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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