model 4 finding unit place of a number Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 6 EXERCISES
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The following question based on number system topic of quantitative aptitude
(a) 9
(b) 1
(c) 7
(d) 3
The correct answers to the above question in:
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
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Read more unit place Based Quantitative Aptitude Questions and Answers
Question : 1
The unit’s digit in the product $7^71 × 6^63 × 3^65$ is
a) 4
b) 1
c) 3
d) 2
Answer »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
Question : 2
What will be the unit digit in the product $7^105$ ?
a) 1
b) 5
c) 9
d) 7
Answer »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
Question : 3
There is a number consisting of two digits, the digit in the units’ place is twice that in the tens’ place and if 2 be subtracted from the sum of the digits, the difference is equal to $1/6$ th of the number. The number is
a) 23
b) 26
c) 24
d) 25
Answer »Answer: (c)
Ten’s digit of original number = x
Unit’s digit = 2x
Number = 10x + 2x = 12x
According to the question,
3x – 2 = $1/6$ × 12x
3x – 2 = 2x
3x – 2x = 2
x = 2
Number = 12x = 12 × 2 = 24
Question : 4
Unit digit in $(264)^102 + (264)^103$ is :
a) 8
b) 0
c) 6
d) 4
Answer »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.
Question : 5
Find the unit digit in the product $(4387)^245 × (621)^72$ .
a) 7
b) 1
c) 5
d) 2
Answer »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
Question : 6
The unit digit in the sum of $(124)^372 + (124)^373$ is
a) 0
b) 5
c) 2
d) 4
Answer »Answer: (a)
$4^1 = 4, 4^2 = 16, 4^3 = 64, 4^4 = 256, 4^5 = 1024$
Remainder on dividing 372 by 4 = 0
Remainder on dividing 373 by 4 = 1
Required unit digit = Unit digit of the sum of 6 + 4 = 0
GET number system PRACTICE TEST EXERCISES
model 1 basic number system
model 2 divisibility, multiples, add and subtract based number system
model 3 fraction of numbers
model 4 finding unit place of a number
model 5 smallest and largest fraction/numbers
model 6 operations of consecutive numbers (odd, even, square, etc.)
number system Shortcuts and Techniques with Examples
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model 1 basic number system
Defination & Shortcuts … -
model 2 divisibility, multiples, add and subtract based number system
Defination & Shortcuts … -
model 3 fraction of numbers
Defination & Shortcuts … -
model 4 finding unit place of a number
Defination & Shortcuts … -
model 5 smallest and largest fraction/numbers
Defination & Shortcuts … -
model 6 operations of consecutive numbers (odd, even, square, etc.)
Defination & Shortcuts …
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