If n=(33)^43 + (43)^33 wat is the unit digit??
The approach which i followed was lyk i multiplied 33*33=1089,43*43 =...9
9+9=18,unit digit 8 but its wrong:(:(
is there any other easy approach??????
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unit digit problem
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Anindya Madhudor
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You need to find the pattern in the exponential.
When the last digit of any number is 3, you have the pattern 3, 9, 7, 1 for powers of 1, 2 ,3,4. This pattern repeats. So, it will be same for powers of 5, 6, 7, 9.
You divide the power by 4 and find the remainder.
43 divided by 4 leaves 3 as remainder. So, the unit digit will be 7.
33 divided by 4 leaves 1 as remainder. So, the unit digit will be 3.
Add the two units digit. Units digit of of n is 0.
When the last digit of any number is 3, you have the pattern 3, 9, 7, 1 for powers of 1, 2 ,3,4. This pattern repeats. So, it will be same for powers of 5, 6, 7, 9.
You divide the power by 4 and find the remainder.
43 divided by 4 leaves 3 as remainder. So, the unit digit will be 7.
33 divided by 4 leaves 1 as remainder. So, the unit digit will be 3.
Add the two units digit. Units digit of of n is 0.
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ceilidh.erickson
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Anindya is correct, you want to look for patterns in the units digits.
I just wanted to mention one more thing... whenever you see something like 33^43, which would be impossible to compute in 10 minutes, let alone 2 minutes, don't do any computation! Ask yourself - what is the shortcut here? There must be one. The GMAT never intends for you to do long multiplication or long division, so try to think about the concepts rather than computing.
I just wanted to mention one more thing... whenever you see something like 33^43, which would be impossible to compute in 10 minutes, let alone 2 minutes, don't do any computation! Ask yourself - what is the shortcut here? There must be one. The GMAT never intends for you to do long multiplication or long division, so try to think about the concepts rather than computing.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
