 # Applications Of Power Cycle

There are various applications of the power cycle in the CAT quantitative aptitude questions. Some of the important applications and related questions are given here. These examples can help the candidates to get well acquainted with the power cycle and its applications in different questions.

### 1. Power Expression of the Form ab

In this, direct questions are asked to find the unit digit of a power expression of the form ab

#### Example 1:

Find the last digit of 455.

### 2. Remainder Questions

In these questions, the remainder based questions are asked where the divisibility of the divisor depends only on its unit digit (like when the divisors are 2,5,10).

### 3. Power Cycle Questions Occurring In Groups

#### Logical Shortcut:

Since there are 10 groups involved, the unit digit of the first group has to be multiplied by 10 to get the answer. There is absolutely no need to even find the unit digit of the first group as any number multiplied by 10 gives 0 as the unit digit.

### 4. To Find The Right Most Non-Zero Integer

#### Example 6:

Find the rightmost non-zero integer of the expression 1430343+1470367?

#### It can be easily observed that 1470367 has more number of zeroes as compared to 1430343. hence, the rightmost non-zero integer will depend on the unit digit of only 1430343, which in turn will depend on the unit digit of 3343 343 can be written as 4k+3 In the power cycle of 3 (3,9,7,1), the third digit is 7. Hence, the last non-zero integer in the expression is 7.

The candidates can visit CAT quantitative aptitude to know learn more topics and know how to solve the numerical questions easily. BYJU’S also provide various engaging video lessons to help the CAT aspirants learn various important CAT exam topics effectively.

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