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# If 3/(10^4) = x%, then x =

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Manager
Status: Persevere
Joined: 08 Jan 2016
Posts: 123
Location: Hong Kong
GMAT 1: 750 Q50 V41
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If 3/(10^4) = x%, then x = [#permalink]

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27 May 2016, 04:02
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Difficulty:

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Question Stats:

63% (00:27) correct 37% (00:26) wrong based on 375 sessions

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If $$\frac{3}{10^4}$$ = x%, then x =

(A) 0.3
(B) 0.03
(C) 0.003
(D) 0.0003
(E) 0.00003
[Reveal] Spoiler: OA
Senior Manager
Joined: 18 Jan 2010
Posts: 257
Re: If 3/(10^4) = x%, then x = [#permalink]

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27 May 2016, 04:35
nalinnair wrote:
If $$\frac{3}{10^4}$$ = x%, then x =

(A) 0.3
(B) 0.03
(C) 0.003
(D) 0.0003
(E) 0.00003

$$\frac{3}{10^4}$$ = x%

$$\frac{x}{100}$$ = $$\frac{3}{10000}$$

x = $$\frac{3}{100}$$ = 0.03

SVP
Joined: 11 Sep 2015
Posts: 1999
Re: If 3/(10^4) = x%, then x = [#permalink]

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30 Nov 2016, 12:52
Expert's post
Top Contributor
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nalinnair wrote:
If $$\frac{3}{10^4}$$ = x%, then x =

(A) 0.3
(B) 0.03
(C) 0.003
(D) 0.0003
(E) 0.00003

Key Concepts:
#1) We can create equivalent fractions by multiplying or dividing numerator and denominator by the same value.
#2) p/100 = p%. For example, 19/100 = 19%

$$\frac{3}{10^4}$$ = $$\frac{3}{10000}$$
Divide numerator and denominator by 100 to get: = $$\frac{0.03}{100}$$
= 0.03%

[Reveal] Spoiler:
B

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Manager
Joined: 03 Oct 2013
Posts: 84
Re: If 3/(10^4) = x%, then x = [#permalink]

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30 Nov 2016, 13:07
3/(10^4) = x/100....Solve for x
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P.S. Don't forget to give Kudos on the left if you like the solution

Intern
Joined: 17 Aug 2016
Posts: 7
Re: If 3/(10^4) = x%, then x = [#permalink]

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12 Dec 2016, 14:31
Guys, I'm really confused and here is the origin of my confusion

OG Thought:

X%= (x/100) or 19%= (19/100)

My thought:

X%= (x/ 100) * 100 or 19%= (19/100) * 100 or 19%= .19 * 100

or otherwords, 19/100 doesn't equal 19%, but rather .19. Only when you multiply .19 by 100 does it equal 19%

I swear I'm not trying to be stubborn, maybe my definitional perspective of the question statement if off

Math Expert
Joined: 02 Sep 2009
Posts: 43358
Re: If 3/(10^4) = x%, then x = [#permalink]

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13 Dec 2016, 00:51
Expert's post
1
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BOOKMARKED
SonofaSaracen wrote:
Guys, I'm really confused and here is the origin of my confusion

OG Thought:

X%= (x/100) or 19%= (19/100)

My thought:

X%= (x/ 100) * 100 or 19%= (19/100) * 100 or 19%= .19 * 100

or otherwords, 19/100 doesn't equal 19%, but rather .19. Only when you multiply .19 by 100 does it equal 19%

I swear I'm not trying to be stubborn, maybe my definitional perspective of the question statement if off

OG is right.

A percentage is a way of expressing a number as a fraction of 100 (per cent meaning "per hundred"). It is often denoted using the percent sign, "%", or the abbreviation "pct". Since a percent is an amount per 100, percents can be represented as fractions with a denominator of 100. For example, 25% means 25 per 100, 25/100 and 350% means 350 per 100, 350/100.

Check Percents chapter here: math-number-theory-88376.html
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Manager
Joined: 02 Nov 2013
Posts: 95
Location: India
Re: If 3/(10^4) = x%, then x = [#permalink]

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13 Dec 2016, 01:50
By definition itself, percentage is nothing but amount in each hundred. i.e. 20% mean 20/100 = 0.2
In the equation,
3/10^4 = 0.0003 which is X%. Let's back calculate as I mentioned. What value of X will the equation will give 0.0003.

X% = 0.0003, i.e. X = 0.03. Answer is B.
Manager
Joined: 21 Jun 2017
Posts: 77
Re: If 3/(10^4) = x%, then x = [#permalink]

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23 Aug 2017, 17:13
The key concept for this question is direction of moving decimal places.

Take the numerator 3. , and move the decimal place four places to the left, for you are dividing by 10^4, meaning the numerator will become small by 4 places, which is the number in the exponent.

After moving the decimal four places left, you get 3.0 ---> 0.0003

Now, with 0.0003 you move the decimal two places to the right, because you are multiplying by 100 (i.e. the percent) Since you are multiplying a decimal by a whole number, the value of the decimal becomes larger, hence, 0.0003 x 100 --- move decimal two to right ---> 0.03 = x

Therefore, the answer is (B) 0.03
VP
Joined: 22 May 2016
Posts: 1260
If 3/(10^4) = x%, then x = [#permalink]

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23 Aug 2017, 17:41
nalinnair wrote:
If $$\frac{3}{10^4}$$ = x%, then x =

(A) 0.3
(B) 0.03
(C) 0.003
(D) 0.0003
(E) 0.00003

$$\frac{3}{10^4}$$ = $$\frac{x}{100}$$

$$3 * 10^2 = x * 10^4$$

$$\frac{3 * 10^2}{10^4} = x$$

$$3 * (10^{2-4}) = x$$

$$3 * 10^{-2} = x$$

$$.03 = x$$

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If 3/(10^4) = x%, then x =   [#permalink] 23 Aug 2017, 17:41
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