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.
It is important to note how a problem is RESTRICTED.
This problem is restricted to POSITIVE INTEGERS: Joanna cannot by 1/2 of a stamp or -2 stamps.
Statement 1: 15x + 29y = 440.
When a problem is restricted to positive integers, BE SUSPICIOUS: quite often 1 linear equation with 2 variables will provide sufficient information to determine the value of each variable.
Here, we need to determine whether more than one combination of positive integers will satisfy the equation 15x + 29y = 440.
Rephrasing the equation, we get:
29y = 440 - 15x = (multiple of 5) - (multiple 5) = multiple of 5.
Since 29y must be a multiple of 5, there are only 3 options:
Case 1: 5*29 = 145.
Case 2: 10*29 = 290.
Case 3: 15*29 = 435.
In each case, the amount remaining must be a MULTIPLE OF 15:
Case 1: 440-145=295, which is not a multiple of 15.
Case 2: 440-290=150, which is a multiple of 15.
Case 3: 440-435=5, which is not a multiple of 15.
Since only ONE CASE is viable, SUFFICIENT.
Statement 2: She bought an equal number of $0.15 stamps and $0.29 stamps.
No way to determine how many 15-cent stamps were purchased.
INSUFFICIENT.
The correct answer is
A.
A savvy test-taker -- one familiar with how DS problems are written and structured -- could take the following approach:
Clearly, the two statements combined provide sufficient information to determine how many 15-cent stamps were purchased.
Eliminate E.
Clearly, statement 2 does not by itself provide sufficient information.
If all we know is that Joanna purchased an equal number of each type of stamp, she could have purchased 1 of each type, 2 of each type, 3 of each type, etc.
Eliminate B and D.
The correct answer must be C or A.
The relationships described by the two statements are extremely straightforward.
If the OA here is C, then virtually EVERYONE will answer the question correctly, rendering the question pretty much useless.
Thus, the correct answer almost certainly is
A.
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