model 4 finding unit place of a number Practice Questions Answers Test with Solutions & More Shortcuts
number system PRACTICE TEST [6 - 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.)
Question : 1 [SSC CGL Tier-II 2015]
By interchanging the digits of a two digit number we get a number which is four times the original number minus 24. If the unit’s digit of the original number exceeds its ten’s digit by 7, then original number is
a) 18
b) 29
c) 58
d) 36
Answer »Answer: (b)
Let the two–digit number be 10x + y where x < y.
Number obtained on reversing the digits =10y + x
According to the question,
10y + x = 4 (10x + y) – 24
40x + 4y – 10y – x = 24
39x – 6y = 24
13x – 2y = 8 ....(i)
Again, y – x = 7
y = x + 7 ....(ii)
13x – 2 (x + 7) = 8
13x – 2x – 14 = 8
11 x = 14 + 8 = 22
x = $22/11$ = 2
From equation (ii),
y – 2 = 7 ⇒ y = 2 + 7 = 9
Number = 10x + y =10×2+9= 29
Question : 2
The last digit of $(1001)^2008$ + 1002 is
a) 6
b) 0
c) 4
d) 3
Answer »Answer: (d)
Last digit of $(1001)^2008$ + 1002 = 1 + 2 = 3
Question : 3
In a two–digit number, the digit at the unit’s place is 1 less than twice the digit at the ten’s place. If the digits at unit’s and ten’s place are interchanged, the difference between the new and the original number is less than the original number by 20. The original number is
a) 47
b) 59
c) 35
d) 23
Answer »Answer: (a)
Ten’s digit = x
Unit’s digit = 2x – 1
Original number = 10x + (2x – 1) = 12x – 1
New number = 10 (2x – 1) + x
= 20x – 10 + x = 21x – 10
(21x – 10) – (12x + 1) = 12x – 1 – 20
9x – 9 = 12x – 21
3x = 12 ⇒ x = 4
Original number = 12x – 1 = 12 × 4 – 1 = 47
Question : 4 [SSC SO 2007]
The unit digit in the expansion of $(2137)^754$ is
a) 9
b) 1
c) 7
d) 3
Answer »Answer: (a)
Expression = $(2137)^754$
Unit’s digit in 2137 = 7
Now, $7^1 = 7, 7^2 = 49, 7^3 = 343, 7^4 = 2401, 7^5$ = 16807, ...
Clearly, after index 4, the unit’s digit follow the same order.
Dividing index 754 by 4 we get remainder = 2
∴ Unit’s digit in the expansion of $(2137)^754$ = Unit’s digit in the expansion of $(2137)^2$ = 9
Question : 5 [SSC CPO S.I.2008]
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
IMPORTANT quantitative aptitude EXERCISES
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Basic Number System Aptitude Questions Practice Test with PDF »
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Top +299 Aptitude Number System (Find Unit Place) Mcq Quiz »
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model 4 finding unit place of a number Shortcuts »
Click to Read...model 4 finding unit place of a number Online Quiz
Click to Start..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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