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a lethal accident

by sanju09 » Mon Apr 19, 2010 4:02 am
Diana's driver is taking small pegs of liquor one after the other while waiting for her to come out of the hotel room. The probability that Diana's driver will meet a lethal accident after taking only one small peg of liquor is 1/8, which increases by 20 percent after every subsequent peg he takes. What is the minimum number of small pegs that Diana's driver must take so as to certainly meet a lethal accident?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13





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Last edited by sanju09 on Thu Apr 22, 2010 12:54 am, edited 1 time in total.
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by liferocks » Mon Apr 19, 2010 4:33 am
IMO ans is 12

if x is the probability of accident after any drink then x[6/5] is the probability after the next drink.If driver must take n drinks so as to certainly meet a lethal accident(i.e probability is approx 1) we will get
[1/8][6/5]^n=1
now [6/5]^4 is approximately 2 ..hence [6/5]^4*[6/5]^4*[6/5]^4 will be approximately 8..so ans should be 12
I didn't calculated the exact value.can you please confirm the OA.
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by outreach » Mon Apr 19, 2010 9:57 am
1/8 is probability
let divide a line into 8 parts. the probability will increase when 4 part is crossed or it is at 4 part

20 percent of 1/8 is 1/40

a) 1/8+7/40=12/40=0.3
(B) 1/8+8/40=13/40 =.325
(C) 1/8+9/40=14/40 =.35
(D) 1/8+10/40=15/40=.375
(E) 1/8+11/40=16/40=.412


E
sanju09 wrote:Diana's driver is taking small pegs of liquor one after the other while waiting for her to come out of the hotel room. The probability that Diana's driver will meet a lethal accident after taking only one small peg of liquor is 1/8, which increases by 20 percent after every subsequent peg he takes. What is the minimum number of small pegs that Diana's driver must take so as to certainly meet a lethal accident?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
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by pradeepkaushal9518 » Mon Apr 19, 2010 10:26 am
why 4 part and how after 4 parts the accident will be certain? plz explain
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by eaakbari » Mon Apr 19, 2010 10:30 am
liferocks wrote:IMO ans is 12

if x is the probability of accident after any drink then x[6/5] is the probability after the next drink.If driver must take n drinks so as to certainly meet a lethal accident(i.e probability is approx 1) we will get
[1/8][6/5]^n=1
now [6/5]^4 is approximately 2 ..hence [6/5]^4*[6/5]^4*[6/5]^4 will be approximately 8..so ans should be 12
I didn't calculated the exact value.can you please confirm the OA.
I like this approach but I dont know how you would evaluate the bold part easily. What if the numbers were more complex and you didnt know that (6/5)^4 approximates to 2
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by liferocks » Mon Apr 19, 2010 10:47 am
I agree ..here the calculation is somewhat easy because 6/5 is 1.2 and its square is 1.44 now square of 14 is 196 so we can easily conclude that [6/5]^4 will be approximately 2
if the calculation was more complex I think i would have used the options to get the solution.Let others put there methods.we can get some better approach.
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by outreach » Mon Apr 19, 2010 10:56 am
what i meant is greater than 50% is needed for greater probability
sanju..whats the OA? can u share a better approach to solve the problem
pradeepkaushal9518 wrote:why 4 part and how after 4 parts the accident will be certain? plz explain
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by sanju09 » Tue Apr 20, 2010 1:25 am
liferoclsks' approach is same as mine, and it's the quickest one to my knowledge
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by pradeepkaushal9518 » Tue Apr 20, 2010 1:59 am
i m not satisfied why 50% chances when certainity means 100%. any expert can help
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by sanju09 » Tue Apr 20, 2010 2:24 am
pradeepkaushal9518 wrote:i m not satisfied why 50% chances when certainity means 100%. any expert can help
Even I am not sure of what is given in that post, may be I am not putting extra thoughts to the amazing maze.

We need n number of pegs to guarantee

1/8 × (1.2)^n ≥ 1

Or (1.2)^n ≥ 8

liferocks' approximation that 1.4^2 is close to 2 may be extended to believe that 1.44^2 is just more than 2,

or 1.2^4 is just more than 2

or (1.2^4)^3 is just more than 2^3

or 1.2^12 is just more than 8

hence [spoiler]E, (we round down because n=1 gives us the probability of the 2nd drink being lethal, not the first): Stuart Kovinsky[/spoiler]
Last edited by sanju09 on Thu Apr 22, 2010 12:57 am, edited 1 time in total.
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by yeahdisk » Tue Apr 20, 2010 6:19 am
The answer is 13 drinks total

Drink1 = 1/8
Drink2 = 1.2/8
Drink3 = 1.44/8
Drink4 = 1.73/8
Drink5 = 2/8
Drink6 = 2.48/8
Drink7 = 2.99/8
Drink8 = 3.58/8
Drink9 = 4.30/8
Drink10 = 5.16/8
Drink11 = 6.19/8
Drink12 = 7.43/8
Drink13 = 8.9/8

Where is this question from?
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by pradeepkaushal9518 » Tue Apr 20, 2010 8:48 am
This question was in jumbo test
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by Stuart@KaplanGMAT » Tue Apr 20, 2010 11:34 am
sanju09 wrote:Diana's driver is taking small pegs of liquor one after the other while waiting for her to come out of the hotel room. The probability that Diana's driver will meet a lethal accident after taking only one small peg of liquor is 1/8, which increases by 20 percent after every subsequent peg he takes. What is the minimum number of small pegs that Diana's driver must take so as to certainly meet a lethal accident?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
This is a very un-GMAT question, since the only way to answer it is to do complex calculations - that's a scenario that will never occur on the actual GMAT.

As noted, we can solve with the formula:

(.125)*(1.2)^n = 1,

and then round down to the next integer (we round down because n=1 gives us the probability of the 2nd drink being lethal, not the first), but there's no shortcut. In real life we'd simply plug into a calculator, something we're never expected to do on the GMAT.

I'd be wary of this source in the future.
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by sanju09 » Wed Apr 21, 2010 2:32 am
pradeepkaushal9518 wrote:This question was in jumbo test
[spoiler]I doubt. I haven't published it anywhere other than this site as yet.[/spoiler]
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by sanju09 » Wed Apr 21, 2010 2:39 am
Stuart Kovinsky wrote:
sanju09 wrote:Diana's driver is taking small pegs of liquor one after the other while waiting for her to come out of the hotel room. The probability that Diana's driver will meet a lethal accident after taking only one small peg of liquor is 1/8, which increases by 20 percent after every subsequent peg he takes. What is the minimum number of small pegs that Diana's driver must take so as to certainly meet a lethal accident?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
This is a very un-GMAT question, since the only way to answer it is to do complex calculations - that's a scenario that will never occur on the actual GMAT.

As noted, we can solve with the formula:

(.125)*(1.2)^n = 1,

and then round down to the next integer (we round down because n=1 gives us the probability of the 2nd drink being lethal, not the first), but there's no shortcut. In real life we'd simply plug into a calculator, something we're never expected to do on the GMAT.

I'd be wary of this source in the future.
GMAT has witnessed more complicated "approximations and deductions based" question situations than this one. I don't think anybody should be wary of this source in the future just because of missing a calculator here. The first responder has already answered the question correctly with effective explanation to support his "2-minute without calculator" claim.
The mind is everything. What you think you become. -Lord Buddha



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