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# Jane gave Karen a 5 m head start in a 100 race and Jane was

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Director
Joined: 07 Aug 2011
Posts: 578
GMAT 1: 630 Q49 V27
Re: Jane gave Karen a 5 m head start in a 100 race and Jane was [#permalink]

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12 Feb 2015, 09:14
gurpreetsingh wrote:
ratio of distance covered = ratio of their speed in time t

hence $$\frac{95}{99.75} = \frac{vK}{vJ}$$ --1

now Jane is 0.25 meter behind, suppose it overtakes him at x from 100m mark.

again using
ratio of distance covered = ratio of their speed in time t

$$\frac{(x+0.25)}{x} = \frac{vJ}{vK}$$---2

multiply equation 1 and 2
$$\frac{95}{99.75} = \frac{x}{(x+0.25)}$$ => x =5

hence Jane needs to cover x+0.25 = 5.25

Very elegant solution !!
doable in 2minutes .
+1 Kudos
thank you .
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Intern
Joined: 09 Dec 2014
Posts: 7
Concentration: Economics, Finance
GPA: 4
Re: Jane gave Karen a 5 m head start in a 100 race and Jane was [#permalink]

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23 Feb 2015, 01:09
How do you calculate 99.75/4.75 so easily ? I solved the problem quite quickly but got completely stuck in that calculation... Do you have a more straightforward way to solve that than doing the division as in primary school ?
Director
Joined: 07 Aug 2011
Posts: 578
GMAT 1: 630 Q49 V27
Jane gave Karen a 5 m head start in a 100 race and Jane was [#permalink]

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23 Feb 2015, 01:45
Lapetiteflo wrote:
How do you calculate 99.75/4.75 so easily ? I solved the problem quite quickly but got completely stuck in that calculation... Do you have a more straightforward way to solve that than doing the division as in primary school ?

Your are missing something , it should be X=95*0.25/4.75 and you do not need to solve all fraction numbers .

0.25 = 1/4
4.75 = 4 3/4

95*1/4* 4/19 = 5.

so 5+0.25 = 5.25 ans.
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Lucky

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7944
Location: Pune, India
Re: Jane gave Karen a 5 m head start in a 100 race and Jane was [#permalink]

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23 Feb 2015, 02:24
Lapetiteflo wrote:
How do you calculate 99.75/4.75 so easily ? I solved the problem quite quickly but got completely stuck in that calculation... Do you have a more straightforward way to solve that than doing the division as in primary school ?

Even if you actually had 99.75/4.75, calculating this is also quite simple.

99.75/4.75 = 9975/475 (get rid of the decimals by multiplying and dividing by 100)

Now, you need to find common factors. Any number ending in 25/50/75/00 will be divisible by 25. Now the question is 9975 is which multiple of 25. Note that if 9975 had another 25, it would have been 10,000 and that is 25*400. So 9975 must be 25*399.
Similarly if 475 had another 25, it would have been 500 and 25*20 = 500. So 25*19 = 475

We get 9975/475 = 399/19 = 21
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Intern
Joined: 22 Jun 2011
Posts: 21
Concentration: Finance, Other
WE: Information Technology (Health Care)
Re: Jane gave Karen a 5 m head start in a 100 race and Jane was [#permalink]

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05 Mar 2015, 07:44
I solved it using easy unitary method and got it right..
Manager
Joined: 06 Jun 2014
Posts: 56
Re: Jane gave Karen a 5 m head start in a 100 race and Jane was [#permalink]

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09 Apr 2015, 14:33
This is what I did, but need to admit it took a while. So i first start to find teh gain of Jane when Karen passes one meter, so I get 99.75/95=1.05. this means that for every meter that Karen goes Jane will have traveled 1.05meter. so now is streight foreward. originaly JAne needs to pass 5 meters to overtake KAren, so JAne will need 5*1.05=5.25 meters.
Intern
Joined: 27 Apr 2015
Posts: 8
Re: Jane gave Karen a 5 m head start in a 100 race and Jane was [#permalink]

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22 May 2015, 08:15
Bunuel wrote:
neoreaves wrote:
Jane gave Karen a 5 m head start in a 100 race and Jane was beaten by 0.25m. In how many meters more would Jane have overtaken Karen?

We are asked: In how many meters more would Jane have overtaken Karen? So I think we are asked to calculate the distance Jane should cover to overtake Karen but all solutions above are calculating the distance Karen should cover. Can you please post answer choices to clear my doubts.

Anyway below is my solution:

Jane covered $$100m-0.25m=99.75m$$ and Karen covered $$100-5=95m$$ (in the same time interval).

Initial distance between them was $$5m$$ and final distance between Jane and Karen was $$0.25m$$. Thus Jane gained $$99.75m-95m=4.75m$$ over Karen in $$99.75m$$, hence Jane is gaining $$1m$$ over Karen in every $$\frac{99.75}{4.75}=21m$$.

Hence, Jane in order to gain remaining $$0.25m$$ over Karen should cover $$21*0.25=5.25m$$.

Bunuel, how would someone go about calculating that 99.75/4.75 = 21 on the test with everything else in 2 min? Is there an easy way to do these decimal divisions?
Math Expert
Joined: 02 Sep 2009
Posts: 43850
Re: Jane gave Karen a 5 m head start in a 100 race and Jane was [#permalink]

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22 May 2015, 08:21
torontoclub15 wrote:
Bunuel wrote:
neoreaves wrote:
Jane gave Karen a 5 m head start in a 100 race and Jane was beaten by 0.25m. In how many meters more would Jane have overtaken Karen?

We are asked: In how many meters more would Jane have overtaken Karen? So I think we are asked to calculate the distance Jane should cover to overtake Karen but all solutions above are calculating the distance Karen should cover. Can you please post answer choices to clear my doubts.

Anyway below is my solution:

Jane covered $$100m-0.25m=99.75m$$ and Karen covered $$100-5=95m$$ (in the same time interval).

Initial distance between them was $$5m$$ and final distance between Jane and Karen was $$0.25m$$. Thus Jane gained $$99.75m-95m=4.75m$$ over Karen in $$99.75m$$, hence Jane is gaining $$1m$$ over Karen in every $$\frac{99.75}{4.75}=21m$$.

Hence, Jane in order to gain remaining $$0.25m$$ over Karen should cover $$21*0.25=5.25m$$.

Bunuel, how would someone go about calculating that 99.75/4.75 = 21 on the test with everything else in 2 min? Is there an easy way to do these decimal divisions?

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Director
Joined: 07 Dec 2014
Posts: 906
Jane gave Karen a 5 m head start in a 100 race and Jane was [#permalink]

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14 Feb 2016, 12:39
J runs 99.75 meters
K runs 95 meters
99.75/95=1.05=21/20
J gains 1 meter on K every 21 meters
J would have gained 1/4 meter and overtaken K in 21/4=5.25 more meters
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Re: Jane gave Karen a 5 m head start in a 100 race and Jane was [#permalink]

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18 Mar 2017, 07:21
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Re: Jane gave Karen a 5 m head start in a 100 race and Jane was   [#permalink] 18 Mar 2017, 07:21

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