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# Sets: Table A/B

A certain question bank has 64 GMAT questions. Of these, 22 deal with integers, and 25 are Problem Solving (PS) questions. How many questions are PS questions that deal with integers? >(1) Of the questions that deal with integers, there are four more non-PS questions than PS questions. >(2) Of the PS questions, there are seven more questions that do not deal with integers than questions that do deal with integers.
Stat. (1): Add "Of the questions that deal with integers, there are four more non-PS questions than PS questions." to the table. Put $$\color{blue}{x+4}$$ in the No-PS/Integer box and $$\color{blue}{x}$$ in the PS/Integer box.

Integer Not-integer
Total
PS $$\color{red}{?} = \color{blue}{x}$$
$$25$$
Non-PS $$\color{blue}{x+4 }$$ $$39$$
Total $$22$$ $$42$$ $$64$$
From the Integer column, it follows that >$$x+(x+4)=22$$ This uniquely determines the value of $$x$$, which is equal to the required quantity. Therefore, **Stat.(1) → S → AD**. So E is incorrect.
Stat. (2): Add "Of the PS questions, there are seven more questions that do not deal with integers than questions that do deal with integers." to the table. Put $$\color{blue}{y+7}$$ in the PS/No-Integer box and $$\color{blue}{y}$$ in the PS/Integer box.

Integer Not-integer
Total
PS $$\color{red}{?} = \color{blue}{y}$$ $$\color{blue}{y+7}$$ $$25$$
Non-PS     $$39$$
Total $$22$$ $$42$$ $$64$$
From the PS row, it follows that >$$y+(y+7)=25$$. This uniquely determines the value of $$y$$, which is equal to the required quantity. Therefore, **Stat.(2) → S → D**.
Stat. (1): Add "Of the questions that deal with integers, there are four more non-PS questions than PS questions." to the table. Put $$\color{blue}{x+4}$$ in the No-PS/Integer box and $$\color{blue}{x}$$ in the PS/Integer box.

Integer Not-integer
Total
PS $$\color{red}{?} = \color{blue}{x}$$
$$25$$
Non-PS $$\color{blue}{x+4 }$$ $$39$$
Total $$22$$ $$42$$ $$64$$
From the Integer column, it follows that >$$x+(x+4)=22$$ This uniquely determines the value of $$x$$, which is equal to the required quantity. Therefore, **Stat.(1) → S → AD**. So C is incorrect.
Stat. (1): Add "Of the questions that deal with integers, there are four more non-PS questions than PS questions." to the table. Put $$\color{blue}{x+4}$$ in the No-PS/Integer box and $$\color{blue}{x}$$ in the PS/Integer box.

Integer Not-integer
Total
PS $$\color{red}{?} = \color{blue}{x}$$
$$25$$
Non-PS $$\color{blue}{x+4 }$$ $$39$$
Total $$22$$ $$42$$ $$64$$
From the Integer column, it follows that >$$x+(x+4)=22$$ This uniquely determines the value of $$x$$, which is equal to the required quantity. Therefore, **Stat.(1) → S → AD**. So B is incorrect.
Stat. (2): Add "Of the PS questions, there are seven more questions that do not deal with integers than questions that do deal with integers." to the table. Put $$\color{blue}{y+7}$$ in the PS/No-Integer box and $$\color{blue}{y}$$ in the PS/Integer box.

Integer Not-integer
Total
PS $$\color{red}{?} = \color{blue}{y}$$ $$\color{blue}{y+7}$$ $$25$$
Non-PS     $$39$$
Total $$22$$ $$42$$ $$64$$
From the PS row, it follows that >$$y+(y+7)=25$$. This uniquely determines the value of $$y$$, which is equal to the required quantity. Therefore, **Stat.(2) → S → BD**. So A is incorrect.
Incorrect. [[snippet]] Now check stat. (1).
Correct. [[snippet]] Now check the statements.
Stat. (1): Add "Of the questions that deal with integers, there are four more non-PS questions than PS questions." to the table. Put $$\color{blue}{x+4}$$ in the No-PS/Integer box and $$\color{blue}{x}$$ in the PS/Integer box.

Integer Not-integer
Total
PS $$\color{red}{?} = \color{blue}{x}$$
$$25$$
Non-PS $$\color{blue}{x+4 }$$ $$39$$
Total $$22$$ $$42$$ $$64$$
From the Integer column, it follows that >$$x+(x+4)=22$$ This uniquely determines the value of $$x$$, which is equal to the required quantity. Therefore, **Stat.(1) → S → AD**.
Incorrect. [[snippet]] Now check stat. (1).
Incorrect. [[snippet]] If you check stat. (1):
Incorrect. [[snippet]] If you check Stat.(2):
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.