3*0.072/0.54 =

Hi Bunuel,
You will have to put the decimal ..

______________
Done. Thank you.

\frac{3*0.072}{0.54} =

(A) 0.04
(B) 0.3
(C) 0.4
(D) 0.8
(El 4.0

Ans: 3*0.072/0.54------> 3*100*72/1000*54-----> 72/54 can be reduced to 4/3
so 3*4/3*1/10----> ans C ie. 0.4

\((3*0.072)/(0.54)\)

\(= (3 * 72 * 0.001)/(54 * 0.01)\)

\(=((3* 18 * 4 )/(18*3))(0.001/0.01)\)

\(=4 * 0.1\)

\(=0.4\)

Answer: (C)

(3*0.072/0.54)*(1000/1000)=3*72/540=72/180=2/5=0.4


C

A solution using powers of 10:

[3 * (0.072)] / 0.54 =
= [3 * ( 72*10^-3)] / 54*10^-2
= 3 * [72*10^(-3+2)] / 54
= 3 * (72*10^-1) / 54
= 3 * (7,2/54)
= 21.6 / 54
= 0.4 ANS C

\(\frac{3*0.072}{0.54} =\) \(\frac{0.072}{0.18}\) \(=\) \(0.40\)

Answer will be (C) 0.4

I love these decimal questions! They are great opportunities to show how time-effective visualizing where the answer is can be over simply grinding your way to the answer. Once we acknowledge that the GMAT is designed to test logic and critical thinking--not our ability to multiply numbers--we can get comfortable with visualizing where an answer should be rather than forcing ourselves to determine exactly what the answer is.

On this particular problem, we can make things easy on ourselves by doing a little rounding. We can round confidently here because the answers are not extremely close to one another, even though it might seem like they are. Once we do that, our translated question becomes:

"What is two times 7% of 3?"

While we usually loath word problems and thus avoid translating backwards, this is a much easier and, most importantly, more intuitive phrasing of the original question. As with any occasion whereby we take a percent of something, we can simply multiply the raw numbers and back the decimal out two places:

7*3 = 21

Then, we simply double 21 to get 42 and move the decimal two places to get 0.42, and...voila!

0.42 is closest to answer choice (C), 0.4.

While I emphatically encourage my students to write every thought they think and every step they take down on paper/yellow grid, it's awfully nice to be able to confidently "think" your way through a problem without making any physical effort to solve the problem. These "mind's eye only" questions are perfect opportunities to slide back to the optimal timing peak (about 2 minutes per quant question), or to slide ahead without sacrificing accuracy.

We can convert the decimals in the given expression to fractions. So, we have:

[(3) x (72/1000)]/(54/100)

(3) x (72/1000) x (100/54)

(3) x (12/10) x (1/9)

(1) x (6/5) x (1/3) = 6/15 = 2/5 = 0.4

Alternate solution:

(3 x 0.072)/0.54

0.216/0.54

216/540

24/60

2/5, or 0.4

Answer: C

\(\frac{3*0.072}{0.54} = \frac{3*72}{540}= \frac{3*3*3*2*2*2}{2*5*3*3*3*2} = \frac{2}{5} = .4\)

IMO C