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If the arithmetic mean of the two number is 10 and then geometric mean is 8, the numbers are

A) 20, 5
B) 16, 4
C) 15, 5
D) 12, 8

Correct Answer:


B) 16, 4

Description for Correct answer:
Let the numbers be x and y.

Arithmetic mean = 10

Therefore, \( \Large \frac{x+y}{2}=10\ i.e.\ x+y=20 \) ...(1)

Geometric mean is 8. \( \Large \sqrt{xy} = 8 \)

\( \Large xy = 64 \) ...(2)

\( \Large y = \frac{64}{x} \)

Put the value of y in (1)

\( \Large x+\frac{64}{x} = 20 \)

\( \Large x^{2}+64 = 20x \)

\( \Large x^{2}-20x+64=0 \)

Factorising \( \Large x^{2}-16x-4x+64 = 0 \)

\( \Large \left(x-16\right) \left(x-4\right) = 0 \)

x = 16, x = 4

If x = 16, then y = 4

If x = 4, then y = 16

Therefore, The numbers are 16, 4

Part of solved Statistics questions and answers : >> Elementary Mathematics >> Statistics

Comments

Similar Questions

1). The mode of the numbers 6, 5, 5, 4, 5, 5, 4, 4, 6 is

A). 4

B). 5

C). 6

D). None of these

2). The less reliable measure of dispersion is

A). Regression coefficient

B). Standard deviation

C). Correlation coefficient

D). Range

3). The mean of 100 observations is 60. What will be the new value of mean if 8 1s subtracted from each observation and then divided by 4.

A). 50

B). 52

C). 13

D). 14

4). The most stable measure of central tendency is

A). the mean

B). the median

C). the mode

D). geometric mean

5). Two dice are thrown together. The probability of getting a total of 3 or 8 is

A). \( \Large \frac{24}{36} \)\

B). \( \Large \frac{8}{36} \)

C). \( \Large \frac{11}{36} \)

D). \( \Large \frac{7}{36} \)

6). The height of 5 persons are 59, 63, 68, 60, 72 inches. The value of range is

A). 10

B). 13

C). 12

D). 15

7). A bag contains 4 white, 6 red and 5 blue balls out of which one ball is drawn at random. The probability that it is neither white nor red is

A). \( \Large \frac{5}{15} \)

B). \( \Large \frac{4}{15} \)

C). \( \Large \frac{6}{15} \)

D). \( \Large \frac{3}{15} \)

8). The probability of throwing either 7 or 11 with two dice is

A). \( \Large \frac{1}{6} \)

B). \( \Large \frac{2}{9} \)

C). \( \Large \frac{1}{8} \)

D). \( \Large \frac{23}{108} \)

9). If A and B are the mutually exclusive events then \( \Large P \left(A\cup B\right) \) will be

A). \( \Large P \left(A\right)+P \left(B\right) \)

B). \( \Large P \left(A\right)+P \left(b\right)+POA\cap B \)

C). \( \Large P \left(a\right)+P \left(B\right)-P \left(A\cup B\right) \)

D). \( \Large P \left(A\right)+P \left(B\right)-P \left(A\cap B\right) \)

10). The sum of deviation taken from Arithmetic mean is

A). 2

B). 0

C). 4

D). 5