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Math Expert V
Joined: 02 Sep 2009
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If 18 is 15 percent of 30 percent of a certain number, what  [#permalink]

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

If 18 is 15 percent of 30 percent of a certain number, what is the number?

(A) 9
(B) 36
(C) 40
(D) 81
(E) 400

Problem Solving
Question: 43
Category: Arithmetic Percents
Page: 67
Difficulty: 600

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Math Expert V
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Re: If 18 is 15 percent of 30 percent of a certain number, what  [#permalink]

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SOLUTION

If 18 is 15 percent of 30 percent of a certain number, what is the number?

(A) 9
(B) 36
(C) 40
(D) 81
(E) 400

Given that $$18=0.15(0.3x)$$. Solving gives $$x=400$$.

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Re: If 18 is 15 percent of 30 percent of a certain number, what  [#permalink]

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30% of 100 = 30
15% of 30 = 4.5

If its 4.5 then required answer is 100 so when its 18 (4.5*4) required answer would be 400(100*4).

ANSWER - (E) - 400
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GMAT 1: 590 Q45 V27 Re: If 18 is 15 percent of 30 percent of a certain number, what  [#permalink]

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Let the certain number be x.

=> (15/100)*(30/100)*x = 18;
450x=18*10000;
45x = 18000;
x=18000/45
=> x=400;

Ans is (E).
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Re: If 18 is 15 percent of 30 percent of a certain number, what  [#permalink]

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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If 18 is 15 percent of 30 percent of a certain number, what is the number?

(A) 9
(B) 36
(C) 40
(D) 81
(E) 400

(15 * 30) / (100 * 100) = 0.045 , So if the number is 100, it will be 4.5. So the number has to be > 100. Hence option E)
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Re: If 18 is 15 percent of 30 percent of a certain number, what  [#permalink]

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If 18 is 15 percent of 30 percent of a certain number, what is the number?

(A) 9
(B) 36
(C) 40
(D) 81
(E) 400

18 is 15 percent of 30 percent of a certain number

Or, $$18 = (15%)(30%)x$$
Or, $$18 = (3/20)(3/10)x$$
Or, $$18 = (9/200)x$$
Or, $$x =(9*2*200)/9=400$$

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Re: If 18 is 15 percent of 30 percent of a certain number, what  [#permalink]

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Answer in 30 seconds by just glancing the answers.

As question states the 15% of 30% of x =18.

A)9 . Less than 18. Not an answer.
B)36 . 30 % is less than 18. Not an answer . Alternatively 1/3 (close to 30%) is 12 < 18. So not an answer
C)40 . 30 % is less than 18. Not an answer . Alternatively 1/3 (close to 30%) is 12 < 18. So not an answer
D)81 . 30 % is less than 18. Not an answer . Alternatively 1/3 (close to 30%) is 27 and 1/6 (close to 15%) 4 < 18. So not an answer
E)400 . E is answer no need to calculation.

Alternatively solution

Start putting the biggest number and get the result in first try 15% of 30% of 400 =18.

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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If 18 is 15 percent of 30 percent of a certain number, what  [#permalink]

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Hi All,

The math involved in this question can be 'set up' (and dealt with) in a variety of ways.

Here, if you're going to take a calculation-based approach, converting the percents to fractions would likely help you speed up (and avoid the last bit of math).

We're told that 18 is 15 percent of 30 percent of a certain number. We're asked for that number.

18 = (.15)(.3)(X)

18 = (3/20)(3/10)(X)

18 = (9/200)(X)

Since 9/200 is a relatively small fraction (it's far less than 10%), we know that 18 is LESS than 10% of X. Based on the given answer choices, there's only one number that is LARGE enough to fit that description....

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Re: If 18 is 15 percent of 30 percent of a certain number, what  [#permalink]

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Solve as question 15% of a number is 18 so

Here we can say that 10% = 12

And 100% = 120

And by the question you can see that this is 30% of the no that we are looking for

So the no is 400 as 120 is 30 % of 400

Hope this helps

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Intern  B
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If 18 is 15 percent of 30 percent of a certain number, what  [#permalink]

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18 = 0.15 * 0.30 * X

Can someone provide me a tip as to how to calculate 18 / 0.045 without a calculator? Bunuel
Math Expert V
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Re: If 18 is 15 percent of 30 percent of a certain number, what  [#permalink]

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Fran94 wrote:
18 = 0.15 * 0.30 * X

Can someone provide me a tip as to how to calculate 18 / 0.045 without a calculator? Bunuel

Hint: notice that 18 = 2*9 = 4*4.5
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Re: If 18 is 15 percent of 30 percent of a certain number, what  [#permalink]

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Answer is Clearly E

let the number is N
N x 0.30 x 0.15 = 18
N = 400
which is E
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Re: If 18 is 15 percent of 30 percent of a certain number, what  [#permalink]

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We need to find a number such that
15 percent of 30 percent of a that number is 18

Let the number be x

0.15*0.3*x = 18
0.045x = 18
x = $$\frac{18}{0.045} = \frac{180 * 100}{45}$$ = 400(Option E)
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Re: If 18 is 15 percent of 30 percent of a certain number, what  [#permalink]

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In the Stem it is asked about 18 = 15 % of 30 % of a number, 15% of a number is 18 means the number should be greater than 100, only answer E having number greater than 100, so answer should be E
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Re: If 18 is 15 percent of 30 percent of a certain number, what  [#permalink]

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nkmungila wrote:
In the Stem it is asked about 18 = 15 % of 30 % of a number, 15% of a number is 18 means the number should be greater than 100, only answer E having number greater than 100, so answer should be E

but you must calculate the answer , if in case the answer choices are above 100 then your method will not work, so my suggestion is although here it is applicable but when there are comparable choices do by actual calculation.
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Re: If 18 is 15 percent of 30 percent of a certain number, what  [#permalink]

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_________________ Re: If 18 is 15 percent of 30 percent of a certain number, what   [#permalink] 04 Feb 2019, 05:50
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