Explanation
In this question, we can translate what we are told in the
question into algebra as the equation
on our
scratch work. Furthermore, we can notate it informally in this way to indicate
that G and D have increased:
This informal trick is used by some scientists and
economists to indicate what's happening when there are changes to the entities
in an equation. It clarifies something: that N goes up only if G goes
up more than D goes up, since G is added and D is subtracted. Let's go to the statements, evaluating them
separately first.
Statement (1): this information is definitely
insufficient, because anything could be going on with deductions. Consider
analysis by cases: they could have barely increased or wildly increased, changing
everything. Insufficient.
Statement (2) is insufficient by comparable logic.
Combining them, we need to get more specific. We know that
. Now, the new N,
call it
, is equal to
If we could factor out the multiples, we could substitute
in
for
and then be
able to get
in terms of
. But we can't do that, and we still don't know the
values of G and D. We can evaluate by cases. If G
and D were both $100, then there
would be a gain of $8, a loss of $16, and a net loss of $8. Another case: if G were $100 and D were $200, the gain would be the same, but the loss doubled, for
a different net loss. We have insufficient information to determine the change.
The correct answer is (E).
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