The average of X1, X2 and X3 is 14. Twice the sum of X2 and X3 is 30. What is the value of X1 ?

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Q: 147 (IAS/1996)
The average of X1, X2 and X3 is 14. Twice the sum of X2 and X3 is 30. What is the value of X1 ?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,6,9,0,6,2,7

keywords: 

{'average': [1, 1, 0, 1], 'sum': [0, 2, 5, 4], 'x1': [0, 1, 0, 0], 'x2': [0, 1, 0, 0], 'x3': [0, 1, 0, 0], 'value': [0, 0, 1, 0]}

We have two equations here:

(1) (X1+X2+X3)/3 = 14, which indicates that the sum of X1, X2, and X3 is 42 (i.e., 14*3),

and

(2) 2*(X2+X3) = 30, which informs us that the sum of X2 and X3 is 15 (i.e., 30/2).

Substituting the value of X2 and X3 from equation (2) into equation (1), gives us X1 = 42 - 15 = 27.

Option 1, 20, and option 3, 16, cannot be the answer as they don`t satisfy these equations. Option 4, 12, is also incorrect as none of the equations can be fulfilled with this value. Option 2, 27, correctly satisfies both equations and is thus the correct answer.