Simple percentage problem

Expert replies

faraz_jeddah: Master | Next Rank: 500 Posts; Posts: 357; Joined: Thu Apr 18, 2013 9:46 amFollowed by: 7 members; Location: Jeddah, Saudi Arabia; Thanked: 42 times; GMAT Score:730

by faraz_jeddah » Fri Aug 23, 2013 2:23 pm

The number is x is 200% of y. The number z is increased by 200% and is 50% of x. What percentage of z is y?

A - 33.3%
B - 100%
C - 200%
D - 300%
E - 333%

My Approach

x is 200% of y

Let y = 1 ==> x = 3

The number z is increased by 200% and is 50% of x

3z = x/2 ==> z = 1/2

if z = 1/2 and y = 1

Since y is double of z

So the answer should be [spoiler]100%[/spoiler]

OA is NOT B

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Source: Beat The GMAT — Problem Solving | Fri Aug 23, 2013 2:23 pm

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by [email protected] » Fri Aug 23, 2013 4:27 pm

Hi faraz_jeddah,

I've caught a couple of mistakes in your logic. I'm going to point out the mistakes, then you can retry the question:

1) There's a difference between saying:

"X is 200% of Y" ----> This means that X = two times Y

and

"X is 200% greater than Y" -----> This means that X = three times Y

2) The question "what percent of z is y" means "y/z = ? % "

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faraz_jeddah: Master | Next Rank: 500 Posts; Posts: 357; Joined: Thu Apr 18, 2013 9:46 amFollowed by: 7 members; Location: Jeddah, Saudi Arabia; Thanked: 42 times; GMAT Score:730

by faraz_jeddah » Fri Aug 23, 2013 4:33 pm

Ahh!

Got it..

y = 1 ; x = 2

z = 1/3

y/z = 3 => [spoiler]300%[/spoiler] which is the OA.

Thanks!

melguy: Master | Next Rank: 500 Posts; Posts: 335; Joined: Mon Mar 21, 2011 11:31 pmFollowed by: 2 members; Location: Australia / India; Thanked: 37 times

by melguy » Fri Aug 23, 2013 8:53 pm

Hi

Just a tip you might find helpful. With percent problem its a good idea to use 100 instead of 1. In this problem 1 might have worked but you will see a lot of problem in which calculations are easier if you pick variable (y) = 100.

faraz_jeddah: Master | Next Rank: 500 Posts; Posts: 357; Joined: Thu Apr 18, 2013 9:46 amFollowed by: 7 members; Location: Jeddah, Saudi Arabia; Thanked: 42 times; GMAT Score:730

by faraz_jeddah » Sat Aug 24, 2013 1:22 am

melguy wrote:Hi

Just a tip you might find helpful. With percent problem its a good idea to use 100 instead of 1. In this problem 1 might have worked but you will see a lot of problem in which calculations are easier if you pick variable (y) = 100.

Roger that

ganeshrkamath: Master | Next Rank: 500 Posts; Posts: 283; Joined: Sun Jun 23, 2013 11:56 pmFollowed by: 26 members; Location: Bangalore, India; Thanked: 97 times; GMAT Score:750

by ganeshrkamath » Sat Aug 24, 2013 7:47 am

faraz_jeddah wrote:The number is x is 200% of y. The number z is increased by 200% and is 50% of x. What percentage of z is y?

A - 33.3%
B - 100%
C - 200%
D - 300%
E - 333%

My Approach

x is 200% of y

Let y = 1 ==> x =

faraz_jeddah wrote:
The number z is increased by 200% and is 50% of x

3z = x/2 ==> z =

1/3

faraz_jeddah wrote: if z =

1/3

faraz_jeddah wrote: and y = 1

Since y is

triple

faraz_jeddah wrote: of z

So the answer should be

[spoiler]300%[/spoiler]

Choose D

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by Scott@TargetTestPrep » Fri Nov 01, 2019 6:26 pm

faraz_jeddah wrote:The number is x is 200% of y. The number z is increased by 200% and is 50% of x. What percentage of z is y?

A - 33.3%
B - 100%
C - 200%
D - 300%
E - 333%

We can create the equations:

X = 2Y

and

3Z = 0.5X

Substituting, we have:

3Z = 0.5(2Y)

3Z = Y

3 = Y/Z

Since Y is thrice Z, then it is 300% of Z.

Answer: D

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