Data Sufficiency

Between 1980 and 1985, Pierre's investment portfolio increased in value by x%. Between 1985 and 1990, the portfolio increased in value by y%. Since 1990, the portfolio has decreased in value by z%. If x, y, and z are all positive integers, is the portfolio currently worth more than it was in 1980?

(1) x + y > z

(2) y − x > z

[spoiler]OA=E[/spoiler].

I am really confused here. Could anyone give me a good explanation here? Thanks in advanced.

I would say choose smart numbers. The key is having a strategy for the numbers you choose. You should be actively be trying to prove INSUFFICIENCY when you're testing numbers because then you only need two examples to answer the question - one "yes" scenario and one "no" scenario. Only if you can't find one of each should you say sufficient.

(1) x + y > z
To start I'll choose numbers where x & y are way greater z
x = 1000% , y = 2000% , z = 1% -----> Clearly this is a "yes" scenario.

now want to choose numbers that will maximize the chance of getting a "no" scenario. To do this I want numbers where x + y is just barely more than z
x = 49%, y = 51%, z = 99%

If we call our original investment P then our final value is P(1.49)(1.51)(.01) which is clearly less than the original ----> Clear "no" scenario

Since we have a "yes" and a "no" -----> INSUFFICIENT

(2) y - x > z
- We can use the first example from statement 1 to get a clear "yes" scenario


To get a no scenario we want a z that is very close to y.
x = 1%, y = 101%, z = 99%

Final value is P(1.01)(2.101)(.01) which is clearly less than P ----> clear "no" scenario

Since we have a "yes" and a "no" -----> INSUFFICIENT

1 & 2) Both our examples from statement 2 work for them combined so no further work needs to be done

Answer: E

Gmat_mission wrote:Between 1980 and 1985, Pierre's investment portfolio increased in value by x%. Between 1985 and 1990, the portfolio increased in value by y%. Since 1990, the portfolio has decreased in value by z%. If x, y, and z are all positive integers, is the portfolio currently worth more than it was in 1980?

(1) x + y > z

(2) y − x > z

Let the original investment = $100.
Question stem, rephrased:
Is the current value greater than $100?

Case 1: z=100%
Implication:
After 1990, Pierre loses 100% of his investment, reducing its value to $0.
In this case, x and y are irrelevant.
The answer to the rephrased question stem is NO.

When we evaluate the two statements, the only question is whether the current value of the portfolio can be GREATER than $100, yielding an answer of YES.
The current value will certainly be more than $100 if the two percent increases (x and y) are significantly greater than the percent decrease after 1990 (z).

Case 2: x=100%, y=200%, z=10%
After a 100% increase between 1980 and 1985, the value of the portfolio = 100 + (100% of 100) = 100 + 100 = 200.
After a 200% increase between 1985 and 1990, the value of the portfolio = 200 + (200% of 200) = 200 + 400 = 600.
After a 10% decrease since 1990, the current value of the portfolio = 600 - (10% of 600) = 600 - 60 = 540.
Since the current value is greater than $100, the answer to the rephrased question stem is YES.

Cases 1 and 2 satisfy both statements.
Since the answer is NO in Case 1 but YES in Case 2, the two statements combined are INSUFFICIENT.

The correct answer is E.