gmat prep exponents

[japan1453]

OA A

[arzanr]

You cannot add exponents when doing addition, but only during multiplication. Therefore:

(2^2)(2^2) = 2^4
but
(2^2)+(2^) != 2^4

As far as I know, you simply have to work out this problem, there is no quick solution -

2+2+4+8+16+32+64+128+256 = 512 = 2^9

[pandeyvineet24]

Another way to solve the problem.

2 + 2 + 2^2 + 2^3 + 2^4 .... + 2^8.

= 4 + 2^2 + 2^3 ....

= 2 (2^2) + 2 ^ 3 + 2^4 + 2^5... + 2^8

= 8 + 2^3 + 2^4 ... + 2^8

= 2(2^3) + 2^4 + ....2^8

trend continues. and finally you will be left with 2(2^8) = 2^9
Which is answer A

[logitech]

You cannot add exponents when doing addition, but only during multiplication. Therefore:

(2^2)(2^2) = 2^4
but
(2^2)+(2^) != 2^4

As far as I know, you simply have to work out this problem, there is no quick solution -

2+2+4+8+16+32+64+128+256 = 512 = 2^9

There is a quick solution:

If you multiply both side with 2

LEFT side = ANSWER

2 x LEFT SIDE = 2 x ANSWER

you will realize that left side can also be arranged as:

ANSWER + 2^9 = 2x ANSWER

so ANSWER = 2^9

[abhijeetsinghai]

there's another quick soln:---2 + (2 + 2^2 + 2^4 +......)

the nom in bracket can be taken as sum of GP(geo metric progr.)

now the sumof terms of GP is: a(r^n-1)/ (r-1)

where a=first term which is 2 in this case
r= general ration or diff
so, answer will be sum + first term i.e 2

2 + 2(2^8-1)/2-1
2 + 2 x 255
2 + 510
512
2^9

[mrsmarthi]

there's another quick soln:---2 + (2 + 2^2 + 2^4 +......)

the nom in bracket can be taken as sum of GP(geo metric progr.)

now the sumof terms of GP is: a(r^n-1)/ (r-1)

where a=first term which is 2 in this case
r= general ration or diff
so, answer will be sum + first term i.e 2

2 + 2(2^8-1)/2-1
2 + 2 x 255
2 + 510
512
2^9

No need of solving it.

2 + 2(2^8-1)/2-1 = 2 + 2^9 -2 = 2^9 is the answer.

[aroon7]

Really good one...
Logitech u r cool

You cannot add exponents when doing addition, but only during multiplication. Therefore:

(2^2)(2^2) = 2^4
but
(2^2)+(2^) != 2^4

As far as I know, you simply have to work out this problem, there is no quick solution -

2+2+4+8+16+32+64+128+256 = 512 = 2^9

There is a quick solution:

If you multiply both side with 2

LEFT side = ANSWER

2 x LEFT SIDE = 2 x ANSWER

you will realize that left side can also be arranged as:

ANSWER + 2^9 = 2x ANSWER

so ANSWER = 2^9