A company recorded the number of daily sales over a 7-day week. The numbers of daily sales… — GMAT

A company recorded the number of daily sales over a 7-day week. The numbers of daily sales, when arranged in ascending order, are $12, 15, 18, x, 22, y, 30$ . If the median of the 7 daily sales figures is $20$ and the arithmetic mean is $21$ , what is the value of $y$ ?

Answer: 30

Answer

The value of

y

is 30.

For an ordered set of 7 numbers, the median is the 4th term, which means

x = 20

. The total sum of the set is found by multiplying the number of terms by the mean:

7 \times 21 = 147

. Adding all known terms (

12 + 15 + 18 + 20 + 22 + 30

) gives 117. Subtracting 117 from 147 yields

y = 30

Step-by-Step Solution

Determine the value of

x

using the median definition.

x = 20

Since the 7 numbers are given in ascending order, the median is the middle (4th) term.

Calculate the total sum of all 7 numbers.

Total sum =

147

The sum of elements in a set equals the number of elements multiplied by the arithmetic mean (

7 \times 21 = 147

Sum all known numbers and set up an equation for

y

117 + y = 147

12 + 15 + 18 + 20 + 22 + 30 = 117

Solve for

y

y = 30

Subtract 117 from 147 to isolate

y

Key Concept

Using properties of median and arithmetic mean to find missing terms in an ordered data set.

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