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On the number line above, the segment from 0 to 1 has been [#permalink]

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03 Nov 2010, 14:45

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On the number line above, the segment from 0 to 1 has been divided into fifths, as indicated by the large tick marks, and also into sevenths, as indicated by the small tick marks. What is the LEAST possible distance between any two of the tick marks?

On the number line above, the segment from 0 to 1 has been divided into fifths, as indicated by the large tick marks, and also into sevenths, as indicated by the small tick marks. What is the LEAST possible distance between any two of the tick marks?

(A)1/70 (B)1/35 (C)2/35 (D)1/12 (E)1/7

The easiest way would be just to write down the values at all marks. Let the total distance be 35 units (LCM of 5 and 7), then the large marks will be at: 7, 14, 21, and 28 and the small marks at 5, 10, 15, 20, 25, and 30: 5-7-10-14-15-20-21-25-28-30. The least distance is 1 unit or 1/35 th: between 14 and 15 and between 20 and 21.

On the number line above, the segment from 0 to 1 has been divided into fifths, as indicated by the large tick marks, and also into sevenths, as indicated by the small tick marks. What is the LEAST possible distance between any two of the tick marks?

(A)1/70 (B)1/35 (C)2/35 (D)1/12 (E)1/7

The easiest way would be just to write down the values at all marks. Let the total distance be 35 units (LCM of 5 and 7), then the large marks will be at: 7, 14, 21, and 28 and the small marks at 5, 10, 15, 20, 25, and 30: 5-7-10-14-15-20-21-25-28-30. The least distance is 1 unit or 1/35 th: between 14 and 15 and between 20 and 21.

Answer: B.

Thanks for efficient method
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The proof of understanding is the ability to explain it.

On the number line, the segment from 0 to 1 has been divided in to fifths and also in to sevenths. What is the Least possible distance between any two tick marks? a) 1/70 b) 1/35 c) 2/35 d) 1/12 e) 1/7 Can someone explain clearly what needs to be the approach for these kind of questions and how the answer will be least common multiple?

Merging similar topics. Please refer to the solutions above ask if anything remains unclear.

Re: On the number line above, the segment from 0 to 1 has been [#permalink]

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11 Nov 2012, 09:49

Man i got a question.... i understood what everyone said.... but number line segment was divided in to 7parts and 5 parts right.... so each one also has ticks at 35! the last point.... so isn't the distance between large and small tick marks 0?

Man i got a question.... i understood what everyone said.... but number line segment was divided in to 7parts and 5 parts right.... so each one also has ticks at 35! the last point.... so isn't the distance between large and small tick marks 0?

The number line shown, is not cut at 0 and 1.
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Official Soln given is attached herewith. Somebody please explain me the official soln.

Step 1: finding the values of small and large tick marks; Step 2: find the least common denominator in order to compare them easily; Step 3: arrange tick marks in ascending order; Step 4: find the least distance between them.

Can you please tell me which step was confusing?
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Re: On the number line above, the segment from 0 to 1 has been [#permalink]

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07 Feb 2013, 02:02

Bunuel wrote:

Sachin9 wrote:

Official Soln given is attached herewith. Somebody please explain me the official soln.

Step 1: finding the values of small and large tick marks; Step 2: find the least common denominator in order to compare them easily; Step 3: arrange tick marks in ascending order; Step 4: find the lest distance between them.

Can you please tell me which step was confusing?

step 3 was confusing. It is now clear. . an exhausted mind couldn't absorb earlier
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

Hi Guys i need help understanding why this methodology for answering this question works.

Q) A one yard pipe has markings at 1/5ths and 1/7ths of its length. The pipe is then cut at these markings. What is the length of the smallest piece? A) 1/35

I want help understanding why simply multiplying 1/7 & 1/5 gives the right answer. This works with all values

Merging similar topics. Please refer to the discussion above.

Re: On the number line above, the segment from 0 to 1 has been [#permalink]

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03 Feb 2015, 06:24

I just started subtracting the parts.

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1) 1/5 - 1/7 = 2/5, is the small part between the first 5th and the first 7th. 2) 3/7 - 2/5 = 1/35, is the difference between the third 7th and the second 5th. 3) 3/5 - 4/7 = 1/35, is the difference between the third 5th and the fourth 7th. 4) 1 - 4/5 = 1/5, is the differenc between the fifth 5th and the fourth fifth.

In other words, 1/35 is the smallest difference between any two pieces. ANS B

Re: On the number line above, the segment from 0 to 1 has been [#permalink]

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06 Jul 2016, 02:00

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