either "2" or "24"

[sanju09]

If the terms of a series are either "2" or "24" and the sum of all the terms of the series is 124, then which of the following could be the number of "2s" in the series?

A. 48

B. 35

C. 32

D. 28

E. 26

OA E

[DanaJ]

The key here is with 24.
Notice that:
1*24 = 24 - 100 is left for 2's, giving us 50 2's

2*24 = 48 - 76 is left for 2's, giving us 38 2's

3*24 = 72 - 52 is left for 2's, giving us 26 2's

4*24 = 96 - 28 is left for 2's, giving us 14 2's

OR you could have all 2's, with 124 = 62*2.

I'm getting two answers.... I may have done some inccorect calculations...

[sanju09]

The key here is with 24.
Notice that:
1*24 = 24 - 100 is left for 2's, giving us 50 2's

2*24 = 48 - 76 is left for 2's, giving us 38 2's

3*24 = 72 - 52 is left for 2's, giving us 26 2's

4*24 = 96 - 28 is left for 2's, giving us 14 2's

OR you could have all 2's, with 124 = 62*2.

I'm getting two answers.... I may have done some inccorect calculations...

Oh no DanaJ! You are absolutely correct on both your approach and calculations; necessary editing has been now made to the question. Thanks

[scoobydooby]

2x+24y=124
=>x+12y=62, x and y must be integers
x values given we need to find if for the given values y is an integer

y=62-x/12

A. x=48, y=14/12 not an integer

B. x=35, y=odd/12 not an integer, (even-odd=odd)

C. x=32, y=30/12 not an integer

D. x=28, y=34/12 not an integer

E. x=26, y=36/12 integer and hence E

[lav]

way to go scooby
short n smart soln