Correct Answer: A
Explanation:
Algebra Applied problems; Simultaneous equations; Inequalities
Let x represent the number of $100 certificates sold, and let y represent the number of $10
certificates sold. Then the given information can
be expressed as x+y = 20 or thus y = 20- x. The
value of the $100 certificates sold is 100x, and
the value of the $10 certificates sold is 10y.
(1) From this, it is known that 100* +10y > 1,650. Since y = 20- x, this value can be substituted for y, and the inequality can be solved
for x:
100* + 10y > 1,650
100* +10(20 -x) >1,650 substitute for y
100* + 200 -10* > 1,650 distribute
90* +200 > 1,650 simplify
90* > 1,450 subtract 200 from both sides
*>16.1
Thus, more than 16 of the $100 certificates were
sold. If 17 $100 certificates were sold, then it must
be that 3 $10 certificates were also sold for a total
of $1,730, which satisfies the condition of being
between $1,650 and $1,800. If, however, 18 $100
certificates were sold, then it must be that 2 $10
certificates were sold, and this totals $1,820,
which is more than $1,800 and fails to satisfy the
condition. Therefore, 3 of the $10 certificates were
sold; SUFFICIENT.
- (2) From this it can be known only that the number of $10 certificates sold was 4 or fewer; NOT sufficient.
The correct answer is A; statement 1 alone is sufficient.