Subject

Quantitative Aptitude

Class

SSCCGL Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

3.

The product of two number is 1575 and their quotient is 9/7. Then the sum of the numbers is

  • 74

  • 78

  • 80

  • 90


C.

80

Let the numbers be x and y.
∴   (x) x (y) = 1575 (given)  ...(i)
And,
 straight x over straight y space equals space 9 over 7  (given)  ...(ii)
Multiply (i) x (ii)
therefore space xy space cross times space straight x over straight y space equals space 1575 space cross times space 9 over 7
space rightwards double arrow space space straight x squared space equals space 2025
rightwards double arrow space space space straight x space equals space square root of 20205 space equals space 45
therefore space space xy space equals space 1575
rightwards double arrow space space straight y space equals space 1575 over straight x space equals space 1575 over 45 space equals space 35
therefore space space straight x space plus space straight y space equals space 45 space plus space 35 space equals space 80


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7.

When (6767 + 67) is divided by 68, the remainder is

  • 1

  • 63

  • 66

  • 67


C.

66

Shortcut Method:
First see power values, i.e. 6767 divide this value by 68. 
  If power is even then remainder would be 1, but if power is odd then divide it in usual manner. Here 67 is less than 68 so we take 67 as remainder.
Now (Remainder  + 67) should be divided by 68
             = (67 + 67) = 134 should be divided by 68, so remainder would be 66.
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2.

If 738A6A is divisible by 11, then the value of A is

  • 6

  • 3

  • 9

  • 1


C.

9

A number is exactly divisible by 11, if the difference between the sum of digits at even and odd places be either 0 or a multiple of 11.
∴  (A + A + 3) - (6 + 8 + 7) = 0
⟹   2A + 3 = 21
⟹   2A = 21 - 3 = 18
therefore space space straight A space equals space 18 over 2 space equals space 9

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10.

Given that square root of 4096 space equals space 64 comma the value of square root of 4096 space plus space square root of 40.96 end root space plus space square root of 0.004096 end root is

  • 70.4

  • 70.464

  • 71.104

  • 71.4


B.

70.464

square root of 4096 space equals space 64
therefore space space square root of 40.96 end root space equals space square root of 4096 over 100 end root space equals space 64 over 10 space equals space 6.4
square root of 0.004096 end root space equals space square root of 4096 over 1000000 end root space equals space 64 over 1000 space equals space 0.064
∴  Expression = 64 + 6.4 + 0.064 = 70.464
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4.

The value of fraction numerator left parenthesis 8.3 right parenthesis to the power of 3.6 end exponent cross times space left parenthesis 9 right parenthesis to the power of 2.7 end exponent over denominator left parenthesis 81 right parenthesis to the power of 4.2 end exponent space cross times space left parenthesis 3 right parenthesis end fraction is

  • 3

  • 6

  • 9

  • 8.2


C.

9

fraction numerator left parenthesis 81 right parenthesis to the power of 3.6 end exponent space cross times space left parenthesis 9 right parenthesis to the power of 2.7 end exponent over denominator left parenthesis 81 right parenthesis to the power of 4.2 end exponent space cross times space 3 end fraction
equals space fraction numerator left parenthesis 3 to the power of 4 right parenthesis to the power of 3.6 end exponent space cross times space left parenthesis 3 squared right parenthesis to the power of 2.7 end exponent over denominator left parenthesis 3 to the power of 4 right parenthesis to the power of 4.2 end exponent cross times 3 end fraction
equals space fraction numerator 3 to the power of 14.4 end exponent cross times 3 to the power of 5.4 end exponent over denominator 3 to the power of 16.8 end exponent cross times 3 end fraction
              open square brackets because space straight a to the power of straight m space cross times space straight a to the power of straight n space equals space straight a to the power of straight m plus straight n end exponent comma space space straight a to the power of straight m over straight a to the power of straight n space equals space straight a to the power of straight m minus straight n end exponent close square brackets
equals space 3 to the power of 14.4 plus 5.4 end exponent over 3 to the power of 16.8 plus 1 end exponent space equals space 3 to the power of 19.8 end exponent over 3 to the power of 17.8 end exponent
equals space 3 to the power of 19.8 minus 17.8 end exponent space equals space 3 squared space equals space 9
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5. square root of 6 plus square root of 6 plus 6 plus.... end root end root is equal to
  • 2

  • 5

  • 4

  • 3


D.

3

Let straight x equals space square root of 6 plus square root of 6 plus square root of 6 plus.... end root end root end root
On squaring both sides,
   straight x squared space equals space 6 plus square root of 6 plus square root of 6 plus square root of 6 plus..... end root end root end root
 rightwards double arrow space space space straight x squared space equals space 6 space plus space straight x
rightwards double arrow space space straight x squared minus straight x minus 6 space equals space 0
rightwards double arrow space space straight x squared minus 3 straight x plus 2 straight x minus 6 space equals space 0
rightwards double arrow space space straight x left parenthesis straight x minus 3 right parenthesis space plus space 2 left parenthesis straight x minus 3 right parenthesis space equals space 0
rightwards double arrow space space left parenthesis straight x space plus space 2 right parenthesis thin space left parenthesis straight x minus 3 right parenthesis space equals space 0

rightwards double arrow space space straight x space equals space 3 space space and space space straight x not equal to negative 2 space because space numbers space are space positive.
Shortcut Method:
Co-Prime factors of 6 are (3, 2) as number is positive, therefore, answer would be highest co-prime factor i.e. 3.

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8.

A can do a piece of work in 24 days, B in 52 days and C in 64 days. All begin to do it together, but A leaves after 6 days and B leaves 6 days before the completion of the work. How many days did the work last?

  • 720/29

  • 20

  • 18

  • 30


A.

