Data Sufficiency

BTGmoderatorLU wrote:Source: Manhattan Prep

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

The OA is A

Current zebra to lion ratio: Z : L :: 5x : 2x

The ratio after z numbers of zebras a killed by lions: Z' : L. We have to determine whether Z' : L is less than 1/2.

Z' : L :: (5x - z) : 2x < 1/2

= (5x - z) / 2x < 1/2

= 5/2 - z/2x < 1/2

= 5/2 - 1/2 < z/2x

= 1/2 < z/2x

=> x < z

The answer is Yes if x < z and this is what Statement 1 states. Sufficient. Statement 2 itself is not sufficient.

The correct answer: A

Hope this helps!

-Jay
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BTGmoderatorLU wrote:Source: Manhattan Prep

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

The OA is A

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

Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Answer: A