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Subject Test Math 2

Question 16 of 28

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SAT Subject Test
number of digital cameras sold during a 3-day sale
  Day 1 Day 2 Day 3
Model X 20 18 3
Model Y 16 5 8
Model Z 19 11 10

The table above shows the number of digital cameras that were sold during a three-day sale. The prices of models X, Y, and Z were $ 99, $ 199, and $ 299, respectively. Which of the following matrix representations gives the total income, in dollars, received from the sale of the cameras for each of the three days?

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open square brackets table row 20 18 3 row 16 5 8 row 19 11 10 end table close square brackets left square bracket table row 99 199 299 end table right square bracket

Correct Answer: 
No

open square brackets table row 20 18 3 row 16 5 8 row 19 11 10 end table close square brackets open square brackets table row cell table row 99 end table end cell row cell table row 199 row 299 end table end cell end table close square brackets

Correct Answer: 
No

left square bracket table row 99 199 299 end table right square bracket open square brackets table row 20 18 3 row 16 5 8 row 19 11 10 end table close square brackets

Correct Answer: 
Yes

open square brackets table row 99 row 199 row 299 end table close square brackets space open square brackets table row 20 18 3 row 16 5 8 row 19 11 10 end table close square brackets

Correct Answer: 
No

99 open square brackets table row 20 18 3 row 16 5 8 row 19 11 10 end table close square brackets plus 199 open square brackets table row 20 18 3 row 16 5 8 row 19 11 10 end table close square brackets plus 299 open square brackets table row 20 18 3 row 16 5 8 row 19 11 10 end table close square brackets

Correct Answer: 
No

The correct answer is C.

A correct matrix representation must have exactly three entries, each of which represents the total income, in dollars, for one of the three days. The total income for Day 1 is given by the arithmetic expression 99 cross times 20 plus 199 cross times 16 plus 299 cross times 19, which is the single entry of the matrix product open square brackets table row 99 199 299 end table close square brackets open square brackets table row 20 row 16 row 19 end table close square brackets; in the same way, the total income for Day 2 is given by 99 cross times 18 plus 199 cross times 5 plus 299 cross times 11, the single entry of open square brackets table row 99 199 299 end table close square brackets open square brackets table row 18 row 5 row 11 end table close square brackets; and the total income for Day 3 is given by 99 cross times 3 plus 199 cross times 8 plus 299 cross times 10, the single entry of open square brackets table row 99 199 299 end table close square brackets open square brackets table row 3 row 8 row 10 end table close square brackets. Therefore, the matrix representation left square bracket table row 99 199 299 end table right square bracket open square brackets table row 20 18 3 row 16 5 8 row 19 11 10 end table close square brackets gives the total income, in dollars, received from the sale of the cameras for each of the three days.
Although it is not necessary to compute the matrix product in order to answer the question correctly, left square bracket table row 99 199 299 end table right square bracket open square brackets table row 20 18 3 row 16 5 8 row 19 11 10 end table close square brackets equals open square brackets table row cell 10 comma 845 end cell cell 6 comma 066 end cell cell 4 comma 879 end cell end table close square brackets.

Question Difficulty: 
medium