phdizzle wrote:

haichao's post below got me thinking about this:

On a certain date, Hannah invested $5,000 at x percent simple annual interest and a different amount at y percent simple annual interest. What amount did Hannah invest at y percent simple annual interest?

(1) The total amount of interest earned by Hannah’s due investments in one year was $900.

(2) Hannah invested the $5,000 at 6 percent simple annual interest.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient

The question throws a lot of numbers at you, but the key is that you have three variables, x, "different amount," and y. Thus you need three equations to be able to solve for the variables. (1) gives you 1 variable and (2) gives you one more. You still have one degree of freedom and the system is underdetermined.

I feel like this approach lets you quickly screen for E on DS questions. I remember having done this before so it must not be a one-time strategy. Other examples?

I'm reluctant to try to turn this into a hard fast rule, since there are students who will simply memorize "3 variables requires 3 equations otherwise the answer is E"

If we are going to turn it into a rule, we might add some extra information.

Here's my counter-example question to help with the discussion:

What is the sum of x+y+z?

(1) The average (arithmetic mean) of x,y and z is 10

(2) Lima is the capital of Peru

Here we have 3 variables, but we don't need three equations to solve the question.

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There is another question that I saw earlier tonight that goes like this:

Joanna bought only $0.15 stamps and $0.29 stamps. How many $0.15 stamps did she buy?

(1) She bought $4.40 worth of stamps.

(2) She bought an equal number of $0.15 stamps and $0.29 stamps.

In this case, the answer is A, even though we have two variable and (1) gives us only one equation.

However, if this question were changed to $0.11 and $0.33 stamps, the answer would be C

So, as you can see, one rule about the number of variables and the number of equations will not suit every question.