model 6 operations of consecutive numbers (odd, even, square, etc.) 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 : 11 [SSC CGL 2000]
The sum of the squares of three consecutive natural numbers is 2030. Then, what is the middle number?
a) 27
b) 25
c) 26
d) 28
Answer »Answer: (c)
Let the three consecutive natural numbers be x, x + 1 and x + 2.
According to question,
$x^2 + (x + 1)^2 + (x + 2)^2$ = 2030
or $x^2 + x^2 + 2x + 1 + x^2 + 4x + 4$ = 2030
or $3x^2 + 6x + 5 = 2030 $
or $3x^2 + 6x – 2025$ = 0
or $x^2 + 2x – 675$ = 0
or $x^2 + 27x – 25x – 675$ = 0
$x (x + 27) – 25 (x + 27)$ = 0
or $(x – 25) (x + 27)$ = 0
$x = 25 and – 27$
∴ Required number = $x$ + 1 = 25 + 1 = 26
Question : 12 [SSC Constable 2012]
The sum of all those prime numbers which are not greater than17 is
a) 41
b) 59
c) 58
d) 42
Answer »Answer: (c)
Prime numbers upto 17⇒ 2, 3, 5, 7, 11, 13, 17
Required sum = 2 + 3 + 5 + 7 + 11 + 13 + 17 = 58
Question : 13 [SSC CGL Tier-II 2014]
Find the sum of all positive multiples of 3 less than 50
a) 408
b) 400
c) 404
d) 412
Answer »Answer: (a)
Sum of all multiples of 3 upto 50
= 3 + 6 + ..... + 48
= 3 (1 + 2 + 3 + .... + 16)
= 3×${16(16+1)}/2$= 3 × ${272}/2$ = 408
[Since 1+2+3+…+n = ${n(n+1)}/2$]
Question : 14 [SSC CGL Prelim 2003]
What is the sum of two consecutive even numbers, the difference of whose square is 84?
a) 42
b) 38
c) 34
d) 46
Answer »Answer: (a)
$(x + 2)^2 – x^2 = 84$
or $x^2 + 4x + 4 – x^2$ = 84
4x = 84 – 4 = 80
x = $80/4$ = 20
x + 2 = 20 + 2 = 22
∴ The required sum = 20 + 22 = 42
Question : 15
Which one of the following is a factor of the sum of first twentyfive natural numbers ?
a) 13
b) 26
c) 24
d) 12
Answer »Answer: (a)
1 + 2 + 3 + ... + n = ${n(n+1)}/2$
1 + 2 + 3 + .. + 25 = ${25(25 + 1)}/2$ = 25 × 13
Hence, 13 is a factor of required sum.
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 255+ Number System Fraction Aptitude Questions Answers »
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Top +299 Aptitude Number System (Find Unit Place) Mcq Quiz »
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199+ Aptitude Number System: Consecutive Numbers MCQ Quiz »
model 6 operations of consecutive numbers (odd, even, square, etc.) Shortcuts »
Click to Read...model 6 operations of consecutive numbers (odd, even, square, etc.) Online Quiz
Click to Start..number system Shortcuts and Techniques with Examples
-
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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