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If a, b, and C are greater than 0 and a is twice as large as

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jeeteshsingh
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If a, b, and C are greater than 0 and a is twice as large as [#permalink] New post  07 Feb 2010, 12:14
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Need Algebric solution - step by step:

If a, b, and C are greater than 0 and a is twice as large as b percent of c, then in terms of b & c, what is a percent of c?

(A) \(\frac{2bc}{100}\)

(B) \(\frac{2bc^2}{1000}\)

(C) \(\frac{bc^2}{5000}\)

(D) \(\frac{b^2c}{5000}\)

(E) \(\frac{5000b}{c^2}\)
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Bunuel
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Re: If a, b, and C are greater than 0 and a is twice as large as [#permalink] New post  07 Feb 2010, 12:29
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jeeteshsingh wrote:
Need Algebric solution - step by step:

If a, b, and C are greater than 0 and a is twice as large as b percent of c, then in terms of b & c, what is a percent of c?

(A) \(\frac{2bc}{100}\)

(B) \(\frac{2bc^2}{1000}\)

(C) \(\frac{bc^2}{5000}\)

(D) \(\frac{b^2c}{5000}\)

(E) \(\frac{5000b}{c^2}\)

Show SpoilerOA
C



\(a\) is twice as large as \(b\) percent of \(c\) --> \(a=2c\frac{b}{100}\)

What is \(a\) percent of \(c\)? --> \(c\frac{a}{100}=?\)

Multiply first equation by \(\frac{c}{100}\) --> \(a\frac{c}{100}=\frac{c}{100}2c\frac{b}{100}\) --> \(c\frac{a}{100}=\frac{c^2b}{5000}\)

Answer: C.
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Re: If a, b, and C are greater than 0 and a is twice as large as [#permalink] New post  31 Oct 2010, 04:43
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Answer: C
Explanation:
We can use Word Translation to translate the wording into mathematics and Algebra to solve step by step;
\(a\) is twice \(b\) percent of \(c\) ==> \(a = 2 * \frac{b}{100} * c = 2bc/100\) --> eq-1
and
What is \(a\) percent of \(c\)? ==> \(x = \frac{a}{100} * c = a*c*\frac{1}{100}\) --> eq-2
As, we know the value of \(a\) from the first equation eq-1 and after putting that value into eq-2, we get;
\(x = \frac{2bc}{100}*c*\frac{1}{100} = \frac{bc}{50} *c*\frac{1}{100}= \frac{bc^2}{50} * \frac{1}{100} = \frac{bc^2}{5000}\).
Which is option C
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jeeteshsingh
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Re: If a, b, and C are greater than 0 and a is twice as large as [#permalink] New post  07 Feb 2010, 12:49
Bunuel wrote:
jeeteshsingh wrote:
Need Algebric solution - step by step:

If a, b, and C are greater than 0 and a is twice as large as b percent of c, then in terms of b & c, what is a percent of c?

(A) \(\frac{2bc}{100}\)

(B) \(\frac{2bc^2}{1000}\)

(C) \(\frac{bc^2}{5000}\)

(D) \(\frac{b^2c}{5000}\)

(E) \(\frac{5000b}{c^2}\)

Show SpoilerOA
C



\(a\) is twice as large as \(b\) percent of \(c\) --> \(a=2c\frac{b}{100}\)

What is \(a\) percent of \(c\)? --> \(c\frac{a}{100}=?\)

Multiply first equation by \(\frac{c}{100}\) --> \(a\frac{c}{100}=\frac{c}{100}2c\frac{b}{100}\) --> \(c\frac{a}{100}=\frac{c^2b}{5000}\)

Answer: C.


Thanks Bunuel.. I misunderstood the question's last part as What percent is a of c.... and hence I was getting 2b as the answer! :(
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Re: If a, b, and C are greater than 0 and a is twice as large as [#permalink] New post  05 Sep 2012, 11:32
As per me the best way to solve this question is to Pick Smart Numbers & then verify the options
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Re: If a, b, and C are greater than 0 and a is twice as large as [#permalink] New post  16 Sep 2012, 06:43
jeeteshsingh wrote:
Need Algebric solution - step by step:

If a, b, and C are greater than 0 and a is twice as large as b percent of c, then in terms of b & c, what is a percent of c?

