model 4 finding unit place of a number Section-Wise Topic Notes With Detailed Explanation And Example Questions
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The following question based on number system topic of quantitative aptitude
(a) 6
(b) 1
(c) 5
(d) 4
The correct answers to the above question in:
Answer: (d)
$(251)^98$ = ......1
$(21)^29$ = ....1
$(106)^100$ = ......6
$(705)^35$ = ....5
$(16)^4$ = .....6
259 = ......9
∴ Required answer = 1 + 1 – 6 + 5 – 6 + 9 = 16 – 12 = 4
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Read more unit place Based Quantitative Aptitude Questions and Answers
Question : 1
The digit in unit’s place of the number $(1570)^2 + (1571)^2 + (1572)^2 + (1573)^2$ is :
a) 3
b) 4
c) 2
d) 1
Answer »Answer: (b)
Unit's digit in $(1570)^2$ = 0
Unit's digit in $(1571)^2$ = 1
Unit's digit in $(1572)^2$ = 4
Unit's digit in $(1573)^2$ = 9
∴ Required unit’s digit = Unit’s digit (0 +1+4 + 9) = 4
Question : 2
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
Question : 3
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 : 4
The unit digit in the product $(122)^173$ is
a) 8
b) 2
c) 6
d) 4
Answer »Answer: (b)
$2^1 = 2, 2^2 = 4, 2^3 = 8, 2^4 = 16, 2^5 = 32$
Unit digit in the product of $(122)^173$
= Unit digit in $(122)^1$ = 2
(1 = remainder when 173 is divided by 4).
Question : 5
The digit in the unit’s place of the product $(2464)^1793×(615)^317×(131)^491$ is
a) 5
b) 0
c) 3
d) 2
Answer »Answer: (b)
$(4)^{2m}$ gives 6 at unit digit.
$(4)^{2m +1}$ gives 4 at unit digit.
$(5)^n$ gives 5.
The same is the case with 1.
Required digit = Unit’s digit in the product of 4×5 × 1 = 0
Question : 6
One’s digit of the number $(22)^23$ is
a) 2
b) 4
c) 8
d) 6
Answer »Answer: (c)
Unit’s digit in the expansion of $(22)^23$
= Unit’s digit in the expansion of $(2)^23$
Now, $2^1 = 2, 2^2 = 4, 2^3 = 8, 2^4 = 16, 2^5 = 32$
i.e. 2 repeats itself after the index 4.
On dividing 23 by 4, remainder = 3
∴ Unit’s digit in $(2)^23$ = Unit’s digit in $(2)^3$ = 8
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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