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# Marks are equally spaced on a number line as shown above. How many mar

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Math Expert
Joined: 02 Sep 2009
Posts: 51214
Marks are equally spaced on a number line as shown above. How many mar  [#permalink]

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12 Jul 2017, 01:54
00:00

Difficulty:

45% (medium)

Question Stats:

63% (01:11) correct 37% (01:11) wrong based on 164 sessions

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Marks are equally spaced on a number line as shown above. How many marks would there be on this number line between the marks at 13 and 16?

(A) 3
(B) 6
(C) 7
(D) 8
(E) 9

Attachment:

2017-07-12_1351.png [ 3.73 KiB | Viewed 1494 times ]

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Re: Marks are equally spaced on a number line as shown above. How many mar  [#permalink]

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Updated on: 12 Jul 2017, 03:27
Bunuel wrote:

Marks are equally spaced on a number line as shown above. How many marks would there be on this number line between the marks at 13 and 16?

(A) 3
(B) 6
(C) 7
(D) 8
(E) 9

Attachment:
2017-07-12_1351.png

There will be 8 tick marks between 13 and 16.

There are 9 intervals between 16 and 13.

Tick marks represent specific values (13, 13$$\frac{1}{3}$$, ...16). Intervals represent distance between those values /tick marks.

16 - 13 = 3, and 3/(1/3) = 9 intervals of $$\frac{1}{3}$$. Then subtract 1 from 9 because you need to omit both 13 and 16 from your count.

(Subtracting 1 for "between" is related to "adding one before you're done" in other contexts such as finding the number of terms in a series.)

In a line divided by tick marks, for any specific range, there will be one more tick mark, inclusive of upper and lower bounds, than there are intervals.

But if you're counting the number of marks between, it's exclusive of both the lower and upper bounds 13 and 16.

If you use what's shown you can count visually to ascertain: The specific values 1 and 0 are tick marks. There are 3 intervals between them, but only 2 marks between.

So between 13 and 16 on this line, there are 8 marks.

Originally posted by generis on 12 Jul 2017, 02:35.
Last edited by generis on 12 Jul 2017, 03:27, edited 3 times in total.
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Re: Marks are equally spaced on a number line as shown above. How many mar  [#permalink]

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12 Jul 2017, 03:19
3
1
Bunuel wrote:

Marks are equally spaced on a number line as shown above. How many marks would there be on this number line between the marks at 13 and 16?

(A) 3
(B) 6
(C) 7
(D) 8
(E) 9

Attachment:
2017-07-12_1351.png

There is 2 fractional marks between 2 integers. So total fractional marks between 13 and 16 = 3*2 = 6

Number of integral marks = 4 (i.e. 13, 14,15,16)

We have to consider the marks between 13 and 16. So, remove 13 and 16. Total number of marks = 6 + 4 - 2 = 8

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Re: Marks are equally spaced on a number line as shown above. How many mar  [#permalink]

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12 Jul 2017, 08:32
there are 2 fractional marks between 2 integers...hence,,,between 13 and 16 there will be 6 marks

plus 13 and 16 will total of 8 marks,,,

ans 8
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Re: Marks are equally spaced on a number line as shown above. How many mar  [#permalink]

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12 Jul 2017, 09:11
1
There are 2 marks between every integer mark. So, there will be 2(16-13) = 6 marks between 13 and 16, if we add 2 integer marks 14 and 15, that would make it 8. Ans - D.
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Marks are equally spaced on a number line as shown above. How many mar  [#permalink]

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Updated on: 19 Jul 2017, 03:53
marks between 13 & 16 will be equal to marks between 0 &3

as you can see in the figure total marks preceding 1 are 3 (do not include 1).
same as total no of marks preceding 2 will be 6 (do not include 2).
and same as total no of marks preceding 3 will be 9 (do not include 3).

now to get the no of marks between 0&3,we have to exclude 0 (3 is already excluded) and we will remain with 8 marks.

OA is 8

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Originally posted by GTExl on 12 Jul 2017, 12:37.
Last edited by GTExl on 19 Jul 2017, 03:53, edited 1 time in total.
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Re: Marks are equally spaced on a number line as shown above. How many mar  [#permalink]

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16 Jul 2017, 16:24
Bunuel wrote:

Marks are equally spaced on a number line as shown above. How many marks would there be on this number line between the marks at 13 and 16?

(A) 3
(B) 6
(C) 7
(D) 8
(E) 9

We see that the distance or spacing between two consecutive marks is 1/3. Thus, we need to see how many 1/3s between 13 and 16. That is, how many 1/3s divide into the difference of 13 and 16:

(16 - 13)/(1/3) = 3 x 3 = 9

However, 9 is the number of “1/3" spacings between 13 and 16; the number of markings will be 1 less than the number of spacings. Thus, there are 8 marks between the marks at 13 and 16.

Alternate Solution:

Let’s count the number of marks, noting that there will not be marks at either 13 or 16.

13 13⅓ 13⅔ 14 14⅓ 14⅔ 15 15⅓ 15⅔ 16

We see that there are 8 marks.

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Re: Marks are equally spaced on a number line as shown above. How many mar  [#permalink]

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19 Jul 2017, 02:59
Hi Bunuel,
I can see the OA is 6,
Is it because 14, 15 are not considered as marks on the number line as they are already integral.
I think everyone committed the same mistake.

Is this official material ?
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Posts: 51214
Re: Marks are equally spaced on a number line as shown above. How many mar  [#permalink]

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19 Jul 2017, 03:11
Hi Bunuel,
I can see the OA is 6,
Is it because 14, 15 are not considered as marks on the number line as they are already integral.
I think everyone committed the same mistake.

Is this official material ?

No, that's because I incorrectly marked the OA. Edited. Thank you!
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Re: Marks are equally spaced on a number line as shown above. How many mar  [#permalink]

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19 Jul 2017, 03:39
2 marks between 2 numbers ..between 13 &16
2*3=6 and 2 marks for 13 &14 .hence 8

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Re: Marks are equally spaced on a number line as shown above. How many mar  [#permalink]

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16 Aug 2018, 06:59
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Re: Marks are equally spaced on a number line as shown above. How many mar &nbs [#permalink] 16 Aug 2018, 06:59
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