The number X is 200% of Y. The number Z increased by 200% is

Question

The number X is 200% of Y. The number Z increased by 200% is 50% of X. What percentage of Z is Y?

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

I'm confused on when to use algebra to solve this and when to substitute..

Vips0000 · Accepted Answer

Both approaches are fine. Just use whichever u r comfortable with.

Alegbra:

from question: 
X =2Y and
3Z = 0.5X
Therefore, 3Z = Y
=> Y is 300% of Z

Ans D.

Picking Numbers:
Start with Z as question asks in terms of Z. 
Let Z =100, thus, X=600 and Y=300 from question stems.
Hence Y is 300% of Z.

Ans D.

Hope it helps.

papua · Answer

Dear Vips0000,

The problem states that "The number Z increased by 200% is 50% of X", doesn't this mean that 2Z=0.5X ?

Thanks in Advance.

Papua

Bunuel · Answer

No. Z increased by 200% is Z + 200/100*Z = 3Z.

papua · Answer

Thank you Bunuel for explanation

fireinbelly · Answer

Hi Bunuel,

As you mentioned in an above post that Z increased by 200% is Z + 200/100*Z = 3Z. 
So by the same logic in this question -

if 3Z = Y then does it not mean that Y is 200% of Z? so the answer would be C in that case?

can you please help! Thanks.

EMPOWERgmatRichC · Answer

Hi All,

This question can be solved by TESTing VALUES. We have to pay very careful attention to the exact wording used (there's a difference between "200% of....." and "increased by 200%...").

First, we're told that X is 200% of Y.

IF....
Y = 100
X = 200

Next, we're told that if Z is INCREASED BY 200%, then Z is 50% of X.

Z + 2Z = (1/2)(X)
3Z = (1/2)(200)
3Z = 100
Z = 100/3

We're asked what percent of Z is Y.....

Y/Z = 100 / (100/3) = 3.0 = 300%

Final Answer:  D

GMAT assassins aren't born, they're made,
Rich

fireinbelly · Answer

Thanks a ton Rich, that was really helpful...difference between 200% of...and increased by 200% was crucial here...

EMPOWERgmatRichC · Answer

Hi fireinbelly,

The GMAT will test you on these differences at least once, so they're important to note.

Here's a pattern that might help you in future questions:

Raising a value by 100% means that you DOUBLE the value

eg
X = 15
raising 15 by 100% of 15 = 15 + 15 = 30
So a 100% increase is the same a multiplying that value by 2

Raising a value by 200% means that you TRIPLE the value

Raising a value by 300% means that you QUADRUPLE the value

Etc.

GMAT assassins aren't born, they're made,
Rich

arunrnair · Answer

Let Y = 100 . X is 200% Y . This means X = 200.

If Z is increased by 200 % then this will be 50% X

50% X = 100 .

If the value of Z is increased by 3 times then resulting number = 100

Therefore Z = 33.33

Now we have to identify 100 is what % of 33.33 .

Answer : 300%

EMPOWERgmatRichC · Answer

Hi briangeorgewebb,

Did you have a question about this prompt (or the approach that I took to solve it?)?

GMAT assassins aren't born, they're made,
Rich

mvictor · Answer

x=2y
the confusion is when we have Z increased by 200%
that means Z + 200% of z, which is 2z
so we have 3z=0.5x
multiply by 2
6z=x
6z=2y
3z=y
y is 300% of z.

GMATGuruNY · Answer

Let Z = 100.

The number Z increased by 200% is 50% of X. 
Z increased by 200% = 100 + (200/100)(100) = 300.
Since this result is 1/2 of X, we get:
X = 600

The number X is 200% of Y. 
Since X=600 is twice the value of Y, we get:
Y = 300

What percentage of Z is Y? 
Y/Z * 100 = (300/100) * 100 = 300

D

ScottTargetTestPrep · Answer

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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