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Consider ab = c, where a > 0, b > 0, and c is a positive constant. If

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Bunuel
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Consider ab = c, where a > 0, b > 0, and c is a positive constant. If [#permalink] New post   23 Apr 2018, 23:57
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Consider ab = c, where a > 0, b > 0, and c is a positive constant. If b increases by 50%, then what percent change in a should occur, so that the equation remains true?

(A) 25% decrease
(B) 33 1/3% decrease
(C) 25% increase
(D) 50% increase
(E) 66 2/3% increase
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Consider ab = c, where a > 0, b > 0, and c is a positive constant. If [#permalink] New post   14 May 2018, 20:19
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Bunuel wrote:
Consider ab = c, where a > 0, b > 0, and c is a positive constant. If b increases by 50%, then what percent change in a should occur, so that the equation remains true?

(A) 25% decrease
(B) 33 1/3% decrease
(C) 25% increase
(D) 50% increase
(E) 66 2/3% increase

Assign values
The integers 120 and 60 often work well for percent increase and decrease problems.

\(a = 6\)
\(b = 10\)
\(c = 60\)
\((a*b)= c\)
\((6*10) = 60\)

\(b\) increases by 50%:
\(b_2=10*1.5=15\)
\(c=60\) is constant

What must \(a\) become?
\(a_2*b_2=c\)
\(a_2*15=60\)
\(a_2=4\)

Percent decrease? \(\frac{New-Old}{Old}*100\)
Percent decrease:\((\frac{6-4}{6})=\frac{2}{6}=\\
(\frac{1}{3}*100)=(.33*100)=33\frac{1}{3}\) %

Answer B

Inverse proportion: flip the fraction
If the product of two variables is constant, percent increase and percent decrease are inversely proportional.

1) Find the fraction for the percent change of the factor (\(b\)) that increases:
50% increase = \(1.5=1\frac{1}{2}=\frac{3}{2}\)
2) Flip that fraction. \(\frac{3}{2}\)=>\(\frac{2}{3}\)
3) subtract from 1. That's the other factor's percent decrease: \(1 - \frac{2}{3}=\frac{1}{3}*100=33\frac{1}{3}\)%
Or, \(a\) is now \(\frac{2}{3}\) of what it was, which is a 33.3% decrease

Answer B
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Re: Consider ab = c, where a > 0, b > 0, and c is a positive constant. If [#permalink] New post   24 Apr 2018, 00:30
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Bunuel wrote:
Consider ab = c, where a > 0, b > 0, and c is a positive constant. If b increases by 50%, then what percent change in a should occur, so that the equation remains true?

(A) 25% decrease
(B) 33 1/3% decrease
(C) 25% increase
(D) 50% increase
(E) 66 2/3% increase


We'll write out what we're told as expressions so we understand what our given data is.
This is a Precise approach.

Saying that b increases by 50% is like saying that it is multiplied by 1.5.
So, we need to divide a by 1.5 so that their ratio remains constant.
That is, we need to multiply it by 1/1.5 = 2/3. This is the same as decreasing it by 33 1/3%.

(B) is our answer.
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Consider ab = c, where a > 0, b > 0, and c is a positive constant. If [#permalink] New post   Updated on: 24 Apr 2018, 00:32
Bunuel wrote:
Consider ab = c, where a > 0, b > 0, and c is a positive constant. If b increases by 50%, then what percent change in a should occur, so that the equation remains true?

(A) 25% decrease
(B) 33 1/3% decrease
(C) 25% increase
(D) 50% increase
(E) 66 2/3% increase


\((a*x)*(1.5*b)=1*c\)
\(1.5*x=1\)
\(x=\frac{2}{3}\) --> \(33\frac{1}{3}\)% decrease from \(1\)(or \(100\)%)

Answer: B

Originally posted by Tulkin987 on 24 Apr 2018, 00:31.
Last edited by Tulkin987 on 24 Apr 2018, 00:32, edited 1 time in total.
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Re: Consider ab = c, where a > 0, b > 0, and c is a positive constant. If [#permalink] New post   24 Apr 2018, 00:31
Option B
ab = c, where a > 0, b > 0, and c is a positive constant.

After increase of "b" by 50%, the new value of "b" = "1.5b"
To compensate the change in "b", the new value of "a"= a/1.5=a*2/3
Therefore change in "a" = a=2/3a= 1/3a =33 1/3 %
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Re: Consider ab = c, where a > 0, b > 0, and c is a positive constant. If [#permalink] New post   11 May 2018, 05:00
Ab=c
If b increase by 50 percent then b becomes (3b/2)

To keep equation same a has to become 2a/3
Means a has to reduce from 100 percent- a
To 2a/3 i.e. 66.66 percent

So change in percent=100-66.66=33.33

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Re: Consider ab = c, where a > 0, b > 0, and c is a positive constant. If [#permalink] New post   14 May 2018, 16:45
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Bunuel wrote:
Consider ab = c, where a > 0, b > 0, and c is a positive constant. If b increases by 50%, then what percent change in a should occur, so that the equation remains true?

(A) 25% decrease
(B) 33 1/3% decrease
(C) 25% increase
(D) 50% increase
(E) 66 2/3% increase



We can let k be a constant such that

(ka)(1.5b) = c

(3/2)k(ab) = c

Since ab = c, so we want:

(3/2)k = 1

k = 2/3

We see that we need to multiply a by 2/3, i.e., decrease a by 1/3 = 33 ⅓% of its value, in order for the equation to remain true..

Answer: B
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Re: Consider ab = c, where a > 0, b > 0, and c is a positive constant. If [#permalink] New post   24 May 2018, 05:49
ab=c
new value of b is 1.5b
new a * 1.5 b =a *b
new a = a*2/3
2/3 => 33.3%
therefore, a should decrease by 33.3%
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Re: Consider ab = c, where a > 0, b > 0, and c is a positive constant. If [#permalink]
24 May 2018, 05:49
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