SSC CGL NUMBER SYSTEM MCQ ENGLISH

Correct Answer : (B)

Explanation : Given:A 60 -page book has n lines per page, when the number of lines were reduced by 3 on each page, then the number of pages will increase by 10 .Total number of lines = Page × Lines per page ⇒60×n=60nNow the number of lines when 3 lines are reduced =n−3Number of pages when lines are reduced =70Total number of lines =70×(n−3)=70n−210So,60n=70n−210⇒10n=210⇒n=21

Correct Answer : (B)

Explanation : Let be assume the age of last year is 1, 4, 9, 16, 25, 36, etc. After 2 years shall be a cube. After 2 years age will be 3, 6, 11, 18, 27, 38, etc. So, now we can say last year age was 25 and the next year is 27 years and his present year is 26 years. Next, his age will be cube = 64 years. The required difference = 64 – 26 = 38

Correct Answer : (A)

Explanation : The number is 5132416p is divisible by 3. Let the number is p⇒ (5+1+3+2+4+1+6+p)3=(22+p)3It is possible value of p is 2, 5, 8…∴ Digit will come in place of ? is 8.

Correct Answer : (C)

Explanation : (10)3=1000(20)3=8000(25)3=15625We can say that largest 4 digit number which is perfect cube lies between (20)3 and (25)3(21)3 will give the unit digit as 1Also from option there is only one possible case⇒(21)3=9261∴ The largest four digit number which is a perfect cube is 9261 .

Correct Answer : (C)

Explanation : Given:39931 unit digit 332 unit digit 933 unit digit 734 unit digit 135 unit digit 3…After 4 power unit digits repeat again.Now,⇒399=(34)24×(33)⇒399=(1)24×7=(1)×7Unit place =1×7=7∴ The place of 399 is 7 .

Correct Answer : (C)

Explanation : Given,741259AB is divisible by 40 .Divisibility rule of 8 : The number from the last 3 -digits should be divided by 8Divisibility rule of 5 : The unit digit should be 0 or 5Checking for 5 :The value of B has to be 0 or 5 to be divisible by 5As it has to be divisible by 40 , it has to be even. So, B has to be 0 .Number becomes 741259A0Now checking for 8 :Last 3 digits =9A0Dividing 9A0 by 8,A has to be 2 or 6( as 1 will remains when 9 will be divided by 8 for it to be completely divisible by 8 .Least value of A=2 ; B=0∴5A+3B=10

Correct Answer : (C)

Explanation : Given:x3+x2+16 is exactly divisible by x , where x is a positive integer.Let a number N be equal to x3+x2+16 .N=x3+x2+16Now divide NxNx=x3+x2+16x⇒x2+x+(16x)As N is divisible by x so 16 must be divisible by x .Values of x that can divide 16 are 1,2,4,8 and 16 .So, there are total 5 values of x that can divide N without leaving the remainder.

Correct Answer : (B)

Explanation : Let, the bigger digit =x and smaller digit =yAccording to the question,⇒x+y=12 …(1)⇒x−y=4 …(2)From (1) and (2) we get, x=8 and y=4∴ The product of the two digits of the number =xy=8×4=32

Correct Answer : (D)

Explanation : Given,Five-digit number 235xy is divisible by 3,7 and 11 .Divisibility rule of 3 : The sum of its digit is divisible by 3 .For 3x+y=2,5,8,11Divisibility rule of 11 :The difference of the sum of odd place and even place is zero or multiples of 11. The result is divisible by 11 .For 11,(7+y)−(3+x)=0 or 11y=2 then x=6,x+y=8Divisibility rule of 7 : To make a pair of 3 from unit digit than subtract left over pair, The result is divisible by 7 .For 7,562−023=539It is also divisible by 7Number =23562 and x=6,y=2Now,3x−4y=18−8=10∴ The value of 3x−4y is 10 .

