Exponent Question Cannot Answer for my life

[ezmack]

Nice menonan!

[ionno]

Originally Posted by dmact

2. If 2^x – 2 ^(x-2) = 3*2^13, what is x?
a.9
b.11
c.13
d.15
e.17
You can solve it like this

1. 2^x – 2 ^(x-2) = 3*2^13
2. 2^x – 2 ^x/2^2 = 3*2^13

now taking 2^ common from LHS u get
3. 2^x (1– 1/2^2) = 3*2^13
Since 2^2 =4 so now
4. 2^x (1– 1/4) = 3*2^13

You can turn 2^x/2^2 TO (1-1)2^2 ?

I'm confused how can 2^X turn into 1-1 ?

[selytch]

for me it was easier this way:
2^x - 2^(x-2) = 3*2^13
find LCM
(4*2^x-2^x)/4=3*2^13
or
4*2^x-2^x=3*2^15
common multiplier 2^x

2^x * (4-1)=3*2^15 - now, what do we need to do to get (4-1)?
3*2^15 equals 4*2^15-2^15, thus

2^x * (4-1)=2^15 * (4-1)
x=15

[selytch]

I'm just starting to prepare for GMAT but I had a revelation!
1. There's usually more than one way of solving problem on the test.
2. Some methods are more efficient than others.
3. They test not only being thorough but the efficiency as well.
4. Even wrong answers can be used to solve the problem.

I wonder if there is info on choosing the most efficient strategy for Q or one just have to be born genius...