0S15863
- Is the integer n a prime number?
(1) 24::; n::; 28
(2) n is not divisible by 2 or 3.
Arithmetic ,., .. , � ..
Determine if the integer n is a prime number.
(1) This indicates that n is between 24 and 28,
inclusive. It follows that the value of n can
be 24, 25, 26, 27, or 28. Each of these is
NOT a prime number. Thus, it can be
determined that n is NOT a prime number;
SUFFICIENT.
(2) This indicates that n is not divisible by 2 or
- If n = 7, then n is not divisible by 2 or 3
and is a prime number. However, if n = 25,
then n is not divisible by 2 or 3 and is a not
prime number since 25 has a factor, namely
5, other than 1 and itself; NOT sufficient.
Th e correct answer ts A· ，
statement 1 alone is sufficient.
0S03615
- What is the average (arithmetic mean) annual salary of
the 6 employees of a toy company?
(1) If the 6 annual salaries were ordered from least
to greatest, each annual salary would be $6,300
greater than the preceding annual salary.
(2) The range of the 6 annual salaries is $31,500.
Arithmetic .. : 亡一；．
Can we determine the arithmetic mean of the
annual salaries of the 6 employees?
(^1 ) Given only that the 6 annual salaries can be
put into a sequence from least to greatest,
with a difference of $6,300 between
adjacent members of the sequence, we can
infer certain things about the mean of the
salaries. For example, because none of the
salaries would be negative, we know from
statement 1 that the mean of the salaries is
greater than or equal to
0 + $6,300+ $12,600 +$18, 900 + $25,200 + $31,500
6
(It is not necessary to perform this
calculation.) However, depending on what
the least of the salaries is—that is, the value
at which the sequence of salaries begins—
5.5 t<'江仔,-,c r Answer Explanations
the average of the salaries could, consistent
with condition 1, take on any value greater
than this quotient; NOT sufficient.
(^2 ) Given the statement that the range of the
salaries is $31,500, reasoning similar to the
reasoning for statement 1 applies. A
difference between least salary and greatest
salary of $31,500 is consistent with any value
for the least salary, so long as the greatest
salary is $31,500 greater than the least salary.
Furthermore, even if we knew what the least
and the greatest salaries are, it would be
impossible to determine the mean merely
from the range; NOT sufficient.
As reflected in the numerator of the quotient in
the discussion of statement 1, we can see that
statement 1 implies statement 2. In the sequence
of 6 salaries with a difference of $6,300 between
adjacent members of the sequence, the difference
between the least salary and the greatest salary is
5 x $6,300 = $31,500. Therefore, because
statement 1 is insufficient for determining
the mean of the salaries, the combination of
statement 1 and statement 2 is also insufficient
for determining the mean of the salaries.
1h e correct answer 1s E·
both statements together are not sufficient.
DSl 7503
225.In a certain order, the pretax price of each regular
pencil was $0.03, the pretax price of each deluxe
pencil was $0.05, and there were 50% more deluxe
pencils than regular pencils. All taxes on the order are
a fixed percent of the pretax prices. The sum of the
total pretax price of the order and the tax on the order
was $44.10. What was the amount, in dollars, of the
tax on the order?
(1) The tax on the order was 5% of the total pretax
price of the order.
(2) The order contained exactly 400 regular pencils.
Arithmetic • 詹噜·
Let n be the number of regular pencils
in the order and let啪be the tax rate
on the order as a percent of the pretax
price. Then the order contains l.5n delll){e
pencils, the total pretax price of the order is
($0.03)n + ($0.05)(l.5n) = $0.l05n, and the sum
of the total pretax price of the order and the tax
