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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] New post 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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Re: tick marks [#permalink] New post 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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Re: tick marks [#permalink] 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}.

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Re: tick marks [#permalink] New post 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.

Answer: B.
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Re: tick marks [#permalink] 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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Re: tick marks [#permalink] 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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Re: On the number line, the segment from 0 to 1 [#permalink] New post 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] 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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Re: On the number line above, the segment from 0 to 1 has been [#permalink] New post 12 Nov 2012, 09:05
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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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Re: On the number line above, the segment from 0 to 1 has been [#permalink] New post 06 Feb 2013, 06:45
Official Soln given is attached herewith. Somebody please explain me the official soln.
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Re: On the number line above, the segment from 0 to 1 has been [#permalink] New post 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 lest 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] 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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Re: On the number line above, the segment from 0 to 1 has been [#permalink] New post 09 Mar 2013, 04:45
The diagram in the problem is wrong or weird. Draw your own if you need visual help.
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Re: On the number line above, the segment from 0 to 1 has been [#permalink] New post 13 Jun 2014, 16:31
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Shortest section of a pipe thats cut in 1/5ths and 1/7ths [#permalink] New post 23 Jun 2014, 01:23
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
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Re: On the number line above, the segment from 0 to 1 has been [#permalink] New post 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

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 1, 3, 5 and 8. Thank you.


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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: On the number line above, the segment from 0 to 1 has been   [#permalink] 23 Jun 2014, 01:32
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