UNITS DIGITS – 2

If you have not gone through unit digit -1 concept, please go through that before going forward with this article. In this article, we are going to solve some GMAT questions related to unit digit concept.

 

Question – 1

If n = (33)^43 + (43)^33 what is the units digit of n?
A. 0
B. 2
C. 4
D. 6
E. 8

Solution –

n = (33)^43 + (43)^33

Let’s find the unit digit of (33)^43

Unit digit of (33)^43 = Unit digit of (3)^43

Now let’s create unit digit cycle for 3,

Now, write 43 in form of 4n + k

43 = 4 * (10) + 3

Hence,

Unit digit of (33)^43 = Unit digit of (3)^43 = Unit digit of (3) ^ 3 = 7

………………….(1)

 

Let’s find the unit digit of (43)^33

Unit digit of (43)^33 = Unit digit of (3)^33

 

We already know the unit digit cycle for 3 has 4 different values. Hence, write 33 in form of 4n + k

33 = 4 * (8) + 1

Hence,

Unit digit of (43)^33 = Unit digit of (3)^33 = Unit digit of (3)^( 4 * (8) + 1) = Unit digit of (3) ^ 1 = 3

………………….(2)

 

Now let’s find the unit value of n,

Unit digit of n = Unit digit of ((33)^43 + (43)^33)

= Unit digit of (33)^43 + Unit digit of (43)^33

= Unit digit of (7 + 3)                                                                     (Using (1) and (2))

= 0

The correct answer is A(0).

 

Question – 2

If n = 27^435 – 27^434 what is the units digit of n?
A. 0
B. 2
C. 4
D. 6
E. 8

 

Solution –

n = 27^435 – 27^434

In question where we are dealing with negative sign, to find the unit digit of expression, first try to remove the negative sign from expression –

n = 27^435 – 27^434

= 27^434 (27 – 1)

= 27^434 * 26

 

Now,

Unit digit of n = Unit digit of (27^434 * 26)

= (Unit digit of 27^434) * (Unit digit of 26)

= Unit digit of ((Unit digit of 7^434) * 6)

………………………(1)

 

To find Unit digit of 7^434, first draw the unit digit cycle for 7

Now that we know that the unit digit cycle of 7 has 4 different values, write 434 in the form of 4n + k

434 = 4 * 108 + 2

Hence,

Unit digit of 7^434 = Unit digit of 7^(4 * 108 + 2)

= Unit digit of 7^2

= 9

………………………(2)

 

Using equation (1) and (2),

Unit digit of n = Unit digit of ((Unit digit of 7^434) * 6)

= Unit digit of (9 * 6)

= Unit digit of (54)

= 4

The correct answer is C(4).

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