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...
my exam is tomrrow - please help with this stupid simple eqn
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sudhir3127
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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.
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.
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
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
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Ian Stewart
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There are (at least) two ways to see why the answer is correct. We can factor:evansbd wrote: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.
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.
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