model 2 divisibility, multiples, add and subtract based number system 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 : 21 [SSC CPO S.I.2010]
A number, when divided by 221, leaves a remainder 64. What is the remainder if the same number is divided by 13 ?
a) 1
b) 0
c) 12
d) 11
Answer »Answer: (c)
Here, the first divisor (221) is a multiple of second divisor (13)
Hence, required remainder = remainder obtained on dividing 64 by 13 = 12
Question : 22 [SSC CGL Prelim 2000]
If $17^200$ is divided by 18, the remainder is—
a) 16
b) 17
c) 2
d) 1
Answer »Answer: (d)
$(17)^200$ = $(18 –1)^200$
We know that
$ (x + a)^n$ =$x^n + nx^(n–1).a + {n(n - 1)}/{1 × 2}x^{n - 2}a^2 +{n(n - 1)(n - 2)}/{1 × 2 × 3}x^{n - 3}a^3+…+a^n$
We see that all the terms on the R.H.S. except $a^n$ has x as one of its factor and hence are divisible by x. So,$(x +a)^n$ is divisible by x or not will be decided by $a^n$ . Let x = 18, a = – 1 and n = 200
∴ $(18 –1)^200$ is divisible by 18 or not will depend on $(–1)^200$ as all other terms in its expansion will be divisible by 18 because each of them will have 18 as one of their factors.
$(–1)^200$ = 1 (Since 200 is even)
1 is not divisible by 18 and is also less than 18.
∴1 is the remainder
Question : 23 [SSC CGL Prelim 2008]
A number when divided by 5 leaves a remainder 3. What is the remainder when the square of the same number is divided by 5 ?
a) 2
b) 1
c) 4
d) 3
Answer »Answer: (c)
If the quotient in the first case be x.
Then, number = 5x + 3
On Squaring, the number
= $(5x + 3)^2$
= $25x^2$ + 30x + 9
On dividing by 5, remainder
= 9 – 5 = 4
Question : 24 [SSC CGL Prelim 2007]
64329 is divided by a certain number. While dividing, the numbers, 175, 114 and 213 appear as three successive remainders. The divisor is
a) 224
b) 184
c) 296
d) 234
Answer »Answer: (d)
Question : 25 [SSC CGL Prelim 2005]
A number when divided by 6 leaves remainder 3. When the square of the same number is divided by 6, the remainder is :
a) 1
b) 0
c) 3
d) 2
Answer »Answer: (c)
The remainder will be same. On dividing 9 by 6, remainder = 3 On dividing 81 by 6, remainder = 3
IMPORTANT quantitative aptitude EXERCISES
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Basic Number System Aptitude Questions Practice Test with PDF »
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Number System on Divisibility Multiple Add Subtract Live Test »
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Top +299 Aptitude Number System (Find Unit Place) Mcq Quiz »
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model 2 divisibility, multiples, add and subtract based number system Shortcuts »
Click to Read...model 2 divisibility, multiples, add and subtract based number system 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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