Two non-zero real numbers, a and b, satisfy ab = a - b. Which of the f

Question

Two non-zero numbers, a and b, satisfy ab = a - b. Which of the following is a possible value of  \frac {a}{b} + \frac {b}{a} - ab ?

(A) - 2

(B)  \frac {-1}{2}

(C)  \frac {1}{3}

(D)  \frac {1}{2}

(E) 2

Riya06 · Answer

b/a +a/b-ab
= (a^2+b^2)/ab - ab
= (a^2+b^2)-(a^2b^2)/ab
=(a-b)^2+2ab-(a-b)^2/ab
=2ab/ab
=2

Option E

udaybarar · Answer

Bunuel  can you please verify the solution

fmcgee1 · Answer

The above solution made no sense to me.

Here's one:

\frac{a}{b}  +  \frac{b}{a}  - ab

\frac{a^2 + b^2 - a^2b^2}{ab}

\frac{(a-b)^2 + 2ab - (ab)(ab)}{ab}

\frac{(ab)^2 + 2ab - (ab)(ab)}{ab}

ab + 2 - ab

= 2

VERBAL1 · Answer

Can you please explain how did you derive the underlined portion?

fmcgee1 · Answer

I canceled out the (ab) in each term.

\frac{(ab)^2 + 2ab - (ab)(ab)}{ab}

Since we have (ab) in the denominator, we can cancel that out, and also cancel out the (ab) in each term in the numerator. But we can't cancel it out twice if a term has it twice, we can only cancel it out once.

\frac{(ab)(ab) + 2(ab) - (ab)(ab)}{ab}

So that becomes  (ab) + 2 - (ab)

Does that make sense?

tleknight · Answer

I think about two number that satisfy ab=a-b , so a=1 and b =1/2 
then substitute into question

answer is 2, E

MathRevolution · Answer

ab = a -b

Squaring both the sides we get,

(ab)^2 = (a - b)^2

=>  a^2b^2 = a^2 + b^2 - 2ab

=>  \frac{a}{b} + \frac{b}{a} - ab: \frac{(a^2 + b^2 - a^2b^2)}{ab}

=>  \frac{a}{b} + \frac{b}{a} - ab: \frac{(a^2 + b^2 -  )}{ab}

=>  \frac{a}{b} + \frac{b}{a} - ab: \frac{2ab}{ab}

=>  \frac{a}{b} + \frac{b}{a} - ab: 2

Answer E

Two non-zero real numbers, a and b, satisfy ab = a - b. Which of the f

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GMAT Problem Solving (PS) Questions

Two non-zero real numbers, a and b, satisfy ab = a - b. Which of the f

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards