The average of four consecutive even numbers A, B,C and D is 37. What is the product of A & C ?

Options

A. 1520
B. 1368
C. 1292
D. 1224

Answer

C

Explanation

Let the even number A,B,C and D be `x,x+2,x+4 and x+6` respectively.
Now, according to the question,
`x+x+2+x+4+x+6=4xx37`
`implies 4x+12=148`
`implies 4x=148-12=136`
`implies x=(136)/(4)=34`
`implies A =34` and `C=(34+4=)38`
`impliesAxxC=34xx38=1292`
Alternative Method:
Average of consecutive even or odd numbers `=a+(n-1)`, where a is the smallest number.
So, average of four consecutive even numbers `=A+(4-1)`
or, 37`=A+3`
or, A=37-3=34
`impliesA =34, B=36,C=38,D=40`
`implies ` Product of A and C `=34xx38=1292`