Question #8736334b - SAT Suite Question Bank

Modded SAT Question Bank by Abdullah Mallik

$Data set A consists of the 5 numbers: 72, 73, 73, 76, and 76. Data set B consists of the 5 numbers: 61, 64, 74, 85, and x.$

Data set A and data set B each contain 5 numbers. If the mean of data set A is equal to the mean of data set B, what is the value of x ?

Toggle Answer

Tip: Press CTRL/Command to toggle answer

Correct Answer: C

Rationale

Choice C is correct. The mean of a data set is found by dividing the sum of the values in the data set by the number of values in the data set. Therefore, the mean of data set A is $the fraction with numerator 72, plus 73, plus 73, plus 76, plus 76, and denominator 5$ , which simplifies to 74. The mean of data set B is represented by the equation $the fraction with numerator 61, plus 64, plus 74, plus 85, plus x, and denominator 5$ , or $the fraction with numerator 284 plus x, and denominator 5$ . It’s given that the mean of data set A is equal to the mean of data set B. Therefore, the equation $74 equals, the fraction with numerator 284 plus x, and denominator 5$ can be used to solve for x. Multiplying both sides of this equation by 5 yields $370 equals, 284 plus x$ . Subtracting 284 from both sides of this equation yields $86 equals x$ .

Choices A, B, and D are incorrect and may result from calculation errors.

Question Difficulty: