content. Learn the strategies. Succeed on the GMAT.