Problem Solving

I got this question off a online practice test, but it looks fishy...

1/(2exp12) + 2/(2exp13) + 3/(2exp14) + 4/(2exp15) = ?

a) 1/(2exp10)

b) 1/(2exp12)

c) 15/(2exp15)

d) 2/(2exp10)

e) 23/(2exp16)


** exp = ^ and the above are the fraction 1/2 , with denominator raised to different powers

I know how to do this question through simplifying, but the official solution started simplifying by what looks to me is either a typo or incorrect assumption.

Can someone give their opinion on how to solve?

OA to follow

No matter how I do it, I get 13/2^14.

We can reduce to:

1/2^12 + 1/2^12 + 3/2^14 + 1/2^13

Our common denominator is 2^14, so:

2^2/2^14 + 2^12/2^14 + 3/2^14 + 2^1/2^14

(4+4+3+2)/2^14 = 13/2^14

You could also use 2^15 as your common denominator. After conversion, you'd get 26/2^15 = 13/2^14.

The OA is A.

It says: If we express the numerators as powers of 2, then we would get

1/(2exp12) + 2/(2exp13)+ 4/(2exp14) + 8/(2exp15)

however I keep getting

1/(2exp12) + (2/2)/(2exp12)+ (3/4)/(2exp12) + (4/8)/(2exp12)

but the OA goes on to say that their simplification reduces to

1/(2exp12) + 1/(2exp12)+ 1/(2exp12) + 1/(2exp12) = 4/(2exp12)

4/(2exp12) = 1/(2exp10)

The way I understand it, if youre simplifying your denominator your factor stays in the demonator which results in the fractions in the manner that I simplified.

Help anyone?

So I'm not crazy that this looks fishy...thanks Stu.

let X = 2exp12.

When I simplify I get

1/x + 1/x + 3/4(x) + 4/8(x)

13/4(x)

I'm tossing this test...

the question stem has a '3' in the numerator and that has to be accounted somewhere in the answer , when it is all 2s in the denominator.

OA is not convincing.

I guess some typo is there in the question.

evansbd wrote:The OA is A.

It says: If we express the numerators as powers of 2, then we would get

1/(2exp12) + 2/(2exp13)+ 4/(2exp14) + 8/(2exp15)

For this to be true, the original question would have to be:

1/2^12 + 2^1/2^13 + 2^2/2^14 + 2^3/2^15

or

1/2^12 + 2/2^13 + 4/2^14 + 8/2^15

which would indeed reduce to:

4(1/2^12) = 2^2/2^12 = 1/2^10