Subject

Quantitative Aptitude

Class

SSCCGL Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

2.

Three bells ring at intervals of 36 seconds, 40 seconds and 48 seconds respectively. They start ringing together at a particular time. They will ring together after every

  • 6 minutes

  • 12 minutes

  • 18 minutes

  • 24 minutes


B.

12 minutes

Required answer is L.C.M. of 36, 40 and 48 seconds = 720 seconds.
                equals open parentheses 720 over 60 close parentheses space minutes space equals space 12 space minutes.

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9.

The sum of three consecutive even numbers is 28 more than the average of these three numbers. Then the smallest of these three numbers is

  • 6

  • 12

  • 14

  • 16


B.

12

Let three consecutive even numbers be x, x + 2 and x + 4.
According to the question,
    left parenthesis straight x space plus space straight x space plus space 2 space space plus space straight x space plus space 4 right parenthesis space minus space fraction numerator straight x space plus space straight x space plus space 2 space plus space straight x space plus space 4 over denominator 3 end fraction space equals space 28
rightwards double arrow space space space left parenthesis 3 straight x space plus space 6 right parenthesis space minus space fraction numerator 3 straight x plus 6 over denominator 3 end fraction space equals space 28
rightwards double arrow space space space space left parenthesis 3 straight x space plus space 6 right parenthesis space minus space left parenthesis straight x space plus space 2 right parenthesis space equals space 28
rightwards double arrow space space space space space 3 straight x space plus space 6 space minus space straight x space minus space 2 space equals space 28
rightwards double arrow space space space space space space 2 straight x space plus space 4 space space equals space 28
rightwards double arrow space space space space space space space 2 straight x space equals space 28 space minus space 4 space equals space 24
rightwards double arrow space space space space space space straight x space equals space 24 over 2 equals space space 12

389 Views

5.

The greater of the two numbers whose product is 900 and the sum exceeds their difference by 30 is

  • 60

  • 75

  • 90

  • 100


A.

60

Let the numbers be x and y where x > y.
According to the question,
    (x + y) -  (x - y) = 30
⟹   x + y - x + y = 30
⟹     2y = 30
rightwards double arrow space space straight y space equals space 30 over 2 space equals space 15
therefore space space space space xy space equals space 900
rightwards double arrow space space space 15 straight x space equals space 900
rightwards double arrow space space space space straight x space equals space 900 over 15 space equals space 60

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1.

Let 0 < x < 1. Then the correct inequality is

  • straight x space less than space square root of straight x space less than space space straight x squared
  • square root of straight x space less than space straight x space less than space straight x squared
  • straight x squared space less than space straight x space less than space square root of straight x
  • square root of straight x space less than space space straight x squared space less than space straight x

C.

straight x squared space less than space straight x space less than space square root of straight x

Given,
 0 < x < 1
Multiply by x
⟹   0. x < x. x < 1. x 
⟹    0 < x2 <  x
Again,
     x < 1
rightwards double arrow space space square root of straight x space less than space 1
therefore space space space straight x squared space less than space straight x space less than space square root of straight x



1067 Views

8.

The sum of three positive numbers is 18 and their product is 162. If the sum of two numbers is equal to the third number, then the sum of squares of the numbers is

  • 120

  • 126

  • 132

  • 138


B.

126

Let the three numbers be x, y and z.
According to the question, we have three equations
x + y + z = 18               ...(i)
xyz = 162                      ...(ii)
and x + y = z                 ...(iii)
From equation (i),
   z + z = 18 
 ⟹   2z =  18 ⟹  z = 9
∴     xyz = 162
⟹   xy = 162/9 = 18    ...(iv)
therefore space space space left parenthesis straight x minus straight y right parenthesis squared space equals space left parenthesis straight x plus straight y right parenthesis squared space minus space 4 xy
space space space space space equals space left parenthesis 9 right parenthesis squared space minus space 4 space cross times space 18
space space space space space space equals space 81 space minus space 72 space equals space space 9
therefore space space space space straight x minus straight y space equals space 3
therefore space space space space straight x space plus space straight y space plus space straight x space minus straight y space equals space 9 space plus space 3
rightwards double arrow space space space space space space 2 straight x space equals space 12 space space rightwards double arrow space space space straight x space space equals space 6

