Find the value of A.
   A A
×    A
---------
2 7 A
---------


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Answer:

5

Step by Step Explanation:
  1. We see that A, when multiplied by A, gives A at the ones digit of the product.
  2. Let us multiply each digit from 1 to 9 with itself and look at the products.
  3. 1 × 1 = 1
  4. 2 × 2 = 4
  5. 3 × 3 = 9
  6. 4 × 4 = 16
  7. 5 × 5 = 25
  8. 6 × 6 = 36
  9. 7 × 7 = 49
  10. 8 × 8 = 64
  11. 9 × 9 = 81

    12. From the above list, we see that A = 5 or 6.

  12. Now, let us calculate the value of AA × A for 5 and 6.
       5 5
    ×    5
    ---------
    2 7 5
    ---------

       6 6
    ×    6
    ---------
    3 9 6
    ---------
  13. On comparing the products with those given in the question, we see that the value of A is 5.

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