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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 [#permalink]

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03 Nov 2010, 14:45
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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
[Reveal] Spoiler: OA

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03 Nov 2010, 14:52
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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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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 $$\frac{1}{35}$$.

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03 Nov 2010, 15:05
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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.

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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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06 May 2011, 10:26
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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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11 May 2011, 05:57
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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

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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

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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.

Thanks for efficient method
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Re: On the number line, the segment from 0 to 1 [#permalink]

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11 Nov 2012, 04:25
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Amateur wrote:
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.

Similar question to practice:
kim-finds-a-1-meter-tree-branch-and-marks-it-off-in-thirds-140038.html

Hope it helps.
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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?
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Re: On the number line above, the segment from 0 to 1 has been [#permalink]

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12 Nov 2012, 09:05
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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Re: On the number line above, the segment from 0 to 1 has been [#permalink]

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06 Feb 2013, 06:45
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Official Soln given is attached herewith. Somebody please explain me the official soln.
Attachments

Capture.JPG [ 28.81 KiB | Viewed 18704 times ]

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

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07 Feb 2013, 00:07
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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 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
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Re: On the number line above, the segment from 0 to 1 has been [#permalink]

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23 Jun 2014, 01:32
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erotoxic wrote:
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.

Similar questions to practice:
kim-finds-a-1-meter-tree-branch-and-marks-it-off-in-thirds-140038.html
if-the-successive-tick-marks-shown-on-the-number-line-above-144053.html
a-straight-pipe-1-yard-in-length-was-marked-off-in-fourths-145031.html

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

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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

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

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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
Re: On the number line above, the segment from 0 to 1 has been   [#permalink] 14 Jan 2017, 06:46
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