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
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gmat prep exponents
Source: Beat The GMAT — Problem Solving |
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
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
There is a quick solution:arzanr wrote: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
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
LGTCH
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"DON'T LET ANYONE STEAL YOUR DREAM!"
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
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.abhijeetsinghai wrote: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
2 + 2(2^8-1)/2-1 = 2 + 2^9 -2 = 2^9 is the answer.
Really good one...
Logitech u r cool
Logitech u r cool
logitech wrote:There is a quick solution:arzanr wrote: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
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
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