Question

In the given question, there are two statements marked I and II. Decide which of the statements are sufficient to answer the question. Choose your answer from the given alternative.

Eco Wild Preserve contains $5x$ zebras and $2x$ lions, where $x$ is a positive integer. If the lions succeed in killing $z$ of zebras, is the new ratio of zebras to lions less than $2$ to $1$?
(1) $z>x$
(2) $z=4$

• A. Statement I alone is sufficient to answer the problem.
• B. Statement II alone is sufficient to answer the problem.
• C. Statement I and II both are needed.
• D. Statement I and II both are not sufficient.

Answer 1

The correct option is A Statement I alone is sufficient to answer the problem.

The ratio of zebras to lions can be sritten as $\frac{5x}{2x}$

If $z$ zebras then meet a sad ending, the new ratio can be written as $\frac{5x-z}{2x}$

(Note that its fine to "mix" the ratio with the variable $z$, since the ratio itself already contains the variable $x$, which is the multiplier- that is, $x$ is the number you would multiply $5$ and $2$ by to get the real, original numbers of zebras and lions.

Thus, you can rephrase the question as:

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

but you can keep simplifying! (If the DS question contains fractions, or the same variable in more than one place, try to simplify a bit more. ) Since you know that $x$ is positive, you can cross-multiply:

$5x-z<4x?$

$-z<-x^2?$

$z>x?$

The question is asking ,"Is $z>x$?"

(1)SUFFICIENT: This statement answers the rephrased question directly.

Alternatively, plugging in values for $z$ and $x$ would also show the statement to be sufficient if you didn't take the algebraic route. For instance, if $z=3$ and $x=2$, then you would start with $10$ zebras and $4$ lions and then losing three zebras would give you $7$ zebras to $4$ lions, which is less than a $2$ to $1$ ratio. Additional examples will yield the same results.

(2) INSUFFICIENT: Knowing that $z=4$ is not sufficient without knowing something about $x$. For instance, if $x=1$ and you began with $5$ zebras and $2$ lions, then losing $4$ zebras would certainly shift the ratio below $2$ to $1$. but what if $x$ were $100$? If you began with $500$ zebras and $200$ lions, then the loss of $4$ zebras would not shift the ratio below $2$ to $1$

The correct answer is (A)