IPMAT Question Paper 2021 | IPM Indore Quantitative Ability

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Question 16 : The unit digit in (743)⁸⁵ – (525)³⁷ + (987)⁹⁶ is ________

1. 9
2. 3
3. 1
4. 5

Video Explanation

Explanatory Answer

Units digit of (743)⁸⁵ - (525)³⁷ + (987)⁹⁶
For this we only need to worry about the unit's digits.
So the question essentially becomes 3⁸⁵ - 5³⁷ + 7⁹⁶

The last digit of the power of 3 goes into cycles of 3, 9, 7, 1 [cyclicity involving 4 numbers]
The last digit of any power of 5 is 5 [cyclicity involving 1 numbers]
And the last digit of the powers of 7 goes into cycles of 7, 9, 3, 1 [cyclicity involving 4 numbers]

So 3⁸⁵  will have the same last digit as 3¹ as 3⁸⁴ will complete the cycle and 3⁸⁵ will end with a 3.
Similarly, 7⁹⁶ will end in with a 1 and 94 is a multiple of 4 and completes the cyclicity of 7.
And the last digit of 5³⁷ will end in a 5.

So (743)⁸⁵ - (525)³⁷ + (987)⁹⁶ becomes
3 - 5 + 1
Or -1
\(\equiv\) 9

The question is " The unit digit in (743)⁸⁵ – (525)³⁷ + (987)⁹⁶ is ________ "

Hence, the answer is '9'

Choice A is the correct answer.

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