Download QUANT SOLUTIONS to 700-800 Level Problems (as Per the New GMAT Book) PDF

TitleQUANT SOLUTIONS to 700-800 Level Problems (as Per the New GMAT Book)
TagsPercentage Matrix (Mathematics) Equations Physics & Mathematics Mathematics
File Size1.9 MB
Total Pages337
Document Text Contents
Page 336

This problem can be solved algebraically or by plugging in the answer choices; both
methods are shown below.

Algebra
Because there are square root signs on both sides of the equation, we can square both
sides to get rid of them, which leaves us with 4 + x

1/2
= x + 2. x

1/2
is the same thing as

, so our next step is to isolate the radical sign and then square both sides again. Once
we do this, we can solve for x.

= x – 2
x = (x – 2)

2


x = x
2
– 4x + 4

0 = x
2
– 5x + 4

0 = (x – 4)(x – 1)

x can equal either 4 or 1; try each to determine which one is the solution to the original
equation:

x = 4: = = , so x can equal 4.

x = 1: , so x cannot equal 1.
Only x = 4 works.

Plugging in the answers
Since the numerical answers represent a possible value for x, we can also plug them into
the equation and see which one works. Remember that we can stop when we find the
right answer and it's also best to start with answer choice C. If C does not work, we can
sometimes determine whether we want to try a larger or smaller number next, thereby
saving some time.



(E) Since D works, the answer can be determined. FALSE

The correct answer is D.

67.
The equation in question can be rephrased as follows:


x

2
y – 6xy + 9y = 0

y(x
2
– 6x + 9) = 0

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