model 2 divisibility, multiples, add and subtract based number system 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) 32
(b) 2
(c) 39
(d) 40
The correct answers to the above question in:
Answer: (c)
Let the required number of persons be x.
According to the question, $2x^2$ = $3042$
or $x^2$ = $3042/2$ = 1521
or x = $√{1521}$ = 39
Practice number system (model 2 divisibility, multiples, add and subtract based number system) Online Quiz
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Read more divide multiple add subtract Based Quantitative Aptitude Questions and Answers
Question : 1
When a number is divided by 893, the remainder is 193. What will be the remainder when it is divided by 47 ?
a) 5
b) 3
c) 33
d) 25
Answer »Answer: (a)
Here, 893 is exactly divisible by 47.
Hence, the required remainder is obtained on dividing 193 by 47.
∴ Remainder = 5
Question : 2
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 : 3
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 : 4
A number consists of two digits. If the number formed by interchanging the digits is added to the original number, the resulting number (i.e. the sum) must be divisible by
a) 9
b) 11
c) 3
d) 5
Answer »Answer: (b)
Let the number be 10x + y
After interchanging the digits, the number obtained = 10y + x
According to the question,
Resulting number
= 10x + y + 10y + x
= 11x + 11y
= 11 (x + y) which is exactly divisible by 11.
Question : 5
When a number is divided by 24, the remainder is 16. The remainder when the same number is divided by 12 is
a) 4
b) 3
c) 8
d) 6
Answer »Answer: (a)
Required remainder = 16 – 12 = 4
(because 24 is a multiple of 12.)
Question : 6
Two numbers, when divided by 17, leave remainders 13 and 11 respectively. If the sum of those two numbers is divided by 17, the remainder will be
a) 11
b) 13
c) 4
d) 7
Answer »Answer: (d)
First number (X) = 17x + 13
Second number (Y) = 17y + 11
∴${X + Y}/17$ = ${17(x + y)}/17 + {13 + 11}/17$
∴Required remainder = Remainder obtained on dividing
11 + 13
i.e. 24 by 17 = 7
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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