Hello,
For the following:
If [ (0.0015)(10^m) ]/[ (0.03)(10^k) ] = 5(10^7), then m - k =
(A) 9
(B) 8
(C) 7
(D) 6
(E) 5
OA: A
However, I am getting E.
Can you please assist with this?
Thanks,
Sri
To find m-k
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Here's one approach:if (0.0015 x 10^m) / (0.03 x 10^k) = 5 x 10^7, then m - k = ?
a. 9
b. 8
c. 7
d. 6
e. 5
First rewrite the equation as:
(0.0015/0.03) x (10^m)/(10^k) = 5 x 10^7
Simplify to get: (0.0015/0.03) x 10^(m-k) = 5 x 10^7
Aside: A quick way to simplify 0.0015/0.03 is to multiply top and bottom by 10,000 to get 15/300.
Simplify to get 1/20
So, we now have (1/20) x 10^(m-k) = 5 x 10^7
Isolate 10^(m-k) by multiplying both sides by 20 to get:
10^(m-k) = (20)(5) (10^7)
Simplify: 10^(m-k) = (100)(10^7)
Simplify: 10^(m-k) = (10^2)(10^7)
Simplify: 10^(m-k) = 10^9
So, m-k must equal 9
Answer: A
Cheers,
Brent
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Another approach is to assign k a "nice" value.if (0.0015 x 10^m) / (0.03 x 10^k) = 5 x 10^7, then m - k = ?
a. 9
b. 8
c. 7
d. 6
e. 5
Let's see what happens when k = 0
we get: (0.0015 x 10^m) / (0.03 x 10^0) = 5 x 10^7
Simplify: (0.0015 x 10^m) / (0.03 x 1) = 5 x 10^7
Simplify: (0.0015 x 10^m) / (0.03) = 5 x 10^7
Multiply both sides by 0.03 to get: 0.0015 x 10^m = 0.15 x 10^7
Eliminate blue decimals by multiplying both sides by 10,000 to get: 15 x 10^m = 1500 x 10^7
Divide both sides by 15 to get: 1 x 10^m = 100 x 10^7
Rewrite 100 as 10^2: 1 x 10^m = 10^2 x 10^7
Simplify: 10^m = 10^9
So, m = 9
In other words, when k = 0, m = 9
So, m - k = 9 - 0 = [spoiler]9 = A[/spoiler]
Cheers,
Brent
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I used an approach similar to the first approach that you have mentioned, but I must say the second approach is interesting. Might be useful when one is getting stuck with long calculations...Another approach is to assign k a "nice" value.
Let's see what happens when k = 0
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Slightly different approach:gmattesttaker2 wrote:Hello,
For the following:
If [ (0.0015)(10^m) ]/[ (0.03)(10^k) ] = 5(10^7), then m - k =
(A) 9
(B) 8
(C) 7
(D) 6
(E) 5
Let k=2.
(0.0015 * 10^m) / (0.03* 10^2) = 5 * 10^7
Convert the decimals to integers:
(15 * 10^(-4) * 10^m) / 3 = 5 * 10^7
Divide 15 by 3:
5 * 10^(-4) * 10^m = 5 * 10^7
Cancel the 5's and divide each side by 10^(-4):
10^m = 10^11
m = 11.
Thus:
m-k = 11-2 = 9.
The correct answer is A.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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