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rss GMAT Practice Question (One of Hundreds)
What is the unit digit of Figure 1?
Correct Answer: D
Notice that 125 is a divisor of 625 (125*5 = 625). So, our left hand term would be Figure 3
  1. If we attempt to solve this problem by performing the calculations, it will take too much time. Consequently, we must proceed with a different approach.
  2. The trick to solving these types of problems lies in evaluating the units digit of each term and then doing the necessary arithmetic operation.
  3. The first term of the expression is:
    Figure 2
    Figure 3
  4. Notice that: (a.) 125 is a divisor of 625, and (b.) the power of the numerator is greater than that of the term in the denominator.
  5. With the following pieces of information
    I. 625 = 125*5
    II.  
    Figure 4
    (where x is some positive integer)
    III. For 5x where x is any positive integer the units digit will always be 5
    We find that the first term of the expression will have its unit digit as 5.
  6. The second term in the expression is 2214. The units digit of this term is 2 and the power of the expression is 14.
  7. The units digit of 2 raised to an integer follows a cyclic pattern as depicted below
  8. Basically, we divide the exponent power by 4, and write the exponent as a sum of the product of the quotient and the divisor, and the remainder. The units digit of the term will be the units digit of the term raised to the power of the remainder. Here in this problem: 14 = (4*3) + 2 (Divisor: 4, quotient:3, remained:2) So, the units digit of 214 is the units digit of 22 = 4.
    If this is confusing, you could simply find the pattern:
    21 --> units digit of 2
    22 --> units digit of 4
    23 --> units digit of 8
    24 --> units digit of 6
    25 --> units digit of 2
    ...
  9. The units digit of the first term is 5, and the units digit of the second term is 4. The units digit of the complete expression will be the sum of the two units digit, which is 5 + 4 = 9. Hence D is the correct answer choice.
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