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# Eco Wildlife Preserve contains 5x zebras and 2x lions

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Re: Eco Wildlife Preserve contains 5x zebras and 2x lions [#permalink]
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Eco Wildlife Preserve contains 5x zebras and 2x lions, where x is a positive integer. If the lions succeed in killing z of the zebras, is the new ratio of zebras to lions less than 2 to 1 ?

(1 ) z > x
(2 ) z = 4

When you modify the original condition and the question, they become (5x-z):2x<2:1?, (5x-z)/2x<2?, 5x-z<4x?, x<z?. Therefore, the answer is A.

-> Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
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COMBINATION OF RATIO AND INEQUALITY [#permalink]
Hello a quick query for resolution.
here is a DS question :-

A forest has 5x zebras and 2x lions
Lions kill z number of the zebras, is the new ratio of zebras to lions less than 2 to 1 ?
(1) z > x
(2) z = 4

MY approach
ORIGINAL RATIO =
# of zebras : # of lions = 5x : 2x
Now am I wrong in cancelling x from both num. and denom. at this stage?
Should I keep the expression (5x : 2x) and work with x or should I cancel out x and simplify work forward with (5 : 2)

my next step is
NEW RATIO =
# of surviving zebras : # of lions

5x-z : 2x < 2: 1

or

5-z : 2 < 2: 1

AND THEN SOLVE STATEMENTS A AND B

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Re: COMBINATION OF RATIO AND INEQUALITY [#permalink]
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LogicGuru1 wrote:
Hello a quick query for resolution.
here is a DS question :-

A forest has 5x zebras and 2x lions
Lions kill z number of the zebras, is the new ratio of zebras to lions less than 2 to 1 ?
(1) z > x
(2) z = 4

MY approach
ORIGINAL RATIO =
# of zebras : # of lions = 5x : 2x
Now am I wrong in cancelling x from both num. and denom. at this stage?
Should I keep the expression (5x : 2x) and work with x or should I cancel out x and simplify work forward with (5 : 2)

my next step is
NEW RATIO =
# of surviving zebras : # of lions

5x-z : 2x < 2: 1

or

5-z : 2 < 2: 1

AND THEN SOLVE STATEMENTS A AND B

Hi,

ratio is correct if you are dealing only in ratios of various things but not when you have some numeric value...
this Q has number z, so you will have to work on 5x, because z are going out of 5x and not 5..
so$$\frac{5x-z}{2x}< \frac{2}{1}......5x-z<4x.........x<z$$
so we are looking for is x<z..
statement I gives you that info so suff....
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Re: Eco Wildlife Preserve contains 5x zebras and 2x lions [#permalink]
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jlgdr wrote:
Eco Wildlife Preserve contains 5x zebras and 2x lions, where x is a positive integer. If the lions succeed in killing z of the zebras, is the new ratio of zebras to lions less than 2 to 1 ?

(1 ) z > x
(2 ) z = 4

Once Lions kill zebras.

$$\frac{Zebras}{Lions}$$ = $$\frac{5x-z}{2x}$$

If $$\frac{5x-z}{2x}$$ < $$\frac{2}{1}$$

Then (since x and z have to be positive values, we can cross multiply)

5x-z < 4x

x < z --> We will check options if this condition is satisfied

We find that Statement 1 is sufficient.

Statement 2 is not sufficient because it dies not say anything about x.

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Re: Eco Wildlife Preserve contains 5x zebras and 2x lions [#permalink]
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jlgdr wrote:
Eco Wildlife Preserve contains 5x zebras and 2x lions, where x is a positive integer. If the lions succeed in killing z of the zebras, is the new ratio of zebras to lions less than 2 to 1 ?

(1 ) z > x
(2 ) z = 4

Given: Eco Wildlife Preserve contains 5x zebras and 2x lions, where x is a positive integer. The lions kill z of the zebras

Target question: Is the new ratio of zebras to lions less than 2 to 1 ?

This is the perfect candidate for rephrasing the target question.

ASIDE: If we take the time to rephrase the question in a simpler form, then we can save a ton of time evaluating the statements.

The NEW population of zebras is 5x - z

So, we can ask "Is (5x - z)/2x < 2/1?"

Not bad, but we can go much further than this!.

Since 2x is POSITIVE, we can safely take (5x - z)/2x < 2/1 and multiply both sides by 2x.
When we do this, we get: 5x - z < 4x
Subtract 4x from both sides: x - z < 0
Add z to both sides: x < z

So, we can write....
REPHRASED target question: Is x < z?

Now onto the statements....

Statement 1: z > x
Perfect!!
The answer to the REPHRASED target question is YES, x < z!
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: z = 4
Given this information, there is no way to conclude whether x < z
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

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Re: Eco Wildlife Preserve contains 5x zebras and 2x lions [#permalink]
+1 for option A.

We can re-phrase this question as - (5x-z)/(2x)<2 --> Solving we get x<z. Now hunt for an option that satisfies this equation.

St 1 - Sufficient
St 2- NS

Hence option A.
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Re: Eco Wildlife Preserve contains 5x zebras and 2x lions [#permalink]
why can't we solve for x for statement 2? Since the z value is given, if we plug it in, x will be smaller than 4 right?
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Re: Eco Wildlife Preserve contains 5x zebras and 2x lions [#permalink]
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hillhuangcp wrote:
why can't we solve for x for statement 2? Since the z value is given, if we plug it in, x will be smaller than 4 right?

The question ask whether x < z. (2) says z = 4. How can we say from that whether x < 4?
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Re: Eco Wildlife Preserve contains 5x zebras and 2x lions [#permalink]
Bunuel wrote:
hillhuangcp wrote:
why can't we solve for x for statement 2? Since the z value is given, if we plug it in, x will be smaller than 4 right?

The question ask whether x < z. (2) says z = 4. How can we say from that whether x < 4?

­understood. Thanks
Re: Eco Wildlife Preserve contains 5x zebras and 2x lions [#permalink]
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