Bull78 wrote:
Martha bought several pencils. If each pencil was either a 23 cent pencil or a 21 pencil, how many 23 cent pencils did martha buy?
(1) Martha bought a total of 6 pencils
(2) The total value of the pencils Martha bought was 130 cents.
Target question: How many 23 cent pencils did Martha buy? Given: Martha bought several pencils. Each pencil was either a 23-cent pencil or a 21-cent pencil. Statement 1: Martha bought a total of 6 pencils Clearly, statement 1 is NOT SUFFICIENT
Statement 2: The total value of the pencils Martha bought was 130 cents.This statement APPEARS to be insufficient. However, since the pencils cost 21 cents and 23 cents, we can't buy many for 130 cents.
So, let's LIST THE POSSIBLE CASES
Case a: Martha bought
ZERO 23-cent pencils (for a total of 0 cents).
This means she spent all 130 cents on the 21-cent pencils. However,
21 cents does not evenly divide into 130 cents So, it cannot be the case that Martha bought
ZERO 23-cent pencils
Case b: Martha bought
ONE 23-cent pencil.
This means she spent the remaining 107 cents on the 21-cent pencils. However,
21 cents DOES NOT evenly divide into 107 cents.
So, it cannot be the case that Martha bought
ONE 23-cent pencil
Case c: Martha bought
TWO 23-cent pencils (for a total of 46 cents).
This means she spent the remaining 84 cents on the 21-cent pencils.
21 cents divides into 84 cents exactly FOUR TIMES.
So, it's possible that Martha bought
TWO 23-cent pencils and
FOUR 21-cent pencils
In this case, the answer to the target question is
Martha bought TWO 23-cent pencilsCase d: Martha bought
THREE 23-cent pencils (for a total of 69 cents).
This means she spent the remaining 61 cents on the 21-cent pencils. However,
21 cents DOES NOT evenly divide into 61 cents.
So, it cannot be the case that Martha bought
THREE 23-cent pencils
Case e: Martha bought
FOUR 23-cent pencils (for a total of 92 cents).
This means she spent the remaining 38 cents on the 21-cent pencils. However,
21 cents DOES NOT evenly divide into 38 cents.
So, it cannot be the case that Martha bought
FOUR 23-cent pencils
Case f: Martha bought
FIVE 23-cent pencils (for a total of 15 cents).
This means she spent the remaining 15 cents on the 21-cent pencils. However,
21 cents DOES NOT evenly divide into 15 cents.
So, it cannot be the case that Martha bought
FIVE 23-cent pencils
Now that we've examined all of the cases, the only possible solution is the one described in case c
So, it MUST be the case that
Martha bought TWO 23-cent pencilsSince we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
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