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The pharmaceutical division's interest on debt expense is 4

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The pharmaceutical division's interest on debt expense is 4 [#permalink] New post   10 May 2020, 13:43
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The pharmaceutical division's interest on debt expense is 4 times that of the chemical division. What percent of the chemical division's payroll expense is the pharmaceutical division's payroll expense, rounded to the nearest whole percent?

A. 37

B. 68

C. 137

D. 146

E. 274

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E
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Re: The pharmaceutical division's interest on debt expense is 4 [#permalink] New post   11 May 2020, 07:34
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Let total pharmaceutical division expense = x

Let total chemical division expense = y

It is given that pharmaceutical division's interest on debt expense is 4 times that of the chemical division = 2% of x = 4 * ( 2% of y)

Hence x = 4 * y


hence pharmaceutical payroll expense / chemical payroll expense = \(\frac{(0.26x) }{ (0.38y)}\)

substituting x with 4y we get = \(\frac{(0.26 * 4y) }{ (0.38 * y)}\)

Taking value of y =1 we get = \(\frac{(26 * 4) }{ (38 * 1) }\) = 2.736

Converting this value to percentage = 2.736 * 100 = 273.6

Answer is E
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Re: The pharmaceutical division's interest on debt expense is 4 [#permalink] New post   14 Jan 2021, 12:10
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The pharmaceutical division's interest on debt expense is 4 times that of the chemical division. What percent of the chemical division's payroll expense is the pharmaceutical division's payroll expense, rounded to the nearest whole percent?


#Pharmaceutical division
Cost of interest of debt. : 4X
Total expense : 4Y (Because ratio of interest of debt to total expense is 2 % same as in chemical division.)
Ratio of interest of debt to total expense : 2%.
Ratio of payroll to total expense : 26 % = 0.26 = 26/100
Cost of payroll in Pharmaceutical = 4Y * 26/100

#Chemical division
Cost of interest of debt: X
Total expense : Y
Ratio of interest of debt to total expense : 2%.
Ratio of payroll to total expense : 38 % = 0.38 = 38/100
Cost of payroll in Chemical = Y * 38/100

What we want is
Quote:
What percent of the chemical division's payroll expense is the pharmaceutical division's payroll expense, rounded to the nearest whole percent?


(4Y * 26/100) / (Y * 38/100)
(4Y * 26) / (Y * 38) = (104 * Y) / (38* Y). = 104 / 38 > 2

E is the only option which is over 200 % , so E is the answer.

Answer : E
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Re: The pharmaceutical division's interest on debt expense is 4 [#permalink] New post   10 May 2020, 14:02
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Re: The pharmaceutical division's interest on debt expense is 4 [#permalink] New post   12 Oct 2020, 20:06
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Set the total expense of pharmaceutical expense is p; the total expense of chemical division is c, we have:
Pharmaceutical interest debt = 2%p = 0.02p
Pharmaceutical payroll = 26%p = 0.26p
Chemical interest debt = 2%c = 0.02c
Chemical payroll = 38%c = 0.38c

As pharma interest debt equals 4 times chemical interest debt ==> 0.02p = 4* 0.02c ==> p = 4c

Hence, the payroll of chemical over that of pharma in percentage will be:

0.38c/0.26p = 0.38c / (0.26*4c) = 0.38c/1.04c = 0.365 ==> 37%

Hence, the answer is A
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Re: The pharmaceutical division's interest on debt expense is 4 [#permalink] New post   05 Feb 2021, 21:18
Quote:
What percent of the chemical division's payroll expense is the pharmaceutical division's payroll expense


how to rephrase this sentence in a mathematical expression, I find it quite confused.
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Re: The pharmaceutical division's interest on debt expense is 4 [#permalink] New post   06 Feb 2021, 05:13
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The pharmaceutical division's interest on debt expense is 4 times that of the chemical division

Translation

x=4y

What percent of the chemical division's payroll expense is the pharmaceutical division's payroll expense, rounded to the nearest whole percent?

what = x

percent is 100

what % is \(\frac{x}{100 }\)

of chemical = 0.38%

is means =

pharmaceutical division's payroll expense = 0.26%

\(\frac{x}{100} * 0.38=0.26\)

\(x=\frac{ 0.38}{0.26} * 100 = 68.4\)

we do know that x= 4y

so \(68.4*4 = 273.6\) which is \(\approx 274\)

E is the answer

See more on translation in our quant book

https://gre.myprepclub.com/forum/gre-quant ... tml#p52458

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Re: The pharmaceutical division's interest on debt expense is 4 [#permalink] New post   25 Mar 2024, 23:10
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