(A) \(\frac{2bc}{100}\)

(B) \(\frac{2bc^2}{1000}\)

(C) \(\frac{bc^2}{5000}\)

(D) \(\frac{b^2c}{5000}\)

(E) \(\frac{5000b}{c^2}\)

Show SpoilerOA
C


It is already given that a=2[bc/100] (Twice as large as b%c)...... Let this be equation 1
We need a%c in terms of b. So Multiply equation 1 with c/100 we get- ac/100=2bc^2/10000
Therefore Ans is C
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Re: If a, b, and C are greater than 0 and a is twice as large as [#permalink] New post  07 Dec 2012, 03:45
b percent of c : \(\frac{bc}{100}\)
a is twice as large as b percent of c: a = \(\frac{2bc}{100}=\frac{bc}{50}\)

What is a percent of c?

a percent of c: \(\frac{ac}{100} = \frac{bc}{50}*\frac{c}{100}=\frac{bc^2}{5000}\)

Answer: C
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Re: If a, b, and C are greater than 0 and a is twice as large as [#permalink] New post  10 Jul 2013, 04:37
lets say a = 10 and b=5
so as per given info. 10 = 2*5*c/100
Which will give c = 100

substitute the value of 'b' and 'c' in in answer choices to get value 'a'.
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If a, b, and C are greater than 0 and a is twice as large as [#permalink] New post  21 Aug 2019, 02:28
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jeeteshsingh wrote:
Need Algebric solution - step by step:

If a, b, and C are greater than 0 and a is twice as large as b percent of c, then in terms of b & c, what is a percent of c?

(A) \(\frac{2bc}{100}\)

(B) \(\frac{2bc^2}{1000}\)

(C) \(\frac{bc^2}{5000}\)

(D) \(\frac{b^2c}{5000}\)

(E) \(\frac{5000b}{c^2}\)


Given:
1. a, b, and C are greater than 0
2. a is twice as large as b percent of c

Asked: In terms of b & c, what is a percent of c?

a = 2 b% c = 2bc/100 = bc/50
a% c = ac/100 = (bc/50)*c/100 = bc^2/5000

IMO C
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Re: If a, b, and C are greater than 0 and a is twice as large as [#permalink] New post  13 Sep 2020, 08:56
let c = 100 ; b = 10 so a = 20
a percent of c is 20
plug in values in given options
optioN C matches \(\frac{bc^2}{5000}\)
:)


jeeteshsingh wrote:
Need Algebric solution - step by step:

If a, b, and C are greater than 0 and a is twice as large as b percent of c, then in terms of b & c, what is a percent of c?

(A) \(\frac{2bc}{100}\)

(B) \(\frac{2bc^2}{1000}\)

(C) \(\frac{bc^2}{5000}\)

(D) \(\frac{b^2c}{5000}\)

(E) \(\frac{5000b}{c^2}\)
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Re: If a, b, and C are greater than 0 and a is twice as large as [#permalink] New post  13 Sep 2020, 09:48
If a, b, and c are greater than 0 and a is twice as large as b percent of c, then in terms of b & c, what is a percent of c?

(A) \(\frac{2bc}{100}\)

(B) \(\frac{2bc^2}{1000}\)

(C) \(\frac{bc^2}{5000}\) --> correct: a is twice as large as b% of c i.e. a= 2*b%*c=\(2*\frac{b}{100}*c=\frac{2bc}{100}\), now a% of c =\(\frac{a}{100}*c=a*\frac{c}{100}=\frac{2bc}{100}*\frac{c}{100} =\frac{bc}{50}*\frac{c}{100}= \frac{bc^2}{5000}\)

(D) \(\frac{b^2c}{5000}\)

(E) \(\frac{5000b}{c^2}\)
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Re: If a, b, and C are greater than 0 and a is twice as large as [#permalink]
13 Sep 2020, 09:48
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