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FIND THE UNIT DIGHT IN THE PRODUCT (132)^436× (56)^43×(178)^53×(459)^582?
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FIND THE UNIT DIGHT IN THE PRODUCT (132)^436× (56)^43×(178)^53×(459)^5...



Unit Digit in the Product of Exponents

  1. Break down the numbers:
    Separate each number into its base and exponent components.


  2. Find the unit digits:
    Determine the unit digits of each base raised to its respective exponent.


  3. Multiply the unit digits:
    Multiply all the unit digits together to find the unit digit of the final product.
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Legrand Casino recently purchased a slot machine; a gaming machine, which had a main unit and five sub-units, labeled as Alpha, Gamma, Beta, Theta and Omega. The main as well as each of the sub-units had five slots, labeled as Red, Blue, Grey, Black and Yellow. The game with this slotting machine involved punching the right coin in the right slot in the right sequence i.e. one after another. For example, if coin number 3 is punched into slot Blue in Gamma sub-unit and if the main unit also pushes the coin to Blue slot, then the punch is said to be a winning shot. If the coin in the sub-unit is punched into the right slot when compared to the corresponding coin in the main unit, then the player gets Rs. 1,000 as reward. On the other hand, if the slots do not match then the player loses Rs. 333. Each player gets 25 coins to play.However, after a couple of days this slotting machine developed a peculiar problem. In the sub-units irrespective of the slot you intended to put in the coin, the sub-unit pushed the coin into the slot it wanted to every time on its own.To find out which slots in the sub-units had developed the snag, the technician played on all the sub-units using 25 coins in each of the sub-units.After some kind of analysis he found that the main machine and each of the sub-units could identify right slots for 15 coins, however for the balance of 10 coins listed below, each of the sub-units assumed different positions as right slots when compared to the main unit whose allocation of slots was the benchmark for performance of other sub-units.On playing with these sub-units, the technician earned Rs. 17,000, Rs. 11,660, Rs. 18,330, Rs. 14,330 and Rs. 18,330 respectively from each of Alpha, Gamma, Beta, Theta and Omega. All the amount being rounded off to previous tens figure. Of the ten slots which had developed the snag, there was atleast one sub-unit which identified the right slot for exactly 9 of the 10 slots.The table below gives the slots identified by each of the sub-units as right slots for the 10 problematic coins.Q. For the 10 incorrectly slotted coins, how many slots were commonly and correctly identified by more than 1 sub-unit?

Legrand Casino recently purchased a slot machine; a gaming machine, which had a main unit and five sub-units, labeled as Alpha, Gamma, Beta, Theta and Omega. The main as well as each of the sub-units had five slots, labeled as Red, Blue, Grey, Black and Yellow. The game with this slotting machine involved punching the right coin in the right slot in the right sequence i.e. one after another. For example, if coin number 3 is punched into slot Blue in Gamma sub-unit and if the main unit also pushes the coin to Blue slot, then the punch is said to be a winning shot. If the coin in the sub-unit is punched into the right slot when compared to the corresponding coin in the main unit, then the player gets Rs. 1,000 as reward. On the other hand, if the slots do not match then the player loses Rs. 333. Each player gets 25 coins to play.However, after a couple of days this slotting machine developed a peculiar problem. In the sub-units irrespective of the slot you intended to put in the coin, the sub-unit pushed the coin into the slot it wanted to every time on its own.To find out which slots in the sub-units had developed the snag, the technician played on all the sub-units using 25 coins in each of the sub-units.After some kind of analysis he found that the main machine and each of the sub-units could identify right slots for 15 coins, however for the balance of 10 coins listed below, each of the sub-units assumed different positions as right slots when compared to the main unit whose allocation of slots was the benchmark for performance of other sub-units.On playing with these sub-units, the technician earned Rs. 17,000, Rs. 11,660, Rs. 18,330, Rs. 14,330 and Rs. 18,330 respectively from each of Alpha, Gamma, Beta, Theta and Omega. All the amount being rounded off to previous tens figure. Of the ten slots which had developed the snag, there was atleast one sub-unit which identified the right slot for exactly 9 of the 10 slots.The table below gives the slots identified by each of the sub-units as right slots for the 10 problematic coins.Q. If the correct slot for coin numbered 8 was Yellow, then what would have been the correct slot for coin number 21?

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FIND THE UNIT DIGHT IN THE PRODUCT (132)^436× (56)^43×(178)^53×(459)^582?
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FIND THE UNIT DIGHT IN THE PRODUCT (132)^436× (56)^43×(178)^53×(459)^582? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about FIND THE UNIT DIGHT IN THE PRODUCT (132)^436× (56)^43×(178)^53×(459)^582? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for FIND THE UNIT DIGHT IN THE PRODUCT (132)^436× (56)^43×(178)^53×(459)^582?.
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