Thus(2^6 )(3^2 ) = 2(x+2) × 3(y+3)
6 = x + 2 2 = y + 3
↓
4 = x −1 = y
↓
x + y = 3- E If the base of an exponential term is between 0 and 1, then as the exponent
increases, the result decreases. Thus a^2 < a. Eliminate A, C, and D. Now
compare B and E. What happens when you take the square root of a fraction?
The opposite of when you square it! Squaring a positive fraction results in a
value smaller than the original fraction, so taking the square root of a fraction
results in a value larger than the original fraction. Thus the answer is E.
For illustration: √0.49 = 0.7. Note that the result (0.7) is larger than the original
value whose square root was taken. - B Split the numerator:^330 + 3 32929 = 333029 +^332929. The first term can be reduced:
330
329 = 3
(^1). The second term can be reduced: 329
329 = 1. Thus the fraction reduces
to 3 + 1 = 4.
- A To simplify exponential expressions, it is generally a good idea to make
the bases similar. In this case, express the denominator as base 10: 100^3 y =
(10^2 )^3 y = 10^6 y.
The inequality now reads: (10^2 x)/(10^6 y) < 1. Multiply both sides by 10^6 y:
102 x < 10^6 y
2 x < 6y
x < 3y - D First, simplify the values inside the radical: 12 − 4 = 8. Next, multiply the
terms underneath the radical: 2 × 8 × 9 = 144. The square root of 144 is 12. - E A good rule of thumb is to eliminate radicals where possible. In the first
equation, you can do so by squaring both sides: √a + b
2
= 8^2 → (a + b) = 64.
In the second equation, you should first add √b to both sides: √a = √b.
Now square both sides:(^) √a^2 = √b^2
a = b
Now substitute a for b in the first equation:
a + a = 64
2 a = 64
a = 32
CHAPTER 11 ■ ALGEBRA 281
03-GRE-Test-2018_173-312.indd 281 12/05/17 11:54 am