my exam is tomrrow - please help with this stupid simple eqn

[desiguy]

2^5+2^5 + 3^5+3^5+3^5

options:
5^6
13^5
2^6+3^6
2^7+3^8
4^5+9^5


how to solve this without breaking it up ?

my exam is tomorrow.....please can someone help !!

[sudhir3127]

take 2^5 comon and 3^5 comon

2^5(2)+ 3^5(3)

hence 2^6+3^6

hope its clear..

All the very best for ur exam...

[desiguy]

Thanks sudhir ...a ton

[evansbd]

The solution provided seems simple...but can someone explain the math?

Are the exponents being multiplied or is there more factoring not shown in the solution.


2(2^5) + 3(3^5)

I see that 2^5 = 32, so 2(2^5) = 64, which is 2^6.
I would have picked the correct answer because the others do not have the same first term on a real GMAT but what about factoring or doing the math of 3^5 or something similar w/o a calculator.

[evansbd]

repost

[Canman]

Don't overthink the problem. No need to multiply out.

Once you recognize that 2^5+2^5+3^5+3^5+3^ = 2(2^5)+3(3^5) you need to just take the next step and realize that you now have:

2^1(2^5) + 3^1(3^5) and add the exponents to arrive at:

2^6+3^6

[Ian Stewart]

The solution provided seems simple...but can someone explain the math?

Are the exponents being multiplied or is there more factoring not shown in the solution.


2(2^5) + 3(3^5)

I see that 2^5 = 32, so 2(2^5) = 64, which is 2^6.
I would have picked the correct answer because the others do not have the same first term on a real GMAT but what about factoring or doing the math of 3^5 or something similar w/o a calculator.

There are (at least) two ways to see why the answer is correct. We can factor:

2^5 + 2^5 + 3^5 + 3^5 + 3^5 = 2^5(1+1) + 3^5(1+1+1) = 2*2^5 + 3*3^5 = 2^6 + 3^6

Or we can understand that when we add something to itself, this is exactly what it means to multiply something by 2: x+x = 2x. Thus 2^5 + 2^5 = 2*2^5 = 2^6. And if you add something to itself three times, that's the same as multiplying by 3: x+x+x = 3x, so 3^5 + 3^5 + 3^5 = 3*3^5 = 3^6.