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# For an employee to qualify for early retirement at a certain

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For an employee to qualify for early retirement at a certain [#permalink]

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26 Nov 2012, 00:12
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65% (hard)

Question Stats:

57% (02:40) correct 43% (01:34) wrong based on 129 sessions

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For an employee to qualify for early retirement at a certain company, the sum of the employee’s age and years of service must be at least 70, If Sue was K years old when she was hired by the company, what is the minimum age at which she could possibly qualify for early retirement.

A. K+35

B. 2K+35

C. (70+K)/2

D. (70-K)/2

E. 2(70-K)
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Oct 2013, 03:37, edited 1 time in total.
Added the OA.
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Re: For an employee to qualify for early retirement at a certain [#permalink]

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17 Feb 2016, 20:41
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what a tough one..took me some time to solve.
suppose
k=20
after 10 years of experience:
30 years, 10 experience = 40 - not enoguh
10 more years
40 years, 20 years experience = 60 total - not enough
5 more years
45 years, 25 experience = 70 total.
so at 45 she can retire.

plug in values
A: K+35 = 55. out
B: 2K+35 = 75 - out
C: (70+20)/2 = 45 - hold
D: (70-20)/2 = 25 - out
E: 2(70-20)=100 - OUT.

only C works.
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Re: For an employee to qualify for early retirement at a certain [#permalink]

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08 Mar 2017, 07:42
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Tricky question!!

Lets say sue served for x years to qualify for early retirement.

so sue's age at that time is - k+x

As per the given rule - Age (k+x) + year of service(x) = 70
k+x+x = 70
k+2x = 70
x =$$\frac{(70-k)}{2}$$

But we need sue's age not the minimum number of year of service.
age = k+x = k+$$\frac{(70-k)}{2}$$=$$\frac{(70+k)}{2}$$.
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Re: For an employee to qualify for early retirement [#permalink]

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26 Nov 2012, 03:48
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ritumaheshwari02 wrote:
For an employee to qualify for early retirement at a certain company, the sum of the employee’s age and years of service must be at least 70, If Sue was K years old when she was hired by the company, what is the minimum age at which she could possibly qualify for early retirement.

A. K+35

B. 2K+35

C. (70+K)/2

D. (70-K)/2

E. 2(70-K)

Say Sue was hired when she was already 70 years old (k=70), then she could retire right away, at the age of 70. Now, plug k=70 in the answer choices and see which yields 70. Only C fits.

Answer: C.

Similar questions to practice:
a-certain-company-retirement-plan-has-a-rule-of-109708.html
to-be-eligible-for-retirement-benefits-at-the-omega-53970.html
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Re: For an employee to qualify for early retirement [#permalink]

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26 Nov 2012, 04:59
Thank You Sir... I got it.

Sir please let me know is there any short cut method to slove below problem.

How many different positive factors does the integer 360 have, including 1 and 360 ?
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Re: For an employee to qualify for early retirement [#permalink]

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26 Nov 2012, 05:28
ritumaheshwari02 wrote:
Thank You Sir... I got it.

Sir please let me know is there any short cut method to slove below problem.

How many different positive factors does the integer 360 have, including 1 and 360 ?

360=2^3*3^2*5 --> the number of factor is (3+1)(2+1)(1+1)=24. Check here: math-number-theory-88376.html

Also, please post new questions in separate topics.
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Re: For an employee to qualify for early retirement [#permalink]

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26 Nov 2012, 22:18
This link is really very helpful sir... thanks for this awesome link...
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For an employee to qualify for early retirement at a certain [#permalink]

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17 Feb 2016, 20:57
ritumaheshwari02 wrote:
For an employee to qualify for early retirement at a certain company, the sum of the employee’s age and years of service must be at least 70, If Sue was K years old when she was hired by the company, what is the minimum age at which she could possibly qualify for early retirement.

A. K+35

B. 2K+35

C. (70+K)/2

D. (70-K)/2

E. 2(70-K)

HI,
If we get hang of what is asked, we can easily do the Q..

INFO FROM Q

1) the sum of age and service should be atleast 70
2) Sue was K yrs old when hired..

WHAT has to be found

minimum age when Sue can retire?
what does this mean- it means she retires at exactly when total is 70...
..

SOLUTION

1. Sue's age= k..
so she has to cover remaining period 70-k..

2. in how much time can she cover this= (70-k)/2
WHY?..
because EACH year accounts for TWO years increase, one in AGE and one in SERVICE...

3. so Sue after joining at age of K years can take earliest retirement after (70-k)/2 years..

4. what will be her age then--
k+ (70-k)/2 = (2k+70-k)/2= (70+k)/2..

C
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Re: For an employee to qualify for early retirement at a certain [#permalink]

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Re: For an employee to qualify for early retirement at a certain [#permalink]

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10 Mar 2017, 10:38
ritumaheshwari02 wrote:
For an employee to qualify for early retirement at a certain company, the sum of the employee’s age and years of service must be at least 70, If Sue was K years old when she was hired by the company, what is the minimum age at which she could possibly qualify for early retirement.

A. K+35

B. 2K+35

C. (70+K)/2

D. (70-K)/2

E. 2(70-K)

If we let n = the number of years Sue works at the company that could qualify her for early retirement, then her minimum retirement age is K + n and we see that:

(K + n) + n = 70

Note that n is doubled in the equation; this is due to the fact that for each additional year that she works for the company, her age has one more year, but so does the number of years she has worked for the company.

K + 2n = 70

n = (70 - K)/2

Thus, Sue’s minimum age is:

K + (70 - K)/2 = 2K/2 + (70 - K)/2 = (70 + K)/2

Answer: C
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Re: For an employee to qualify for early retirement at a certain [#permalink]

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10 Mar 2017, 12:00
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Hi Ritumaheshwari02,

This question can be easily solved by using simple logic. The question states that an employee qualifies for early retirement if the sum of the employee’s age and years of service must be at least 70.

To qualify for early retirement

Age of employee now + Years of Service >= 70 ------> 1

Now think about what exactly is Years of Service,

Years of service = Age of the employee now - Age of the employee at the time of Joining -----> 2

Substituting 2 in 1 we get

Age of employee now + Age of employee now - Age of employee at the time of joining >= 70

2 Age of employee now - Age of employee at the time of joining >= 70

We have been given the age of Sue at the time of joining as 'K'

2 Age of employee now - K >= 70

2Age of employee now >= 70 + K -----> Age of employee now > = (70 + K)/2

Hope this helps!

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Re: For an employee to qualify for early retirement at a certain   [#permalink] 10 Mar 2017, 12:00
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