VJesus12 wrote: ↑Sat Jan 30, 2021 11:12 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.
Answer:
A
Source: Official Guide
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
