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# x or y

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Founder
Joined: 18 Apr 2015
Posts: 6647
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Kudos [?]: 1275 [0], given: 6017

x or y [#permalink]  24 Sep 2018, 12:01
Expert's post
00:00

Question Stats:

45% (01:52) correct 54% (02:20) wrong based on 33 sessions
Attachment:

triangle.jpg [ 11.83 KiB | Viewed 742 times ]

$$\overline{AD} =2$$
$$\overline{DC}=x$$
$$\overline{CE}=8$$
$$\overline{BE}=y$$

$$\overline{DE}$$ is parallel to $$\overline{AB}$$

 Quantity A Quantity B x y

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

_________________
Intern
Joined: 06 Jul 2018
Posts: 32
Followers: 0

Kudos [?]: 1 [0], given: 3

Re: x or y [#permalink]  08 Nov 2018, 06:00
Can any one explain ?
Supreme Moderator
Joined: 01 Nov 2017
Posts: 370
Followers: 5

Kudos [?]: 111 [1] , given: 4

Re: x or y [#permalink]  08 Nov 2018, 21:48
1
KUDOS
Expert's post
Carcass wrote:
Attachment:
triangle.jpg

$$\overline{AD} =2$$
$$\overline{DC}=x$$
$$\overline{CE}=8$$
$$\overline{BE}=y$$

$$\overline{DE}$$ is parallel to $$\overline{AB}$$

 Quantity A Quantity B x y

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Hi..
since $$\overline{DE}$$ is parallel to $$\overline{AB}$$, triangle ABC and CDE are similar triangles. This means the sides are in proportion..
ABC similar DEC .. thus
$$\frac{AB}{DE}=\frac{BC}{EC}=\frac{CA}{CD}.............\frac{15}{10}=\frac{8+y}{8}=\frac{x+2}{x}$$..
$$\frac{15}{10}=\frac{8+y}{8}........15*8=10*(8+y)......y=\frac{8*(15-10)}{10}=4$$
$$\frac{15}{10}=\frac{x+2}{x}........15*x=10*(x+2)......x=\frac{20}{(15-10)}=4$$

so x=y

C
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Intern
Joined: 04 Nov 2018
Posts: 44
Followers: 0

Kudos [?]: 6 [0], given: 8

Re: x or y [#permalink]  10 Nov 2018, 08:27
Solving this took using the explanation from chetan2u took me over 4 minutes. Is there a way to solve with brevity and still arrive at the correct answer?
Supreme Moderator
Joined: 01 Nov 2017
Posts: 370
Followers: 5

Kudos [?]: 111 [0], given: 4

Re: x or y [#permalink]  10 Nov 2018, 09:35
Expert's post
Mercychee wrote:
Solving this took using the explanation from chetan2u took me over 4 minutes. Is there a way to solve with brevity and still arrive at the correct answer?

This will take exactly half a minute if you know the rules of similar triangles.

The question is based on similar triangles, which is tested on GRE and you have no option but to grasp the topics tested in GRE.
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Intern
Joined: 04 Nov 2018
Posts: 44
Followers: 0

Kudos [?]: 6 [0], given: 8

Re: x or y [#permalink]  14 Nov 2018, 14:02
chetan2u wrote:
Mercychee wrote:
Solving this took using the explanation from chetan2u took me over 4 minutes. Is there a way to solve with brevity and still arrive at the correct answer?

This will take exactly half a minute if you know the rules of similar triangles.

The question is based on similar triangles, which is tested on GRE and you have no option but to grasp the topics tested in GRE.

Thank you for the resources!
Manager
Joined: 22 Feb 2018
Posts: 163
Followers: 2

Kudos [?]: 109 [0], given: 22

Re: x or y [#permalink]  28 Nov 2018, 19:20
Because DE is parallel to AB, triangles are equivalent and we have:
CD/ DA = CE / EB
Also we have CD/CA = CE/ CB

CD/ DA = CE / EB
x / 2 = 8 / y
xy = 16

CD/CA = CE/ CB = DE/AB
x / 2+x = 8 / 8+y = 10/15
y = 4 and x = 4, So they are equal
_________________

Director
Joined: 09 Nov 2018
Posts: 509
Followers: 0

Kudos [?]: 23 [0], given: 1

Re: x or y [#permalink]  11 Jan 2019, 17:28
chetan2u wrote:
Mercychee wrote:
Solving this took using the explanation from chetan2u took me over 4 minutes. Is there a way to solve with brevity and still arrive at the correct answer?

This will take exactly half a minute if you know the rules of similar triangles.

The question is based on similar triangles, which is tested on GRE and you have no option but to grasp the topics tested in GRE.

yes, correct.
Re: x or y   [#permalink] 11 Jan 2019, 17:28
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