232 and 256 only.
The inequality could be simplified using exponent
rules, but all the numbers are small enough either to have memorized or to
quickly calculate:
To isolate
x
, multiply all three parts of the inequality by 48:
192 <
x
< 384
The only choices in this range are 232 and 256.
27.
(B).
Since a number to the
power equals the square root of that
number,
could also be written as
. This, however, does not appear in
the choices. Note, however, that
can be simplified:
This matches choice (B). Alternatively, convert the answer choices. For
instance, in incorrect choice (A),
. Since this is not
equal to
, eliminate (A). Correct choice (B) can be converted as such:
.
28.
(B).
Exponents questions usually involve prime factorization, because you
always want to find common bases, and the fundamental common bases are
prime numbers. Test some values to see what leads to zeros at the end of an
integer.
10 = 5 × 2
40 = 8 × 5 × 2
100 = 10 × 10 = 2 × 5 × 2 × 5
1,000 = 10 × 10 × 10 = 2 × 5 × 2 × 5 × 2 × 5
Ending zeros are created by 10’s, each of which is the product of one 2 and
one 5. So, to answer this question, determine how many pairs of 2’s and 5’s
are in the expression:
125
14
48
8
= (5
3
)
14
× (2
4
× 3)
8
= 5
42
× 2
32
× 3
8
Even though there are 42 powers of 5, there are only 32 powers of 2, so you
can only form 32 pairs of one 5 and one 2.
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