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Q.)Average of five numbers is 61. If the average of first and third number is 69 and the average of second and fourth number is 69, what is the fifth number?

(a) 31

(b) 29

(c) 25

(d) 35

[SNAP Question , SNAP 2013 Question , Number System , Average]

Solution : Let the five numbers be ${ X }_{ 1 },{ X }_{ 2 },{ X }_{ 3 },{ X }_{ 4 },{ X }_{ 5 }$

Average of five numbers is 61

=> $\frac { { X }_{ 1 }{ +X }_{ 2 }+{ X }_{ 3 }+{ X }_{ 4 }+{ X }_{ 5 } }{ 5 } =61$

=> ${ { X }_{ 1 }{ +X }_{ 2 }+{ X }_{ 3 }+{ X }_{ 4 }+{ X }_{ 5 } }$ = 61*5 = 305 ——– (I)

Average of first and third number is 69

=> $\frac { { X }_{ 1 } + { X }_{ 3 } }{ 2 } =69$

=> ${ X }_{ 1 } + { X }_{ 3 }$ = 69*2 = 138 ————(II)

Average of second and fourth number is 69

=> $\frac { { X }_{ 2 } + { X }_{ 4 } }{ 2 } =69$

=> ${ X }_{ 2 } + { X }_{ 4 }$ = 69*2 = 138 ————(III)

Now , (I) – (II) – (III), We get ,

${ X }_{ 5 } $ = 305 – 138 – 138 = 305 – 276 = 29

Hence , the fifth number = 29.

Hence ,OPTION(b)