# Tag Archive for 'algebra'

### GRE Math: Two Example Algebra Problems and Solutions

Algebra Problem 1

Example Algebra Problem #1

This problem presents you with a system of equations. As you can see, you have two variables, x and y, and you have two equations that use x and y. When you have multiple variables, the rule of thumb is that you need the same number of equations as you have variables to solve for them, and here, you have two variables and two equations, so you’re fine.

### GRE Math: Two Example Math Problems

Example Problem #1

Example Geometry Problem

This is a fun problem.  The problem tells us that ∆ABC and ∆DEF have the same area.  It also tells us that AD > CF.  The problem is asking us about altitude, which is height.

From this second piece of information, we know that the base of ∆ABC is longer than the base of ∆DEF.  How do we know this?  From the picture, we see that the base of ∆ABC is composed of two segments: AD + DC.  The base of ∆DEF is also composed of two segments: DC + CF.  Both triangles share DC — this is the same for both triangles.  But we know that AD is bigger than CF, which means that AD + DC > DC + CF.  Thus, the base of triangle ∆ABC is larger.

Now, since we know that both triangles have the same area, but the base of ∆ABC is bigger, this means that the height of ∆DEF has to be bigger in order to compensate.  The answer should be B, but let’s prove it.

In math terms:

Area∆ABC = Area∆DEF
½b1h1 = ½b2h2

We know that b1 (base of ∆ABC) is bigger than b2 (base of ∆DEF), so let’s just choose some arbitrary numbers to make it a bit easier to see the relationship.  Let’s let b1 = 6 and b2 = 4.

½(6)(h1) = ½(4)(h2)
3h1 = 2h2
h1 = ⅔h2

Therefore, we know that the height of ∆ABC is smaller than the height of ∆DEF.  Thus, the answer is B.