720/29

Let the work be finished in x days.
∴ Work done by A in 6 days + Work done by B in (x - 6) days  + Work done by C in x days = 1
Use formula:
open parentheses fraction numerator No space of space days space straight a space person space does over denominator No space of space days space straight a space person space can space do end fraction plus fraction numerator begin display style No space of space days space straight a space person space does end style over denominator begin display style No space of space days space straight a space person space can space do end style end fraction plus fraction numerator begin display style No space of space days space straight a space person space does end style over denominator begin display style No space of space days space straight a space person space can space do end style end fraction space equals space 1 close parentheses
therefore space space 6 over 24 space plus space fraction numerator left parenthesis straight x minus 6 right parenthesis over denominator 52 end fraction space plus space straight x over 64 space equals space 1
rightwards double arrow space space space fraction numerator straight x minus 6 over denominator 52 end fraction plus straight x over 64 space equals space 1 minus 1 fourth space equals space 3 over 4
rightwards double arrow space space fraction numerator 16 left parenthesis straight x minus 6 right parenthesis space plus space 13 straight x over denominator 13 cross times 16 cross times 4 end fraction space equals space 3 over 4
rightwards double arrow space space 16 straight x space minus space 96 space plus space 13 straight x space equals space 13 space cross times space 16 space cross times 3
rightwards double arrow space space space 29 straight x space equals space 624 space plus space 96 space equals space 720
rightwards double arrow space space space space straight x space equals space 720 over 29



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9.

The square root of:
fraction numerator left parenthesis 0.75 right parenthesis cubed over denominator 1 minus 0.75 end fraction space plus space left square bracket 0.75 space plus space left parenthesis 0.75 right parenthesis squared plus 1 right square bracket is 

  • 1

  • 2

  • 3

  • 4


D.

4

equals space fraction numerator left parenthesis 0.75 right parenthesis cubed over denominator left parenthesis 1 minus 0.75 right parenthesis end fraction space plus space open square brackets 0.75 space plus space left parenthesis 0.75 right parenthesis squared space plus space 1 close square brackets
equals space fraction numerator left parenthesis 0.75 right parenthesis cubed space plus space left parenthesis 1 minus 0.75 right parenthesis left square bracket left parenthesis 0.75 right parenthesis squared plus 0.75 space cross times 1 space plus space 1 squared right square bracket over denominator 1 minus 0.75 end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets because space straight a cubed minus straight b cubed space equals space left parenthesis straight a minus straight b right parenthesis thin space left parenthesis straight a squared plus ab plus straight b squared right parenthesis close square brackets
equals space fraction numerator left parenthesis 0.75 right parenthesis cubed space plus space 1 cubed space minus space left parenthesis 0.75 right parenthesis cubed over denominator 0.25 end fraction space equals space fraction numerator 1 over denominator 0.25 end fraction equals space space 100 over 25 space equals space 4

∴ Required square rootspace equals space square root of 4 space equals space 2
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1.

In a division sum, the divisor is 4 times the quotient and twice the remainder. If a and b are respectively the divisor and the dividend, then

  • fraction numerator 4 straight b minus straight a squared over denominator straight a end fraction equals 3
  • fraction numerator 4 straight b minus 2 straight a over denominator straight a squared end fraction space equals space 2
  • left parenthesis straight a plus 1 right parenthesis squared space equals space 4 straight b
  • fraction numerator straight a left parenthesis straight a plus 2 right parenthesis over denominator straight b end fraction space equals space 4

D.

fraction numerator straight a left parenthesis straight a plus 2 right parenthesis over denominator straight b end fraction space equals space 4

Divisor  = a,  Dividend  = b (given)
   Quotient = straight a over 4
   Remainder = straight a over 2
∴   Dividend = Divisor X Quotient + Remainder
  rightwards double arrow space space space straight b space equals space straight a space cross times space straight a over 4 plus straight a over 2
equals space fraction numerator straight a squared plus 2 straight a over denominator 4 end fraction space equals space fraction numerator straight a left parenthesis straight a plus 2 right parenthesis over denominator 4 end fraction
rightwards double arrow space space space 4 straight b equals space space straight a left parenthesis straight a plus 2 right parenthesis

rightwards double arrow space space space fraction numerator straight a left parenthesis straight a plus 2 right parenthesis over denominator straight b end fraction space equals space 4

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6.

The sum of the squares of two natural consecutive odd numbers is 394. The sum of the numbers is

  • 24

  • 32

  • 40

  • 28


D.

28

Let x and x+2 be the two consecutive odd numbers.
rightwards double arrow space space space straight x squared plus space left parenthesis straight x plus 2 right parenthesis squared space equals space 394
rightwards double arrow space space straight x squared plus straight x squared plus 4 plus 4 straight x space equals space 394
rightwards double arrow space space 2 straight x squared plus 4 straight x minus 390 space equals space 0
rightwards double arrow space straight x squared plus 2 straight x minus 195 space equals space 0

rightwards double arrow space straight x squared plus 15 straight x minus 13 straight x minus 195 space equals space 0
rightwards double arrow space space straight x left parenthesis straight x plus 15 right parenthesis space minus 13 left parenthesis straight x plus 15 right parenthesis space equals space 0
rightwards double arrow space left parenthesis straight x minus 13 right parenthesis thin space left parenthesis straight x plus 15 right parenthesis space equals space 0
rightwards double arrow space space straight x space equals space 13 space comma space minus 15
rightwards double arrow space straight x space equals space 13
So, the numbers are (x = 13), (x+2 = 13+2 = 15)
∴  The required sum = 13 + 15 = 28

Shortcut Method:
By mental operation,
   132 + 152 = 169 + 225  = 394
∴  The required sum = 13 + 15 = 28
   



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