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On the number line above, the segment from 0 to 1 has been divided int

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metallicafan
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On the number line above, the segment from 0 to 1 has been divided int [#permalink] New post   03 Nov 2010, 15:45
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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?

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


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Re: On the number line above, the segment from 0 to 1 has been divided int [#permalink] New post   03 Nov 2010, 16:05
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metallicafan wrote:
0---:-|---:--|-:--:-|--:---|-:----1

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.
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Re: On the number line above, the segment from 0 to 1 has been divided int [#permalink] New post   03 Nov 2010, 15:52
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1/35
Total number length should be divisible by 5 and by 7 =>35

if divided in 5 parts: 7, 14, 21, 28, 35
If divided in 7 parts: 5, 10, 15, 20, 25, 30, 35

Smallest distance is 1/35 (between 20 and 21).

Sorry, I do not know better/more mathematical way to approach this...
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Re: On the number line above, the segment from 0 to 1 has been divided int [#permalink] New post   03 Nov 2010, 20:47
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Bunnel must say, you are the undisputed champ!! an excellent takeaway in this problem is the LCM of the two fractions.
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Re: On the number line above, the segment from 0 to 1 has been divided int [#permalink] New post   06 May 2011, 11:26
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7*5 = 35.

let 1 represent 35.

then for 1/5 divisions are 5,10,15,20,25,30,35
then for 1/7 divisions are 7,14,21,28,35

between 14 and 15 difference is 1. this is equal to 1/35.
Hence B.
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Re: On the number line above, the segment from 0 to 1 has been divided int [#permalink] New post   11 May 2011, 06:57
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1/7,2/7,3/7,4/7,5/7,6/7,7/7

= 5/35, 10/35, 15/35, 20/35, 25/35, 30/35, 35/35

1/5,2/5,3/5,4/5,5/5

= 7/35, 14/35, 21/35, 28/35, 35/35


3rd 7 mark and 2nd 5 mark :

= 1/35

Answer - B
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Re: On the number line above, the segment from 0 to 1 has been divided int [#permalink] New post   16 Mar 2012, 00:46
Bunuel wrote:
metallicafan wrote:
0---:-|---:--|-:--:-|--:---|-:----1

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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Re: On the number line above, the segment from 0 to 1 has been divided int [#permalink] New post   03 Dec 2019, 20:16
Bump up!

Bunuel, Your approach is just insane.! Thank you
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Re: On the number line above, the segment from 0 to 1 has been divided int [#permalink] New post   25 Feb 2024, 23:46
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Hope it helps.­­­
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Re: On the number line above, the segment from 0 to 1 has been divided int [#permalink]
25 Feb 2024, 23:46
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