This question wants you to use your basic understanding of the process of simplification when dealing with fractions and fraction division and multiplication in particular.
On GMAT DS questions always try to utilize information and make logical inferences before you move to statements!
In the statements,
analyze if there is an easy kill and you can spot a statement that can be easily proved sufficient or insufficient. Eliminate the corresponding answer choices and move to the next statement.
Some GMAT basics for fraction multiplicationFraction MultiplicationWhen multiplying fractions, multiply the numerators (value of p in a fraction p/q) together, and multiply the denominators (value of q in a fraction p/q) together. This gives you the answer in lowest terms:
1. Multiply the numerators (top numbers) together, and put that result over the denominator (bottom number) of the original fractions.
2.
Reduce (or simplify) the fraction by dividing both the numerator and denominator by their greatest common factor.
Ex: \(\frac{2}{3 }\)* \(\frac{9}{4}\) = \(\frac{18 }{ 12}\) = \(\frac{3}{2}\)
Let’s get to the question now.
So how would a LOGICAL & SMART GMAT aspirant think through this question? GMAT Track of Thought 1What do I have from the Question stem?
abc ≠ 0 and hence we know that none of the fractions on LHS and RHS are equal to 0.
I am asked – Is \(\frac{a}{b / c}\) =\(\frac{ a }{b/c}\) ?
GMAT Tip: Avoid rushing through questions like this and note carefully the Numerator and Denominator.
You are a SMART thinker and this question and questions like this have to be nailed by you avoiding
ALL ERRORS OF FOCUS ! Let me
simplify the LHS first which is (a/b) / c
= \(\frac{a}{b} \)* \(\frac{1}{c }\) = \(\frac{a}{bc}\)
Let me
simplify the RHS now which is a /(b/c)
= a * \(\frac{c}{b} \)= \(\frac{ac}{b}\)
So I am asked is \(\frac{a}{bc} \) = \(\frac{ac}{b }\)?
Cancelling the common terms ‘a’ & ‘b’ from the Numerator and Denominator respectively, I have
Is \(\frac{1}{c }\)= c or
Is \(c^2 \)= 1? (On cross multiplying)From Is \(\frac{a}{b / c}\) = \(\frac{a }{(b/c)}\) ? , I have reduced and simplified the question stem to Is \(c^2\) = 1 ?
It’s a
YES/NO type of DS question and I must have a definite YES or a Definite NO as an answer to this.
I need to know the value of c or \(c^2 \)or any relation between the variables to lead me to it.
GMAT Track of Thought 2Which of the statements is an easy kill?
Scanning the statements quickly, I can see c =1 in statement 2.
That alone is sufficient since it implies \(c^2\) =1 (upon squaring).
This answers my simplified question stem with a definite YES and I can eliminate A,C, E right away!
GMAT Track of Thought 3Now let me look at statement 1.
It says a = 1. I am NOT provided with any value of c and nor can I connect a & c with any relationship from the statement and/or the Q. Stem.
Eliminate Statement 1 and hence option A
Mark answer option B as the correct answer choice for this question.
You can break any complex looking statement with a stepwise approach and simplify it. On doing so you would sometimes be happily surprised on looking at the statements that may provide you with a direct answer in GMAT DS questions.
Hope this post of mine has lent clarity and added value to your learning.
Devmitra Sen
GMAT Mentor _________________
Crackverbal Prep Team
www.crackverbal.com