# Sets: Table A/B

Every day, Guy takes the same \$\$N\$\$ sandwiches to work. Of these, how many more sandwiches contain only ginger jam than contain only peanut butter? >(1) Every day, Guy takes five more sandwiches with no peanut butter than sandwiches with no ginger jam. >(2) Every sandwich Guy takes to work contains only peanut butter, only ginger jam, or only a mixture of the two.
Incorrect. [[snippet]] According to Stat. (1+2) combined, the two statements allow for a more direct translation of Stat. (1). If a sandwich does not contain peanut butter, it must contain ginger jam, or \$\$J\$\$. Stat. (2) dictates that there are no other options. Likewise, a sandwich that does not contain ginger jam must contain peanut butter, or \$\$P\$\$. Thus, Stat. (1) can be translated as \$\$J = P+5\$\$, so \$\$J-P=5\$\$. **Stat.(1+2) → S → C**.
Incorrect. [[snippet]] Stat. (1) looks tempting, but notice that the question stem does _not_ limit Guy's choice of sandwiches to _only_ peanut butter, _only_ ginger jam, or _only_ a mixture of the two. For example, if Guy also takes sandwiches which contain avocado and ginger jam, these will be counted among the "sandwiches with no peanut butter." Without knowing the make of the sample space, it is not possible to find \$\$J-P\$\$, so **Stat.(1) → IS → BCE**. Stat. (2) provides an important piece of information: each of the sandwiches is either \$\$P\$\$ or \$\$J\$\$, or a mixture of the two. However, this does not enable you to calculate \$\$J-P\$\$, so **Stat.(2) → IS → CE**.
Correct. [[snippet]] Stat. (1) looks tempting, but notice that the question stem does _not_ limit Guy's choice of sandwiches to _only_ peanut butter, _only_ ginger jam, or _only_ a mixture of the two. For example, if Guy also takes sandwiches which contain avocado and ginger jam, these will be counted among the "sandwiches with no peanut butter." Without knowing the make of the sample space, it is not possible to find \$\$J-P\$\$, so **Stat.(1) → IS → BCE**. Stat. (2) provides an important piece of information: each of the sandwiches is either \$\$P\$\$ or \$\$J\$\$, or a mixture of the two. However, this does not enable you to calculate \$\$J-P\$\$, so **Stat.(2) → IS → CE**. According to Stat. (1+2) combined, the two statements allow for a more direct translation of Stat. (1). If a sandwich does not contain peanut butter, it must contain ginger jam, or \$\$J\$\$. Stat. (2) dictates that there are no other options. Likewise, a sandwich that does not contain ginger jam must contain peanut butter, or \$\$P\$\$. Thus, Stat. (1) can be translated as \$\$J = P+5\$\$, so \$\$J-P=5\$\$. **Stat.(1+2) → S → C**.
Incorrect. [[snippet]] Stat. (2) provides an important piece of information: each of the sandwiches is either \$\$P\$\$ or \$\$J\$\$, or a mixture of the two. However, this does not enable you to calculate \$\$J-P\$\$, so **Stat.(2) → IS → ACE**.
Incorrect. [[snippet]] Stat. (1) looks tempting, but notice that the question stem does _not_ limit Guy's choice of sandwiches to _only_ peanut butter, _only_ ginger jam, or _only_ a mixture of the two. For example, if Guy also takes sandwiches which contain avocado and ginger jam, these will be counted among the "sandwiches with no peanut butter." Without knowing the make of the sample space, it is not possible to find \$\$J-P\$\$, so **Stat.(1) → IS → BCE**.
Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient to answer the question asked.
Statement (2) ALONE is sufficient, but Statement (1) alone is not sufficient to answer the question asked.
BOTH Statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
EACH statement ALONE is sufficient to answer the question asked.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

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