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Founder  Joined: 18 Apr 2015
Posts: 6631
Followers: 107

Kudos [?]: 1274 , given: 6002

x or y [#permalink]
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 741 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 , given: 3

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

Kudos [?]: 111  , given: 4

Re: x or y [#permalink]
1
This post received
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 , given: 8

Re: x or y [#permalink]
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 , given: 4

Re: x or y [#permalink]
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 , given: 8

Re: x or y [#permalink]
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 , given: 22

Re: x or y [#permalink]
Answer: C
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
_________________

Follow your heart

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

Kudos [?]: 23 , given: 1

Re: x or y [#permalink]
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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