Correct Answer : (A)

Explanation : Given,When positive numbers x,y and z are divided by 31 , the remainders are 17,24 and 27 .If a number (x) is divided by (a) leaves remainder (b), then x=a×n+b [where n is an integer]Let the numbers be,x=31×1+17=48y=31×1+24=55z=31×1+27=58(4x−2y+3z)=256Now,256=31×8+8∴ When (4x−2y+3z) is divided by 31, the remainder will be 8 .

Correct Answer : (B)

Explanation : The unit place of 71=7,72=9,73=3,74=1The unit place of 795=723×4×73=3The unit place of 31=3,32=9,33=7,34=1The unit place of 359=314×4×32=9The unit of 795 is 3 , which is less than 9Then take 3 has 13 (by carry rule)The unit place of N=795−358=13−9=4∴ The unit digit of N is 4 .

Correct Answer : (C)

Explanation : For finding the pieces we have to divide 42.5 by 0.85.⇒ (42.5)0.85 = 50∴ The correct answer is 50.

Correct Answer : (B)

Explanation : 5−[4−{3−(3−3−6)}]=5−[4−{3+6}]=5+5=10∴ The required value =10

Correct Answer : (C)

Explanation : When we divide 1056 by 23,The remainder is 2When we add 2 to 1056 it becomes 1058 and it becomes divisible by 23.

Correct Answer : (B)

Explanation : Let number be x then its reciprocal be 1x .According to the question,2x+3x=252⇒2×2+3=25×2⇒4×2+6=25x⇒4×2−25x+6=0⇒(4x−1)(x−6)=0⇒x=6,14Value of number cannot be a fraction.So, the number is 6 .

Correct Answer : (A)

Explanation : Let the number be xNow, (x−12)×12=18 ⇒(2x−12)×12=18 ⇒4x−2=1 ⇒x=34

Correct Answer : (D)

Explanation : Let the number be ’10x + y’. The number after reversing the digits will be ’10y + x’.10x + y – (10y + x) = 27 ⇒ 9x – 9y = 27 ⇒ x – y = 3. So, the difference between both digits must be 3. Such numbers will be 41, 52, 63, 74, 85, and 96. There are six such numbers.

Correct Answer : (D)

Explanation : Given,I=a2+b2+c2 , where a and b are consecutive integers and c=abLet a and b be 1 and 2 respectively. ∵ ( a and b are consecutive numbers)So, c=1×2=2NowI=12+22+22I=9Now let the values of a and b be 2 and 3 respectively.So, c=2×3=6Now,I=22+32+62I=49In both cases, it is coming out to be the square of an odd integer.

Correct Answer : (A)

Explanation : As we know,(xn−an)→ divisible by (x+a) if n is even number.By using the formula, we get(xn−an)→ divisible by (x+a) if n is even number. Where,⇒(172020−12020)(17+1)=(−1)202018When 172020 is divided by 18 getting remainder 1 ,=17202018=(18−1)202018=(−1)2020=1

Correct Answer : (B)

Explanation : Given:The sum of the digits of a two-digit number =13The difference between the number and that formed by reversing the digits =27Calculation:Let the digit in the 10th place and unit place are a and b respectively.So, the two-digit number is 10a+b .According to the question,a+b=13…(1)Again, according to the question,(10b+a)−(10a+b)=27=10b+a−10a−b=27=9b−9a=27=9(a−b)=27=a−b=3−(2)By adding equation (1) and (2) , we get(a+b)+(a−b)=13+3=2a=16=a=8From equation (1) ,b=13−a=13−8=5Now, the product of the digits =8×5=40∴ The product of the digits of the number is 40 .

Correct Answer : (C)

Explanation : Given,The average of twenty-five numbers is 54 and The average of the first 13 numbers and that of the last 13 numbers is 52.8 and 62.2Average = Sum of the observationNumber of the observationSum of the 25 numbers =54×25=1350Sum of the first 13 numbers =13×52.8=686.4Sum of the last 13 numbers =13×62.2=808.613th number =( Sum of the first 13 numbers + Sum of the last 13 numbers )−( Sum of the 25 numbers )=(686.4+808.6)−(1350)=1495−1350=145Sum of the remaining 24 numbers =(1350−145)=1205Average of the remaining 24 numbers =120524=50.2∴ The average of the remaining 24 numbers is 50.2

