The average distance between the Sun and a certain planet is approxima

Good question.

I took \(2.3 x 10^{14}\)and rounded down to \(2*10^{14}\), and took \(3.9*10^4\) and rounded up to \(4*10^4\).

Then, I did a unit conversion from Inches to Kilometers: \((2*10^{14} Inches) * (\frac{1 Kilometer}{(4*10^4 Inches)})\)

Canceling out, we get \(\frac{(2*10^{14} Inches)}{(4*10^4 Inches)}*1 Kilometer = 0.5*10^{10} Kilometer\) or \(5*10^9 Kilometers\)

Since we rounded to begin with, we have to look for the solution that is both closest to our answer AND makes the most sense. In this case, the answer is

1 km/3.9 * 10^4 inches = X km /2.3 * 10^14 inches

cross multiply

X = 2.3 * 10^4/ 3.9 * 10^4

now we have to approximate

2.3 * 10 * 10^9 / 4

therefore 23*10^9/4 = 5.6 * 10^9 so which is close to answer B 5.9 * 10^9

Bro Bunuel, I wonder who you are and BB also declared you as the mystery man.. but you are doing an awesome job out here! thank you for all your help.
My Question is

what if 6.1 x 10^9 is also one of the answer choices? what will your approach be in this case?

I wouldn't expect such option to be thrown by the GMAC, but in this case the answer still would be the same:

\(\frac{2.3*10^{14}}{3.9*10^4}={\frac{23*10^{13}}{3.9*10^4}}={\frac{23}{3.9}*10^9}\).

Now, since \(\frac{23}{3.9}\) is less than 6 (3.9*6=23.4), then 5.9 x 10^9 would be the closest answer choice than 6.1 x 10^9.

Hope it's clear.

This problem is a unit conversion with an added twist of scientific notation. We need to convert 2.3 x 10^14 inches to KILOMETERS. We are given that 1 kilometer is approximately 3.9 X 10^4 inches. We also should recognize that we are being asked which of the following is CLOSEST to the average distance between the Sun and the planet, in Kilometers. Because we are being asked for an approximation, we can use some estimation here.

To convert 2.3 x 10^14 inches to kilometers, we need to multiply 2.3 x 10^14 inches by the ratio of:

1 km/(3.9 x 10^4 inches)

However, before doing this multiplication, it will make things easier to clean up each scientific notation expression. Let’s start with 2.3 x 10^14 inches.

2.3 x 10^14 inches

is equivalent to

23 x 10^13 inches

Notice that because we turn 2.3 into 23, or move the decimal one place to the right, we have to then turn 10^14 into 10^13, or move the decimal one place to the LEFT to “counterbalance” the fact that we’ve moved the decimal one place to the right for 2.3.

Next we can adjust 3.9 x 10^4 inches. However, we can simply round this value up to 4 x 10^4 inches.

Since we’ve rounded 3.9 up to 4, let’s round 23 up to 24 also. That is, we are converting 24 x 10^13 inches into kilometers given that 1 km is approximately 4 x 10^4 inches:

(24 x 10^13 inches) x 1 km/(4 x 10^4 inches)

(24 x 10^13)/(4 x 10^4) km

We can break this work up into two separate calculations:

1) 24/4 = 6

2) 10^13/10^4 = 10^9

Thus, our answer is about 6 x 10^9 km.

We see that the closest answer is B.

Hi All,

Here, we’re told that the distance between the Sun and a planet is 2.3 x 10^14 INCHES. We’re asked which answer is closest to that distance in KILOMETERS. This is just a ‘unit conversion’ question (and the prompt tells us that 1 km = 3.9 x 10^4 inches), so we just have to keep track of the decimal points and the ‘powers of 10’…

Since 2.3 is less than 3.9, we can make the division a little easier to “look at” by ‘rewriting’ the first piece of information by distributing one of the 10s. This gives us:

23 x 10^13 inches

Now, when we divide this by 3.9 x 10^4, we can think in terms of how many times 3.9 divides into 23. Rounding 3.9 “up” to 4, we can see that it’s a little less than 6 times. Looking at the answer choices, we can clearly see that 5.9 is the best match. The last step is to divide 10^13 by 10^4 – and that’s fairly easy: we “subtract” the exponents – and that gives us 10^9.

Final Answer:

GMAT Assassins aren’t born, they’re made,
Rich

Hi, what I ended up doing was \(\frac{23*10^{13}}{39*10^{3}}\) which gave me \({{\frac{23}{39}}*10^{10}}\) so I immediately chose C without calculating the fraction, because I thought it is an approximation problem so as long as the power is correct, the other number can be a bit off. I guess I am asking how to avoid making such errors? While I understand how this works for the most part, how do I think in a way so as to approximate the 3.9 to 4 in the denominator but not do the same to approximate 2.3 to 2 for the numerator?

Hi spacedoutinspace,

Your approach was fine - but you chose to 'stop working' at the wrong spot (re: when you saw the exponent). You don't have to do too much math to determine that 23/39 is a little more than 1/2... meaning that the calculation that you were working on is a little more than 0.5 x 10^10.

However, Answer C is 1.6 x 10^10... meaning that answer C is 3 TIMES the value of your calculation (as 1.6 is approximately triple 0.5). Regardless of how you might think about 'approximating' values, whatever rounding you might do cannot justify choosing an answer that is so much bigger than the calculation you've performed - so Answer C cannot possibly be correct. Based on how the answers are written, a smaller exponent would be necessary and with just a little more work, you would have the correct answer.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: Rich.C@empowergmat.com
www.empowergmat.com