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Re: The pharmaceutical division's interest on debt expense is 4 [#permalink]
4
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]
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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]
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]
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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

Regards
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Re: The pharmaceutical division's interest on debt expense is 4 [#permalink]
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