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Two employees are hired at the beginning of 2006 at the same

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Two employees are hired at the beginning of 2006 at the same [#permalink] New post   07 Jul 2006, 22:48
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Two employees are hired at the beginning of 2006 at the same starting salary of $62,000 per year. At the end of each calendar year each employee is given a pay rise ranging from 20 to 50%. One employee’s salary is guaranteed not to double the other’s until the beginning of which year?

(A) 2008 (B) 2009 (C) 2010 (D) 2011 (E) 2012



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Re: Two employees are hired at the beginning of 2006 at the same [#permalink] New post   07 Jul 2006, 23:54
B = 2009

In all we need to find until what value of n, A = (1.2/1.5)^n will be greater than 1/2.

At n = 4 A is greater than 1/2. So until three years one employee’s salary is guaranteed not to double that of other.
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Re: Two employees are hired at the beginning of 2006 at the same [#permalink] New post   08 Jul 2006, 23:29
kevincan wrote:
Two employees are hired at the beginning of 2006 at the same starting salary of $62,000 per year. At the end of each calendar year each employee is given a pay rise ranging from 20 to 50%. One employee’s salary is guaranteed not to double the other’s until the beginning of which year?

(A) 2008 (B) 2009 (C) 2010 (D) 2011 (E) 2012


2 [62000 (1.2)^n] = 62000 (1.5)^n
2 (1.2)^n = (1.5)^n
(1.5/1.2)^n = 2
(1.5/1.2)^n = 2
(1.25)^n = 2
n ln 1.25 = ln 2
n (0.09691) = 0.301029996
n = 3.10628372

so the salary of one of the emplyoee will doubled that of the other after 3.11 years. therefore, it is guarantee that one employee’s salary wont double the other’s until the beginning of 2009 (2006+3).

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Re: Two employees are hired at the beginning of 2006 at the same [#permalink] New post   19 Sep 2006, 03:31
Two employees are hired at the beginning of 2006 at the same starting salary of $62,000 per year. At the end of each calendar year each employee is given a pay rise ranging from 20% to 50%. One employee’s salary is guaranteed not to double the other’s until the beginning of which year?

(A) 2008 (B) 2009 (C) 2010 (D) 2011 (E) 2012

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Re: Two employees are hired at the beginning of 2006 at the same [#permalink] New post   19 Sep 2006, 03:55
Hallo kevin,
May be i do not get the question but if the employees get same pay rise then there is no solution
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Re: Two employees are hired at the beginning of 2006 at the same [#permalink] New post   19 Sep 2006, 04:13
I think B is the answer.

At the begining of 2009, the min salary of one can be $107,136 and max salary of another can be $209,250. At the begining of 2010 the salary can be double.
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Re: Two employees are hired at the beginning of 2006 at the same [#permalink] New post   19 Sep 2006, 05:36
Don't understand this question. The question isn't "What year CAN one salary double the other?", the question is "One employee’s salary is guaranteed not to double the other’s until the beginning of which year?" It could go on past the years you listed. I.e. if they get the same pay raises every year?
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Re: Two employees are hired at the beginning of 2006 at the same [#permalink] New post   19 Sep 2006, 05:48
Yeah B it is.

At the end of 2009, if one employee has been getting 20% hikes only and the other has been getting 50% hikes, then the ratio b/w there salaries will be around 1.95. Next year, it exceeds 2.

Used the compound interest formula.
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Re: Two employees are hired at the beginning of 2006 at the same [#permalink] New post   19 Sep 2006, 08:06
C.

By the beginning of 2010, one employee salary (who gets 20% rise) will not be the double to that of the other who gets 50% rise.


Two person, A B
2006 2007 2008 2009
A --> X --> 1.2X --> 1.2X*1.2 --> 1.2X*1.2*1.2 = 1.728X

B --> X --> 1.5X --> 1.5X*1.5 --> 1.5X*X*X = 3.375X

BY end of 2009 the salary of A is not doubled to that of B. so the answer is C. beginning of 2010



kevincan wrote:
Two employees are hired at the beginning of 2006 at the same starting salary of $62,000 per year. At the end of each calendar year each employee is given a pay rise ranging from 20% to 50%. One employee’s salary is guaranteed not to double the other’s until the beginning of which year?

(A) 2008 (B) 2009 (C) 2010 (D) 2011 (E) 2012
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Re: Two employees are hired at the beginning of 2006 at the same [#permalink] New post   19 Sep 2006, 08:14
SunShine wrote:
C.

By the beginning of 2010, one employee salary (who gets 20% rise) will not be the double to that of the other who gets 50% rise.


Two person, A B
2006 2007 2008 2009
A --> X --> 1.2X --> 1.2X*1.2 --> 1.2X*1.2*1.2 = 1.728X

B --> X --> 1.5X --> 1.5X*1.5 --> 1.5X*X*X = 3.375X

BY end of 2009 the salary of A is not doubled to that of B. so the answer is C. beginning of 2010



kevincan wrote:
Two employees are hired at the beginning of 2006 at the same starting salary of $62,000 per year. At the end of each calendar year each employee is given a pay rise ranging from 20% to 50%. One employee’s salary is guaranteed not to double the other’s until the beginning of which year?

(A) 2008 (B) 2009 (C) 2010 (D) 2011 (E) 2012


:beat Thats right ! :oops:
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Re: Two employees are hired at the beginning of 2006 at the same [#permalink] New post   19 Sep 2006, 12:33
I agree (c) 2010 bc only by then is the 20% raise guy getting less than half whent the 50% guy is getting.
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Re: Two employees are hired at the beginning of 2006 at the same [#permalink] New post   19 Sep 2006, 13:16
kevincan wrote:
Two employees are hired at the beginning of 2006 at the same starting salary of $62,000 per year. At the end of each calendar year each employee is given a pay rise ranging from 20% to 50%. One employee’s salary is guaranteed not to double the other’s until the beginning of which year?

(A) 2008 (B) 2009 (C) 2010 (D) 2011 (E) 2012




Answer is B.i.e 2009 since the question is "when one emp's salary is guaranteed NOT to double..."
One emp's salary is guranateed to double the other in 2010.
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Re: Two employees are hired at the beginning of 2006 at the same [#permalink] New post   19 Sep 2006, 13:33
Answer: C. 2010

At the end of 2009 the ratio of the two salary (one getting 20% raise and the other 50%) is 172.8 : 337.xx.

After this point salary doubles.



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