daretodream wrote: ↑Thu Feb 18, 2010 11:26 pm
Joanna bought only $0.15 stamps and $0.29 stamps. How many $0.15 stamps did she buy?
(1) She bought $4.40 worth of stamps.
(2) She bought an equal number of $0.15 stamps and $0.29 stamps.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Given: Joanna bought only $0.15 stamps and $0.29 stamps.
Let C = number of $0.15 stamps purchased
Let E = number of $0.29 stamps purchased
Target question: What is the value of C?
Statement 1: She bought $4.40 worth of stamps
We can write the equation
0.15C + 0.29E = 4.40
IMPORTANT: In high school we learned that, if we're given 1 equation with 2 variables, we cannot find the value of either variable.
However, if we
restrict the variables to positive integers within a certain range of values, then there are times when we can find the value of a variable if we're given 1 equation with 2 variables.
To determine whether this is the case here, let's examine all possible values of E.
If E = 0, then the entire $4.40 was spent on $0.15 stamps. Since 0.15 does NOT divide evenly into 4.40,
it cannot be the case that E = 0
If E = 1, then $0.29 was spent on $0.29 stamps, leaving the remaining $4.11 to be spent on $0.15 stamps. Since 0.15 does NOT divide evenly into 4.11,
it cannot be the case that E = 1
If E = 2, then $0.58 was spent on $0.29 stamps, leaving the remaining $3.82 to be spent on $0.15 stamps. Since 0.15 does NOT divide evenly into 3.82,
it cannot be the case that E = 2
If E = 3, then $0.87 was spent on $0.29 stamps, leaving the remaining $3.53 to be spent on $0.15 stamps. Since 0.15 does NOT divide evenly into 3.53,
it cannot be the case that E = 3
IMPORTANT: At this point, we might speed up our solution by recognizing that, in order for 0.15 to divide evenly into a number,
that number must end with 5 or 0.
Also recognize that, in order for the resulting value to end with a 5 or 0,
E must be divisible by 5
So, from this point on, we'll just check values of E that are divisible by 5.
If E = 5, then $1.45 was spent on $0.29 stamps, leaving the remaining $2.95 to be spent on $0.15 stamps. NICE! $2.95 ends with a 5. So this MIGHT work. Unfortunately, 0.15 does NOT divide evenly into 2.95. So,
it cannot be the case that E = 5
Keep going!
If E = 10, then $2.90 was spent on $0.29 stamps, leaving the remaining $1.50 to be spent on $0.15 stamps. 1.50/0.15 = 10 = C. So, one possible solution is E = 10 and C = 10
If E = 15, then $4.35 was spent on $0.29 stamps, leaving the remaining $0.05 to be spent on $0.15 stamps. Doesn't work.
If E = 20, then $5.80 was spent on $0.29 stamps. Hmmm. Looks like we can stop here!
So, there is only
one possible scenario that meets the given conditions.
So, it MUST be the case that E = 10 and
C = 10
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: She bought an equal number of $0.15 stamps and $0.29 stamps.
We have no idea how much money Joanna spent on stamps.
As such, there are infinitely many scenarios that satisfy statement 2. Here are two:
Case a: She bought 3 $0.29 stamps and 3 $0.15 stamps. In this case, the answer to the target question is
C = 3
Case b: She bought 8 $0.29 stamps and 8 $0.15 stamps. In this case, the answer to the target question is
C = 8
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