Correct Answer : (D)

Explanation : The first n natural numbers are 1,2,3,…,nNow, 1+2+3+…+nn=15⋯(1)We know that sum of first n natural numbers is n(n+1)2⇒1+2+3+…+n=n(n+1)2⋯(2)Substituting (2) in (1) we get⇒n(n+1)2n=15 ⇒n+1=30⇒n=30−1=29

Correct Answer : (C)

Explanation : Given:Sum of three numbers 264.Now,Let the first, second, third number be x, y, z.According to the question,⇒ x = 2y⇒ z = 13 xThen, z = 13 × 2y = 23 yNow, Sum of three numbers 264.⇒ x + y + z = 264⇒ 2y + y + 23 y = 264⇒ 113 y = 264⇒ y = 72∴ The second number is 72.

Correct Answer : (A)

Explanation : Given:p,q,r , and s be positive natural numbers having three exact factors including 1 and the number itselfq>p and both are two-digit numbersr>s and both are one-digit numbersAs know we know,If n=a2Here ‘ a ‘ is a prime number.Then its factors =(1,a,a2)Here, q>p and both are two-digit numbersSo, possible values =52 and 72According to the concept,p=52 or 25 [Factors =1,5,25]q=72 or 49[ Factors =1,7,49]Here, r>s and both are one-digit numbersSo, possible values =22 and 32s=22 or 4 [Factors =1,2,4 ]r=32 or 9 [Factors =1,3,9]p−q−1r−s=25−49−19−4⇒−255=−5−5=−4−1=−s−1∴ Required answer is −s−1 .

Correct Answer : (B)

Explanation : Given:d(n) is the number of positive divisors of a positive number n .d(5)=2 (positive divisors of 5 are 1 and 5 )d(11)=2 (positive divisors of 11 are 1 and 11 )d(16)=5 (positive divisors of 16 are 1,2,4,8 and 16 )d(55)=4 (positive divisors of 55 are 1,5,11 and 55 )Checking Choices1. d(5)=d(11)⇒2=22. d(5)⋅d(11)=d(55)⇒2×2=4⇒4=43. d(5)+d(11)=d(16)⇒2+2=5We can conclude that choice 1 and 2 are correct.

Correct Answer : (D)

Explanation : Let the number be x .According to the question,53×x=145We multiply the above equation by 35 on both side.⇒x=145×35⇒x=29×3⇒x=87∴ The number is 87 .

Correct Answer : (B)

Explanation : Remainder when 15 divided by 4=1Remainder when 25 or 32 divided by 4=0Remainder when 35 or 243 divided by 4=3Remainder when 45 or 1024 divided by 4=0Remainder when 55 or 3125 divided by 4=1Remainder =1+3+1=5Remainder when 5 divided by 4=1

Correct Answer : (A)

Explanation : Given:An eleven digit number 23P62971335 .As we know,A number is divisible by 9 when the sum of all its digits is divisible by 9 .Now,23P62971335 is divisible by 9 (the smallest odd composite number is 9 ).So sum of digits of 23P62971335 must be divisible by 9 .Sum of digits =2+3+P+6+2+9+7+1+3+3+5=41+PAt P=4 we get 45 which is divisible by 9 .

Correct Answer : (B)

Explanation : Let the given number is xNow, 16% of x + 21 =xx−16×100=21 ⇒84×100=21 ⇒x=1004=25

Correct Answer : (D)

Explanation : Given:An=Pn+1 , where Pn is the product of the first n prime numbersAs we know,The product of first prime numbers becomes also a prime number.Odd number + odd number = always an even numberOdd number + even number = always an odd numberEven number + enev number = always an even numberNow,Here Pn=2,3,5,7,11,13,…We know that when we add one in the product of first prime numbers it becomes also a prime numberSo, An is a prime number, not a composite numberAll the prime number ( except 2) are an odd numberSo, An+2 is always an odd number.(∵ Odd number + even number = always an odd number )And An+1 is always an even number.(∵ Odd number + odd number = always even number )