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A one foot long rod was marked off in sevenths and also in fourths. If

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contactakanksha
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A one foot long rod was marked off in sevenths and also in fourths. If [#permalink] New post   04 Mar 2020, 07:02
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A one foot long rod was marked off in sevenths and also in fourths. If the rod is then cut into separate pieces along the markings, which one of the following gives all the different lengths (in feet) of the pieces thus formed?

(A) \(\frac{1}{4} , \frac{1}{7} , \frac{1}{14} , \frac{1}{28}\)

(B) \(\frac{1}{4} , \frac{1}{7} , \frac{1}{14} , \frac{3}{28}\)

(C) \(\frac{1}{4} , \frac{1}{7} , \frac{1}{28} , \frac{3}{28}\)

(D) \(\frac{1}{4} , \frac{1}{14} , \frac{1}{28} , \frac{3}{28}\)

(E) \(\frac{1}{7} , \frac{1}{14} , \frac{1}{28} , \frac{3}{28}\)
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Re: A one foot long rod was marked off in sevenths and also in fourths. If [#permalink] New post   04 Mar 2020, 07:11
If you cut it in each marked place you will never get 1/4 because 1/7 is smaller and thus the 1/4 will have a split for sure which makes the answer to be (E) within 10sec.

For calculation, you can have 2/7-1/4 and 4/7-2/7 and get the numbers

Answer E
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Re: A one foot long rod was marked off in sevenths and also in fourths. If [#permalink] New post   04 Mar 2020, 07:26
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contactakanksha wrote:
A one foot long rod was marked off in sevenths and also in fourths. If the rod is then cut into separate pieces along the markings, which one of the following gives all the different lengths (in feet) of the pieces thus formed?

(A) \(\frac{1}{4} , \frac{1}{7} , \frac{1}{14} , \frac{1}{28}\)

(B) \(\frac{1}{4} , \frac{1}{7} , \frac{1}{14} , \frac{3}{28}\)

(C) \(\frac{1}{4} , \frac{1}{7} , \frac{1}{28} , \frac{3}{28}\)

(D) \(\frac{1}{4} , \frac{1}{14} , \frac{1}{28} , \frac{3}{28}\)

(E) \(\frac{1}{7} , \frac{1}{14} , \frac{1}{28} , \frac{3}{28}\)

**The source did not provide an OA


Since we want to find the fractions, we can assume some other length of the rod which will make calculation easier. Take the length of the pipe to be 28-feet long (the least common multiple of 4 and 7).

In this case the branch would be cut at 4, 7, 8, 12, 14, 16, 20, 21, 24, 28 feet (in black are given sevenths of the length and in red fourths thirds of the length).

Distinct lengths would be: 4=4/28=1/7, 7-4=3=3/28, 8-7=1=1/28, and 14-12=2=2/28=1/14 feet long pieces.

Answer: E.
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Re: A one foot long rod was marked off in sevenths and also in fourths. If [#permalink] New post   04 Mar 2020, 07:27
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contactakanksha wrote:
A one foot long rod was marked off in sevenths and also in fourths. If the rod is then cut into separate pieces along the markings, which one of the following gives all the different lengths (in feet) of the pieces thus formed?

(A) \(\frac{1}{4} , \frac{1}{7} , \frac{1}{14} , \frac{1}{28}\)

(B) \(\frac{1}{4} , \frac{1}{7} , \frac{1}{14} , \frac{3}{28}\)

(C) \(\frac{1}{4} , \frac{1}{7} , \frac{1}{28} , \frac{3}{28}\)

(D) \(\frac{1}{4} , \frac{1}{14} , \frac{1}{28} , \frac{3}{28}\)

(E) \(\frac{1}{7} , \frac{1}{14} , \frac{1}{28} , \frac{3}{28}\)


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Hope it helps.
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Re: A one foot long rod was marked off in sevenths and also in fourths. If [#permalink]
04 Mar 2020, 07:27
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