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# Data Sufficiency: Simultaneous Equations

What is the total cost of five identical chairs and five identical tables? >(1) Three chairs and two tables cost a total of \$195. >(2) Two chairs and three tables cost a total of \$255.
Did you solve for the separate values of a chair and a table?
Good work! Solving for each variable separately, unless asked for, is usually a waste of precious time. Don't even bother to solve for the separate or combined cost. As long as the statements generate two _different_ equations (i.e. equations that are _not_ multiples of one another), it is possible to solve them and to find the required value. Remember that data sufficiency questions only ask if you _can_ solve for the desired value.
Incorrect. [[snippet]] Stat. (1) gives you only one two-variable equation. >\$\$3C+2T=195\$\$ It is not possible to find \$\$5C+5T\$\$, so **Stat. (1) → IS → BCE**.
Incorrect. [[snippet]] Stat. (2) by itself gives you only one two-variable equation. >\$\$2C+3T=255\$\$ It is still not possible to find \$\$5C+5T\$\$, so **Stat. (2) → IS → ACE**.
Incorrect. [[snippet]] Each statement by itself gives you only one two-variable equation, so each is insufficient on its own.
Incorrect. [[snippet]] As long as you have two different equations with two different unknowns, you can solve the equations and find the necessary value.
Actually, you don't need to do that. Solving for each variable separately, unless asked for, is usually a waste of precious time. Don't even bother to solve for the separate or combined cost. As long as the statements generate two _different_ equations (i.e. equations that are _not_ multiples of one another), it is possible to solve them and to find the required value. Remember that data sufficiency questions only ask if you _can_ solve for the desired value.
Correct. [[snippet]] Stat. (1) gives you only one two-variable equation. >\$\$3C+2T=195\$\$. It is not possible to find \$\$5C+5T\$\$ so **Stat. (1) → IS → BCE**. Stat. (2) by itself gives you only one two-variable equation. >\$\$2C+3T=255\$\$ It is still not possible to find \$\$5C+5T\$\$, so **Stat. (2) → IS → CE**. Combining both statements gives you two different two-variable equations. From here it is possible to solve for \$\$C\$\$ and \$\$T\$\$ and to find the value of \$\$5C+5T\$\$. So **Stat. (1+2) → S → C**.
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.
Of course! How else would I calculate the cost of five chairs and five tables?
No, I didn't.
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