Given below are two statements: Statement I: The set of numbers (7,8,9, \a, \b, 10,8,7) has an arithmetic mean of 9 and mode(most frequently occurring number) as 8 , Then \a \times \b=120. Statement II : Let \a and \b be two positive integers such that \a+\b+\a \times \b=84, then \a+\b=20. In the light of the above statements, choose the most appropriate answer from the options given below

Correct Answer is : Both Statement I and Statement II are correct

Both Statement I and Statement II are correct

Both Statement I and Statement II are incorrect

Statement I is correct but Statement II is incorrect

Statement I is incorrect but Statement II is correct

CMAT 2022 Solved Question Paper

Question : 19 of 100

Marks: +1, -0

Given below are two statements:
Statement I: The set of numbers

(7,8,9, \a, \b, 10,8,7)

has an arithmetic mean of 9 and mode(most frequently occurring number) as 8 , Then

\a × \b=120

.

Statement II : Let

\a

and

\b

be two positive integers such that

\a+\b+\a × \b=84

, then

\a+\b=20

.

In the light of the above statements, choose the most appropriate answer from the options given below

Solution:

Statement I:
Given arithmetic mean of

(7,8,9, \a, \b, 10,8,7)

is 9 and mode is 8

7+8+9+\a+\b+10+8+7=9× 8

49+\a+\b=72

\a+\b=23

It is mentioned that mode is 8,8 occurred twice and 7 also occurred twice. Therefore, a or b should be 8
If

\a=8, \b=15

\b=8, \a=15

\a \b=120

Statement I is true Statement II:

\a+\b+\a \b=84

1+\a+\b+\a \b=85

(1+\a)(1+\b)=85

85=1 × 85 \or 5 × 17

It cannot be

1 × 85

, as it is mentioned both a and b are positive integers
If

1+\a=5,1+\b=17

\a=4

and

\b=16

1+\a=17,1+\b=5

\a=16

and

\b=4

In both cases,

\a+\b=20

Statement II is true
Answer is option A.

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