model 4 finding unit place of a number Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (a)

$7^1 = 7, 7^2 = 49, 7^3 = 343, 7^4 = 2401, 7^5$ = 16807

i.e. The unit’s digit repeats itself after power 4.

Remainder after we divide 245 by 4 = 1

Unit’s digit in the product of $(4387)^245 × (621)^72$ = Unit’s digit in the product of $(4387)^1 × (621)^72$ = 7 × 1 = 7

Answer: (b)

Unit digit in $(264)^4$ i.e. 4 × 4 × 4 × 4 is 6

Unit digit in $(264)^100$ is also 6.

Now, $(264)^102 = (264)^100 × (264)^2$

= (Unit digit 6) × (Unit digit 6)=36

∴ Unit digit is 6

Similarly,

$(264)^103 + (264)^100 × (264)^3$

= (Unit digit 6) × (Unit digit 4)=24

∴ Unit digit is 4

Therefore, the unit digit in $(264)^102 + (264)^103$ is

6 + 4 = 10 i.e. 0.

Answer: (c)

Unit’s digit in $3^4$ = 1

So, unit digit in $3^164$ = 1

Now, unit's digit in $(2153)^167$ = unit digit in $3^167$

= unit digit in $3^3$ = 7

Answer: (a)

$7^1 = 7, 7^2 = 49, 7^3 = 343, 7^4 = 2401$

$3^1 = 3; 3^2 = 9; 3^3 = 27; 3^4 = 81;$

i.e. the digit at unit’s place gets repeated after power 4. Unit 6 remains same for any power.

∴ Required unit’s digit = Unit’s digit in the product of $7^3 × 6 × 3^1$ = 4

Answer: (d)

$7^1 = 7$, $7^2 = 9$, $7^3 = 3$, $7^4 = 1$

$7^5 = 7$, $7^6 = 9$, $7^7 = 3$, ... $7^104 = 1$

ie, $105/4$ = [R(1)]

ie, $7^105$= 7