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In the figure above, if x, y and z are the lengths indicated, what is

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In the figure above, if x, y and z are the lengths indicated, what is  [#permalink]

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New post 12 Jul 2017, 01:42
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A
B
C
D
E

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  45% (medium)

Question Stats:

62% (02:14) correct 38% (02:07) wrong based on 97 sessions

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In the figure above, if x, y and z are the lengths indicated, what is an arrangement of x, y and z in order of increasing length?

(A) x, y, z
(B) z, x, y
(C) y, x, z
(D) z, y, x
(E) y, z, x


Attachment:
2017-07-12_1240.png
2017-07-12_1240.png [ 16.11 KiB | Viewed 1384 times ]

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Re: In the figure above, if x, y and z are the lengths indicated, what is  [#permalink]

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New post 12 Jul 2017, 03:25
Is it E?

The method by which I got the answer as E:

x= 3/7-1/7= 2/7= 0.2

y= 1/3-1/4= 1/12= 0.08

z= 3/7-1/3= 2/21= 0.09

y<z<x

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Re: In the figure above, if x, y and z are the lengths indicated, what is  [#permalink]

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New post 12 Jul 2017, 04:43
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x = \(\frac{1}{4} - \frac{1}{7} = \frac{3}{28} = \frac{3}{4*7}\)
y = \(\frac{1}{3} - \frac{1}{4} = \frac{1}{12} = \frac{1}{3*4}\)
z = \(\frac{3}{7} - \frac{1}{3} = \frac{2}{21} = \frac{2}{3*7}\)

To make the three values have the same base,
x = \(\frac{3}{4*7} = \frac{3*3}{3*4*7} = \frac{9}{84}\)
y = \(\frac{1}{3*4} = \frac{1*7}{3*4*7} = \frac{7}{84}\)
z = \(\frac{2}{3*7} = \frac{2*4}{3*4*7} = \frac{8}{84}\)

Since the fractions have same denominator, the increased lengths is y,z,x
Hence, Option E is the correct answer.
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Re: In the figure above, if x, y and z are the lengths indicated, what is  [#permalink]

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New post 12 Jul 2017, 05:33
Bunuel wrote:
Image
In the figure above, if x, y and z are the lengths indicated, what is an arrangement of x, y and z in order of increasing length?

(A) x, y, z
(B) z, x, y
(C) y, x, z
(D) z, y, x
(E) y, z, x


Attachment:
2017-07-12_1240.png


z = 3/7 - 1/3 = 2/21

y = 1/3 - 1/4 = 1/12

x = 1/4 - 1/7 = 3/28

y < z (2/24 < 2/21)
z < x (6/63 < 6/56)

So, y < z < x

Answer E
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In the figure above, if x, y and z are the lengths indicated, what is  [#permalink]

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New post 12 Jul 2017, 18:09
Bunuel wrote:
Image
In the figure above, if x, y and z are the lengths indicated, what is an arrangement of x, y and z in order of increasing length?

(A) x, y, z
(B) z, x, y
(C) y, x, z
(D) z, y, x
(E) y, z, x

x = \((\frac{1}{4}\) - \(\frac{1}{3})\) = \((\frac{7-4}{28})\) = \(\frac{3}{28}\)

y = \((\frac{1}{3}\) - \(\frac{1}{4})\) = \((\frac{4-3}{12})\) = \(\frac{1}{12}\)

z = \((\frac{3}{7}\) - \(\frac{1}{3})\) = \((\frac{9-7}{21})\) = \(\frac{2}{21}\)

Compare by cross multiplying. If first cross product is larger, first fraction is larger. If second cross product is larger, second fraction is larger.

x and z: \(\frac{3}{28}\) [?] \(\frac{2}{21}\) = 63 | 56 --> x, \(\frac{3}{28}\) is larger

z and y: \(\frac{2}{21}\) [?] \(\frac{1}{12}\) = 24 | 21 --> z, \(\frac{2}{21}\) is larger

y < z < x
Answer E
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Re: In the figure above, if x, y and z are the lengths indicated, what is  [#permalink]

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New post 14 Jul 2017, 10:49
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Bunuel wrote:
Image
In the figure above, if x, y and z are the lengths indicated, what is an arrangement of x, y and z in order of increasing length?

(A) x, y, z
(B) z, x, y
(C) y, x, z
(D) z, y, x
(E) y, z, x


Attachment:
2017-07-12_1240.png


I'm landing on answer E:

Using 84 as a common denominator:

X = 21/84 - 12/84 = 9/ 84
Y = 28/84 - 21/84 = 7/84
Z = 36/84 - 28/84 = 8/84

Therefore, Y < Z < X, (E)

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Re: In the figure above, if x, y and z are the lengths indicated, what is  [#permalink]

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New post 14 Jul 2017, 13:32
ilovefrankee wrote:
Bunuel wrote:
Image
In the figure above, if x, y and z are the lengths indicated, what is an arrangement of x, y and z in order of increasing length?

(A) x, y, z
(B) z, x, y
(C) y, x, z
(D) z, y, x
(E) y, z, x


Attachment:
2017-07-12_1240.png


I'm landing on answer E:

Using 84 as a common denominator:

X = 21/84 - 12/84 = 9/ 84
Y = 28/84 - 21/84 = 7/84
Z = 36/84 - 28/84 = 8/84

Therefore, Y < Z < X, (E)

My first Kudos please if this answer was helpful!

My pleasure - it's a good answer (and not one I was energetic enough to try). Kudos are good things. Pay it forward, yes? :)
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Re: In the figure above, if x, y and z are the lengths indicated, what is  [#permalink]

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New post 14 Jul 2017, 19:28
For questions like these where you are going to have to subtract different fractions from each other and compare the results you should, as several posters above have mentioned, always convert to a common denominator.

You can try converting to decimals but usually these questions will use non-terminating decimals to screw you up.

In this case the common denominator is 84, so convert all fractions to the same denominator.

z = 3/7 - 1/3 = 36/84 - 28/84 = 8/84
y = 1/3 - 1/4 = 28/84 - 21/84 = 7/84
x = 1/4 - 1/7 = 21/84 - 12/84 = 9/84

We can see that y < z < x, which is (E).

One other thing to note is it is often a good idea to avoid reducing these fractions when you are solving problems like this because not all fractions will reduce and you then partially obscure your point of comparison (which is the entire point of the problem).
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Re: In the figure above, if x, y and z are the lengths indicated, what is  [#permalink]

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New post 16 Jul 2017, 17:19
Bunuel wrote:
Image
In the figure above, if x, y and z are the lengths indicated, what is an arrangement of x, y and z in order of increasing length?

(A) x, y, z
(B) z, x, y
(C) y, x, z
(D) z, y, x
(E) y, z, x


Lets first solve for x:

x = 1/4 - 1/7 = 7/28 - 4/28 = 3/28

Next for y:

y = 1/3 - 1/4 = 4/12 - 3/12 = 1/12

Next for z:

z = 3/7 - 1/3 = 9/21 - 7/21 = 2/21

To compare x, y, and z, we can express them with the same numerator (which is much easier than using the same denominator). We will make the numerator 6. Also, keep in mind that if two positive fractions have the same numerator, the larger the denominator, the smaller the fraction.

x = 3/28 = 6/56

y = 1/12 = 6/72

z = 2/21 = 6/63

Thus, y < z < x.

Answer: E
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Re: In the figure above, if x, y and z are the lengths indicated, what is   [#permalink] 16 Jul 2017, 17:19
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