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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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Question Stats:

65% (01:11) correct 35% (01:04) wrong based on 862 sessions

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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
_________________

The proof of understanding is the ability to explain it.

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?
_________________

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

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.

0---:-|---:--|-:--:-|--:---|-:----1

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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25 Jun 2017, 16:28

I resolved it differently by assuming that the graph does represent right proportion. The smallest distance between fifths and sevenths on the graph is right in the middle, either after 2nd fifth or before 3rd So it's 3/7 - 2/5 = x x=15/35- 14/35 = 1/35

or 3/5 - x = 4/7 x = 3/5-4/7= 21/35 - 20/35 = 1/35