The company employs 150 persons who are 25 years or older: 30% of the

Question

The company employs 150 persons who are 25 years or older: 30% of the employees in the age group25-35, and 63% are in the 35+ age group contribute to the defined benefits plan. . If 52% of all the employees contribute to the plan , how many of them are over 35 years of age?

A. 90
B. 95
C. 100
D. 105
E. 110

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Official Answer

C

A. 90
B. 95
C. 100
D. 105
E. 110

Are You Up For the Challenge: 700 Level Questions

Nidzo · Answer

Let the amount of people over 35 = x

\frac{63}{100}x + \frac{30}{100}(150-x) = 78

\frac{63}{100}x - \frac{30}{100}x + 45 = 78

\frac{33}{100}x = 33

33x = 3300

x = 100

Answer C

zhanbo · Answer

Let x be number of employees over 35 years of age.
So the number of employees in the age group25-35 is (150-x)

0.3*(150-x)+0.63*x=0.52*150=78

0.63x must be an integer; not many integer x between 0 and 150 can satisfy it. 
The most likely number from five options is 100.
Try it out. It is the right x. 
(It turns out there is only one such number.)

So the answer is  (C) .

cjhyou700 · Answer

I am confused when I read the questions.

In the question, we have been told that 150 person who are over 25 years or older and 30% of the employees aged 25-35. Pardon me, but what does 30% of the employees mean? Imo, I simply think 150*0.3. If 30% of the employees aged 25-35, the remaining without a doubt that aged 35+ since 150 person are either 25years or older.

Also, in the end, "If 52% of all the employees contribute to the plan , how many of them are over 35 years of age?" I wrongly interpreted that "In 52% of all the employees, how many of them are over 35 years of age?"

It is really hard to understand the question. If anyone understand my confusions, please guide me. Thank you.

Nidzo · Answer

cjhyou700 seems like it was just a small misunderstanding

The question is not asking how many employees are 35+ years old. It is asking how many employees who are 35+ years old contribute towards this fund. We are told that there are 150 employees. We are also told that there are only people who are 25 years and older who work for the company. No one younger. These 150 employees are grouped into two groups: 1) those between the ages 25-35 , and 2) those 35+ . When the question says, " 30% of the employees in the age group25-35 " the question is not stating that those aged 25-30 make up 30%. Rather, it is telling us that 30% of the 25-30 group contribute to the benefits plan . Same goes for when the question states, " 63% are in the 35+ age group contribute to the defined benefits plan ". That means that 63% of those 35+ contribute to the plan , not 63% of all employees. We are, however, told 52% of all the employees contribute to the plan which means that: 150*0.52 = 78 of all of the employees contribute towards the defined benefits plan. Looking at how I wrote out the equation may help make the above a little clearer: Let the amount of people over 35 = x \frac{63}{100}x + \frac{30}{100}(150-x) = 78 Here I am saying that 63% of the 35+ group pay into the fund, and 30% of the 25-35 group pay into the fund (I write this as 150-x because if there are 150 employees and I subtract the amount of those 35+, I am left with only those in the 25-35 group). The sum of those that contribute to the fund is 52% of all of the 150 employees which is 78. Hope this clears things up for you

cjhyou700 · Answer

Nidzo, thank you for your detailed reply! I completely understand now. I should really practice my SC. The comma between "30%..." and "63%.." totally tricked me. I thought they are independent. That's why I came out 150*0.3. When I read your explanation, I figure out my confusions. Many thanks:))

Kinshook · Answer

Given: The company employs 150 persons who are 25 years or older: 30% of the employees in the age group25-35, and 63% are in the 35+ age group contribute to the defined benefits plan. .

Asked: If 52% of all the employees contribute to the plan , how many of them are over 35 years of age?

Age 25-35  Age 35+  Total  
  Contribute to DBP  30%*x%  63%*y%  52%  
  Don't contribute to DBP  70%*x%  27%*y%  48%  
  Total  x%  100%-x%=y%  100%

y% = 100% - x%
.3x% + .63y% = .3x% + .63(100%-x%) = 52%
63% - .33x% = 52%
x% = 11%/.33 = 1100/33 % = 33.33%

y% = 100% - x% = 66.67% 
Employees over 35 years of age = 150*66.67% = 150*2/3 = 100

IMO C

The company employs 150 persons who are 25 years or older: 30% of the

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	Age 25-35	Age 35+	Total
Contribute to DBP	30%*x%	63%*y%	52%
Don't contribute to DBP	70%*x%	27%*y%	48%
Total	x%	100%-x%=y%	100%

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The company employs 150 persons who are 25 years or older: 30% of the

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