Aptitude Questions : Number System Set 6

Hello Aspirants. Welcome to Online Quantitative Aptitude Section with explanation in AffairsCloud.com. Here we are creating question sample in Number System, which is common for all the competitive exams. We have included Some questions that are repeatedly asked in bank exams !!

1. What will be the Unit digit of 27!
   A.0
   B.1
   C.3
   D.4
   E.None of these
   
   Answer & Explanation

   Answer – A.0
   Explanation :
   1*2*3*………………………………26*27
   Factorial after 6 should end with 0
   
   
   
2. x ^p × x ^q × x ^r = 1 then p³+q³+r³ is  equal to
   A.0
   B.1
   C.pqr
   D.3pqr
   E.None of these
   
   Answer & Explanation

   Answer – D.3pqr
   Explanation :
   x ^p × x ^q × x ^r = 1
   x ^p+q+r  = 1
   x ⁰ = 1 => p+q+r = 1
   p³+q³+r³ – 3pqr = (p+q+r)(p2+q2+r2-pq-qr-rp)
   p³+q³+r³ – 3pqr = 0
   p³+q³+r³ = 3pqr
   
   
   
3. If the divisor is five times the quotient and six times the remainder, if the remainder is 5 then the dividend is
   A.225
   B.300
   C.185
   D.412
   E.None of these
   
   Answer & Explanation

   Answer – C.185
   Explanation :
   Q=6, R = 5
   Dividend = divisor*Q + R
   Dividend = 30*6 + 5 = 180+5 = 185
   
   
   
4. If the sum and the product of 2 numbers are 25 and 144 respectively then the difference of the number should be
   A.11
   B.9
   C.7
   D.15
   E.None of these
   
   Answer & Explanation

   Answer – C.7
   Explanation :
   A+B = 25
   AB = 24
   (a-b)² = (a+b)² – 4ab
   (a-b)² = 25² – 4(144)
   (a-b)² = 625 – 576
   (a-b)² = 49
   a-b =  7
   
   
   
5. The sum of the two digit number is 11. The number obtained by reversing the digit is 27  less than the original number.Then the original number is
   A.74
   B.47
   C.65
   D.83
   E.None of these
   
   Answer & Explanation

   Answer – A.74
   Explanation :
   4+7 = 11
   74-47 = 27
   
   
   
6. The product of 2 consecutive even number is 1224, then one of the number is
   A.26
   B.36
   C.28
   D.42
   E.None of these
   
   Answer & Explanation

   Answer – B.36
   Explanation :
   34*36 = 1224
   
   
   
7. 21²+22²+23²+…………………30² = ?
   A.5640
   B.9455
   C.6585
   D.2870
   E.None of these
   
   Answer & Explanation

   Answer – C.6585
   Explanation :
   1²+2²+3²+…………………n² = 1/6[n(n+1)(2n+1)]
   = 30*31*61/6 – 20*21*41/6
   = 9455 – 2870 = 6585
   
   
   
8. A number when divided by 361 gives a remainder 47. If the Same number is divided by 19 ,the remainder is
   A.18
   B.11
   C.9
   D.13
   E.None of these
   
   Answer & Explanation

   Answer – C.9
   Explanation :
   47÷19=> remainder 9
   Ex : 769 ÷ 361 => remainder 47
   769 ÷ 19 => remainder 9
   
   
   
9. The respective ratio between the  two digit of a number is 5:3, if the digit at the one’s place is twice the digit at ten’s place.What is the number ?
   A.63
   B.21
   C.12
   D.Can’t be determined
   E.None of these
   
   Answer & Explanation

   Answer – D.Can’t be determined
   Explanation :
   2x/x = 5/3
   6x = 5x
   
   
   
10. N is the smallest number which when added to the 2000 makes the resulting number divisible by 12, 16, 18 and 21, Then the N is
    A.11
    B.7
    C.9
    D.16
    E.None of these
    
    Answer & Explanation

    Answer – D.16
    Explanation :
    LCM of 12, 16, 18, 21 = 1008
    1008*2 = 2016
    N = 16
    
    
    

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