At company X, do at least 40 percent of the workers over the age of 40

Question

At company X, do at least 40 percent of the workers over the age of 40 years have 401(k) accounts?

(1) At company X, 16 percent of the workers age 40 years and younger have 401(k) accounts and 29 percent of all workers at the company have 401(k) accounts.
(2) At company X, there are more workers age 40 years of age and younger than workers over the age of 40.

Tulkin987 · Answer

(1) tells us that  the percent of workers over the age of 40 years who have 401k account  = 29%-13% = 16%.
Since, answer is definately NO, sufficient.
(2) according to the given info, the distribution might be   45 to 55   or   35 to 65  . Hence, not sufficient.

Answer: A

viv007 · Answer

SIMPLY 
one can see that ques stem says do at least 40% workers have this account or not?

ST.1 in second part of statement it is clearly saying 29% of all worker have this account that means clearly 40% will not have .
so answer is NO

st.2 no information about percentage or distribution so clearly insufficient.

ans A.

chetna14 · Answer

To answer the question, we need to know the  number of workers over the age of 40 .

number of workers over the age of 40 = X
number of workers age 40 years and younger = Y
total number of workers = X+ Y

Lets say X + Y = 100

From Statement 1:

Total 29 workers have 401(k) accounts

16% of Y have 401(k)

Y is unknown  hence Not sufficient

From Statement 2:

Y > X

Not sufficient  to answer the Question.

Statement 1 + Statement 2

from Statement 2,

Y > X

=> Y > 50 as ( X + Y = 100)

From statement 1

as no of workers will always be integer,  \frac{16}{100} * Y must be integer

=> Y is multiple of 25,

combining St 1 and St 2

=> Y = 75

=>no of workers less than or equal to 40 years of age having 401(k) =  \frac{4}{25} * 75  = 12

=> 29-12 = 17 of 25 workers greater than 40 years of age have 401(k)

=> more than 40% of workers greater than 40 years of age have 401(k)

IMO C

amanvermagmat · Answer

Let there be 'x' workers less than equal to 40 years of age, and let there be 'y' workers greater than 40 years of age. We need to know whether 0.4y or above have those accounts or not.

(1) So 16% of x, and 29% of (x+y) have those accounts. But what is the ratio of x:y? Without knowing the answer to that question, we cannot conclude the percentage of y that have those accounts. Not sufficient.

(2) Not sufficient clearly.

Combining the statements, we know that 16% of x and 29% of (x+y) have those accounts and x > y or x/y > 1 given. 
Let there be a% of those y workers having these accounts. Using weighted average alligation method, ratio of x and y must be (a-29)/(29-16) or (a-29)/13. Since this ratio has to be greater than 1 (given), we can take:
(a-29)/13 > 1 or a-29 > 13 or a > 42.

So the % of y workers who have these accounts must be greater than 42%, which is greater than 40% definitely. sufficient.

Hence  C answer

adityan92 · Answer

IMO C is the answer

STATEMENT 1 : NS

All we know is 13% of overall employees above the age of 40 have 401k but we don't know if it is 40% of the total employees aged 40 and above.

Statement 2 : NS

Clearly in sufficient.

Combining both, we know that majority of the company's employees are 40 and younger, hence, the answer to the question is No.

Sufficient.

bumpbot · Answer

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At company X, do at least 40 percent of the workers over the age of 40

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At company X, do at least 40 percent of the workers over the age of 40

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