What is the value of x? (1) (3x - 2)(2x + 1) = 0 (2) (2/3 - x)(1/2 -x)

Question

What is the value of  x ?

(1)   (3x - 2) (2x + 1) = 0

(2)   (\frac{2}{3} - x) (\frac{1}{2} - x) = 0

Papist · Answer

Statement 1: x=2/3 and x=-1/2 are both solutions. NOT SUFFICIENT.

Statement 2: x=2/3 and x=1/2 are both solutions. NOT SUFFICIENT.

S1+S2: The only solution to both of the equations is x=2/3. SUFFICIENT.

Russ19 · Answer

IanStewart  ,  TestPrepUnlimited , Could you please solve the problem above?

IanStewart · Answer

There is really only one good way to solve a question like this - that's the solution Papist gives above.

If you see an equation like this one:

A*B = 0

then it must be true either that A = 0 or B = 0 (since when you multiply things together, you only ever get zero as a result if you have multiplied by zero somewhere). So if you see an equation like

(3x - 2)(2x + 1) = 0

then it must be true either that 3x - 2 = 0, or that 2x + 1 = 0. By solving these two equations, we arrive at the two possible values of x.

As Papist demonstrates (I won't repeat their solution entirely), each Statement alone gives two possible values of x.

Statement 1: x = 2/3 or x = -1/2
Statement 2: x = 2/3 or x = 1/2

In a "what is the value of x?" type of DS question, when you look at two Statements together, you always want to consider where your solutions from each Statement overlap. Here the solutions overlap in just one value, x = 2/3. So that's the only possible value of x if both Statements are true, and the answer is C.

hiranmay · Answer

What is the value of  x ?

(1)   (3x - 2) (2x + 1) = 0  -->  insuff: x = + 2/3 or x=-1/2 i.e. no definite/single value of x

(2)   (\frac{2}{3} - x) (\frac{1}{2} - x) = 0  -->  insuff: x = + 2/3 or x=+ 1/2 i.e. no definite/single value of x

Combining (1) & (2), we get x=+2/3 i.e. a definite/single value of x
 Answer: C

What is the value of x? (1) (3x - 2)(2x + 1) = 0 (2) (2/3 - x)(1/2 -x)

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