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

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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
[Reveal] Spoiler: OA

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Re: tick marks [#permalink]

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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: tick marks [#permalink]

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New post 03 Nov 2010, 14:55
you can use the strategy of picking numbers.

So choose a length of 35 (5 x 7)' then the large tick marks would be at the positions 7 14 21 28 and the small tick marks would be at 5 10 15 20 25 30

look at the differences ( a little graph helps a lot) between the large and small tick marks, these would be

2 3 4 1 5 1 4 3 2

so the least difference is 1, but remember we scaled it, so tge answer is \(\frac{1}{35}\).

B

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Re: tick marks [#permalink]

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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: tick marks [#permalink]

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New post 03 Nov 2010, 19:47
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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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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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: GMAT Prep Geometry [#permalink]

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New post 11 May 2011, 17:11
divisions are 0 1/7 2/7 3/7 4/7 5/7 6/7 1

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

expressing the same in terms of the lcm of 5,7 ,i.e 35

0 7/35 14/35 21/35 28/35 35/35
5/35 10/35 15/35 20/35 25/35 30/35

by comparing the divisions with each other we can see 1/35 is the shortest possible distance between any two selected divisions.

1/35

Answer is B.

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Re: tick marks [#permalink]

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New post 15 Mar 2012, 23:46
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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New post 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?

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Amateur wrote:
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.
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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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New post 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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On the number line above, the segment from 0 to 1 has been [#permalink]

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

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New post 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

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

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New post 20 Jun 2015, 15:14
The LCM OF 5 and 7 is 35.

Lets assume that whole line is of 35 units.

Markups of 7 = 7, 14, 21, 28, 35
Markup on Line of 5 = 5,10,15,20,25,30,35

Lets write them in ascending order

5,710,1415,20,21,25,28,30,35

The closest distance is between 20 and 21

But since we have assumed distance between 0 to 1 as 35 Units.

lets nullify that

35 Units = 1 real unit given in the question

21-20 =1

so what will be 1 in terms of real unit =
1/35

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

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New post 14 Jan 2017, 06:46
I just calculated 1/5 * 1/7 and also got the correct solution "1/35".

However, calculating it this way was just a gut feeling, can someone explain me why this way to solve it is also correct please :)

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

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New post 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

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Re: On the number line above, the segment from 0 to 1 has been   [#permalink] 25 Jun 2017, 16:28
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