 ## Blog

### The Quest for 700: Weekly GMAT Challenge (Answer)

Yesterday, Manhattan GMAT posted a GMAT question on our blog.  Today, they have followed up with the answer:

Solution:

First, solve the given equation:

x4 – 25×2 = -144
x4 – 25×2 + 144 = 0

Substitute z = x2:

z2 – 25z + 144 = 0

Use trial and error to find a pair of factors of 144 that sum to 25.  Start with 12 & 12, which sum to 24; then try 16 and 9, which work.

(z – 16)(z – 9) = 0
z = 16 or z = 9

Now put x2 back in:

x2 = 16 or x2 = 9
x = -4 or 4, or x = -3 or 3.  There are four possible solutions.

Possible sums of two solutions include the following:
-7 = -4 + -3
-1 = -4 + 3
0 = -4 + 4 or -3 + 3
7 = 4 + 3

However, 3 itself is NOT a possible sum of two solutions of the equation.

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