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# Mr. X bought a new car and went for a trip. There was a slight defect

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Math Expert
Joined: 02 Sep 2009
Posts: 64248
Mr. X bought a new car and went for a trip. There was a slight defect  [#permalink]

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23 Jul 2018, 21:58
00:00

Difficulty:

75% (hard)

Question Stats:

42% (02:13) correct 58% (02:42) wrong based on 48 sessions

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Mr. X bought a new car and went for a trip. There was a slight defect with the odometer (which shows the distance travelled) where the digit 9 was missing. At the end of the trip the odometer read 001245. What is the exact distance traveled by X in the new car? (Assume that the odometer read 000000 when Mr. X bought it)

A. 755
B. 931
C. 932
D. 1000
E. 1300

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Posts: 3381
Mr. X bought a new car and went for a trip. There was a slight defect  [#permalink]

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23 Jul 2018, 23:48
1
3

Solution

Given:
• The digit 9 was missing in the odometer reading
• The reading in the faulty odometer was 001245

To find:
• The exact distance travelled by X

Approach and Working:
When we say the digit 9 is missing, it means we are considering a base system 9 in which the numbers are written

To find the exact distance measured, we need to convert it to the base system 10.
• $$(1245)_9 = (1 * 9^3 + 2 * 9^2 + 4 * 9^1 + 5 * 9^0)_{10} = (729 + 162 + 36 + 5)_{10} = (932)_{10}$$

Hence, the correct answer is option C.

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Mr. X bought a new car and went for a trip. There was a slight defect  [#permalink]

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Updated on: 24 Jul 2018, 05:50
I have never come across such type of question in OG. Does such type of question come in GMAT?

Originally posted by raks85 on 24 Jul 2018, 02:30.
Last edited by raks85 on 24 Jul 2018, 05:50, edited 1 time in total.
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Re: Mr. X bought a new car and went for a trip. There was a slight defect  [#permalink]

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24 Jul 2018, 04:21
Same here, never have I encountered such a problem. That being said. the different bases in a number system only make it a exponents question - so it is not out of the syllabus in some manner of speaking.
raks85 wrote:
I have never come across such type of question in OG. Does such question comes in GMAT?

Also, if you have a good grasp on exponents and how powers go, you'll be able to understand the different bases within an hour of practice.
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Re: Mr. X bought a new car and went for a trip. There was a slight defect  [#permalink]

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25 Jul 2018, 16:45
2
Bunuel wrote:
Mr. X bought a new car and went for a trip. There was a slight defect with the odometer (which shows the distance travelled) where the digit 9 was missing. At the end of the trip the odometer read 001245. What is the exact distance traveled by X in the new car? (Assume that the odometer read 000000 when Mr. X bought it)

A. 755
B. 931
C. 932
D. 1000
E. 1300

We are given that the odometer is missing the digit 9. That is, when the car travels 9 miles, the odometer will show 10 miles since it skips the number 9. Similarly, when the car travels 19 miles, the odometer will show 21 miles since it skips the numbers 9 and 19.

The odometer showed 1245 miles traveled, which is greater than the actual mileage. Let’s break the 1245 odometer reading down.

For the first 100 miles shown on the odometer, the numbers 9, 19, 29, 39, 49, 59, 69, 79, 89, and all numbers 90-99, inclusive, were skipped. So in the first hundred miles, 19 numbers were skipped.

Similarly, for the 100s, 200s, 300s, and up through the 800s on the odometer, we see that 19 numbers were skipped for each of these hundreds. Thus, we have 8 x 19 = 152 skipped numbers.

All numbers in the 900s were skipped. This adds an additional 100 skipped numbers.

For the odometer reading from 1000 to 1200, we again have 19 skipped numbers, twice, so we have 38 additional skipped numbers.

Finally, from 1200 to 1245, we have 9, 19, 29, and 39 skipped, adding 4 more skipped numbers.

The total number of skipped numbers is 19 + 152 + 100 + 38 + 4 = 313. The difference between this and the odometer reading of 1245 is 1245 – 313 = 932. Thus, the new car actually traveled 932 miles.

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Re: Mr. X bought a new car and went for a trip. There was a slight defect  [#permalink]

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08 Aug 2019, 09:16
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Re: Mr. X bought a new car and went for a trip. There was a slight defect   [#permalink] 08 Aug 2019, 09:16