therefore space space space space space straight x space plus space straight y space plus space straight z space equals space 18
rightwards double arrow space space space 6 space plus space straight y space plus space 9 space equals space 18
rightwards double arrow space space space space straight y space equals space 18 space minus space 15 space equals space 3
therefore space space space straight x squared plus straight y squared plus straight z squared
space space space space equals space left parenthesis 6 right parenthesis squared space plus space left parenthesis 3 right parenthesis squared space plus space left parenthesis 9 right parenthesis squared
space space space space equals 36 space plus space 9 space plus space 81 space equals space 126 space




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4.

Which of the following is correct?

  • 2 over 3 space less than space 3 over 5 space less than thin space 11 over 15
  • 3 over 5 less than 2 over 3 less than 11 over 15
  • 11 over 15 space less than space 3 over 5 space less than space 2 over 3
  • 3 over 5 space less than space 11 over 15 space less than space 2 over 3

B.

3 over 5 less than 2 over 3 less than 11 over 15

Just multiply numerator by 10.
rightwards double arrow space space space fraction numerator 2 space cross times space 10 over denominator 3 end fraction space equals space 20 over 3 space equals space 6.67
rightwards double arrow space space fraction numerator 3 space cross times space 10 over denominator 5 end fraction space equals space 6
rightwards double arrow space space space fraction numerator 11 space cross times space 10 over denominator 5 end fraction space equals space 22
Clearly, 3 over 5 thin space less than thin space 2 over 3 space less than space 11 over 15

  

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3.

If the sum of the digits of a three-digit number is subtracted from that number, then it will always be divisible by

  • 3 only

  • 9 only

  • Both 3 and 9

  • All of 3, 6 and 9


C.

Both 3 and 9

Let the 3-digit number be 100x + 10y + z.
Sum of the digits  = x + y + z
According to the question,
  Difference
     = 100x + 10y + z - (x + y + z)
     =  99x + 9y
     = 9(11x + y)
Clearly, it is a multiple of 3 and 9.

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7.

Find the cube root of (-13824). or Find the value of cube root of negative 13824 end root

  • 38

  • -38

  • 24

  • -24


D.

-24

Shortcut Method:
check the last digit and go with option
Multiplication of ... -4 x -4 x -4 = -64
Therefore the unit digit is 4.
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6.

The smallest fraction, which should be added to the sum of 2 1 half comma space space 3 1 third comma space space 4 1 fourth and 5 1 fifth to make the result as a whole number, is

  • 13 over 60
  • 1 fourth
  • 17 over 60
  • 43 over 60

D.

43 over 60
2 1 half space plus space 3 1 third space plus space 4 1 fourth space plus space 5 1 fifth
equals space left parenthesis 2 space plus space 3 space plus space 4 space plus space 5 right parenthesis space plus space open parentheses 1 half space plus space 1 third space plus space 1 fourth space plus space 1 fifth close parentheses
equals space 14 space plus space open parentheses fraction numerator 30 space plus space 20 space plus space 15 space plus space 12 over denominator 60 end fraction close parentheses
equals space 14 space plus space 77 over 60 space
or
14 plus space 1 space 17 over 60 space equals space 15 17 over 60
space
∴  Required fraction 
equals space 1 minus 17 over 60 space equals space fraction numerator 60 minus 17 over denominator 60 end fraction space equals space 43 over 60
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10.

In a division sum, the divisor 'd' is 10 times the quotient 'q' and 5 times the remainder 'r'. If r = 46, the dividend will be

  • 5042

  • 5328

  • 5336

  • 4276


C.

5336

Divisor (d) = 5r = 5 x 46 = 230
Now,
Divisor (d) = 10 x quotient (q)

rightwards double arrow space space space space 230 space equals space straight q space cross times space 10
rightwards double arrow space space space space straight q space equals space 230 over 10 space equals space 23

Dividend  = Divisor x Quotient  + Remainder
               = 230 x 23  + 46
               = 5290 + 46 = 5336

437 Views