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# A faulty car odometer proceeds from digit 3 to digit 5, always skippin

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Math Expert
Joined: 02 Sep 2009
Posts: 59587
A faulty car odometer proceeds from digit 3 to digit 5, always skippin  [#permalink]

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24 Mar 2019, 21:28
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1
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Difficulty:

95% (hard)

Question Stats:

21% (02:13) correct 79% (01:59) wrong based on 42 sessions

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A faulty car odometer proceeds from digit 3 to digit 5, always skipping the digit 4, regardless of position. If the odometer now reads 002005, how many miles has the car actually traveled?

(A) 1404
(B) 1462
(C) 1604
(D) 1605
(E) 1804

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A faulty car odometer proceeds from digit 3 to digit 5, always skippin  [#permalink]

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25 Mar 2019, 21:43
5
When the odometer says that it traveled for 5miles then it means that it actually only travelled 4 miles

So +1 added to the odometer with out travelling.

Similarly 4,14,24,34,54,64,74,84,94 -(40-is skipped ) . Here a Total of 9*1 + 10 = 19 miles are added for a hundred
Similarly 400 ,1400 are also skipped - 200 more added

Total extra miles added before 2000 = 19(18) +200 = 342 + 200 = 542
for 2005 , 1 mile is for five miles travelled after 2000 , So Grand Total = 542+1 = 543

miles travelled = 2005-543 = 1462- Option B

If its clear - Kudos Please
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Re: A faulty car odometer proceeds from digit 3 to digit 5, always skippin  [#permalink]

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24 Mar 2019, 22:36
No of times 4 appears in a hundred=20
In 2005, 4 has appeared=20*20=400
Therefore car has actually travelled=2005-400=1605

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Re: A faulty car odometer proceeds from digit 3 to digit 5, always skippin  [#permalink]

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25 Mar 2019, 00:29
Bunuel wrote:
A faulty car odometer proceeds from digit 3 to digit 5, always skipping the digit 4, regardless of position. If the odometer now reads 002005, how many miles has the car actually traveled?

(A) 1404
(B) 1462
(C) 1604
(D) 1605
(E) 1804

I am not sure what concept is this question really checking and is it really relevant to gmat..

my take below
odometer works where in 1 unit position keeps moving with distance and its total gets accumulated over the range
so here suppose inital reading is 000000
so first reading 000001,000002,00003,000005 now meter is skipping after every3rd unit so it skips total 10 times in range from 0-100
given total final reading 002005 ; meter must have skipped 2005/100; 200.5 times
so actual reading 2005-200.5 = ~ 1804
IMO E
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Re: A faulty car odometer proceeds from digit 3 to digit 5, always skippin  [#permalink]

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04 Apr 2019, 23:59
Bunuel wrote:
A faulty car odometer proceeds from digit 3 to digit 5, always skipping the digit 4, regardless of position. If the odometer now reads 002005, how many miles has the car actually traveled?

(A) 1404
(B) 1462
(C) 1604
(D) 1605
(E) 1804

Total miles actually travelled = Odometer reading - No. of times 4 appear between 0000 to 2005

No. of times 4 appear between 0000 to 2005 = No. of times 4 appear between 000 to 999 + No. of times 4 appear between 1000 to 2005

now,

between 000 to 999 , there are 1000 different numbers and each number is a 3 digit number so , in and all there 1000*3 digits = 3000 digits

by symmetry, each digit between 0 to 9 appears equal no. of times so every digit appears 3000/10 no. of times .... hence 4 appears 300 no. of times

similary 4 appears 300 no. of times between 1000 to 1999
and 4 appears 1 no. of times between 2000 to 2005

so in an all 4 appears 300+300+1 = 601 no. of times
so, Total miles actually travelled = 2005 - 601 = 1404
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Re: A faulty car odometer proceeds from digit 3 to digit 5, always skippin  [#permalink]

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05 Apr 2019, 00:08
baru wrote:
When the odometer says that it traveled for 5miles then it means that it actually only travelled 4 miles

So +1 added to the odometer with out travelling.

Similarly 4,14,24,34,54,64,74,84,94 -(40-is skipped ) . Here a Total of 9*1 + 10 = 19 miles are added for a hundred
Similarly 400 ,1400 are also skipped - 200 more added

Total extra miles added before 2000 = 19(18) +200 = 342 + 200 = 542
for 2005 , 1 mile is for five miles travelled after 2000 , So Grand Total = 542+1 = 543

miles travelled = 2005-543 = 1462- Option B

If its clear - Kudos Please

Inyour calculation you have accounted only one 4 in 44, the other 4 is not accounted for... so it would mean 20 nos. of 4s in every 100

Moreover you have not considered these 20 nos. of 4s which will appear in 400 and 1400 series..... so that would mean there will be total 542 +18 + 20 + 20 + 1 4s in all
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Re: A faulty car odometer proceeds from digit 3 to digit 5, always skippin  [#permalink]

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05 Apr 2019, 01:18
1
Thought of this as a combinations problem and that made it quite easy.
Single digit number without 4 = 9
Double digit numbers without 4 = 8x9 = 72
Triple = 8x9x9 = 648
4 digit with first fixed as 1 = 1x9x9x9 = 729
Add all plus 4 miles for 2000-2005 gives:
9+72+648+729+4 = 1462

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Re: A faulty car odometer proceeds from digit 3 to digit 5, always skippin  [#permalink]

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06 Apr 2019, 04:07
Consider it as 4digit numbers

_ _ _ _ in how many ways we can fill this up to 2005
Considering first blank to be 0, 1 it is 2 ways rest is 10
So total number ways this can be filled for digits 1-1999
2*10*10*10-1(considering one number where all are zeroes)=1999
Now number starting with 2 is 2000,2001,2002,20032004,2005 so total is 1999+6=2005
same way if 4 is not considered 4 digit number up to 1999 can be filled in 2*9*9*9-1(considering all as zero)=1457
Rest digit with from 2000-2005 with excluding 2004 is 5digirs
So total is 1457+5=1462

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Joined: 23 Oct 2013
Posts: 43
Re: A faulty car odometer proceeds from digit 3 to digit 5, always skippin  [#permalink]

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06 Apr 2019, 04:08
Consider it as 4digit numbers

_ _ _ _ in how many ways we can fill this up to 2005
Considering first blank to be 0, 1 it is 2 ways rest is 10
So total number ways this can be filled for digits 1-1999
2*10*10*10-1(considering one number where all are zeroes)=1999
Now number starting with 2 is 2000,2001,2002,20032004,2005 so total is 1999+6=2005
same way if 4 is not considered 4 digit number up to 1999 can be filled in 2*9*9*9-1(considering all as zero)=1457
Rest digit with from 2000-2005 with excluding 2004 is 5digirs
So total is 1457+5=1462

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Re: A faulty car odometer proceeds from digit 3 to digit 5, always skippin   [#permalink] 06 Apr 2019, 04:08
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