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Problems on Numbers

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Question
SSCCGLENQA12042438
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Each member of a club contributes as much rupees and as much paise as the number of members of the club. If the total contribution is Rs. 2525, then the number of members of the club is

  • 60

  • 45

  • 55

  • 50

Solution

D.

50

Let Number of members in the club  = x
According to the question,
straight x squared plus straight x squared over 100 space equals space 2525
rightwards double arrow fraction numerator 100 straight x squared plus straight x squared over denominator 100 end fraction space equals space 2525 rightwards double arrow space 101 straight x squared space equals space 252500 rightwards double arrow space space straight x squared space equals space 252500 over 101 space equals space 2500 rightwards double arrow space straight x space equals space square root of 2500 space equals space 50

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Question
SSCCGLENQA12042497
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If the sum of squares of two real numbers is 41 and their sum is 9. Then the sum of cubes of these two numbers is

  • 169

  • 209

  • 189

  • 198

Solution

C.

189

Let the two real numbers be x and y.
According to the question,
       straight x squared plus straight y squared space equals space 41 space straight x plus straight y space equals space 9
therefore space space left parenthesis straight x plus straight y right parenthesis squared space equals space straight x squared plus straight y squared plus 2 xy rightwards double arrow space space space 81 space equals space 41 space plus space 2 xy rightwards double arrow space space 2 xy space equals space 81 space minus space 41 space space equals space 40 rightwards double arrow space space xy space equals space 40 over 2 space equals space 20
therefore space space straight x cubed plus straight y cubed space equals space left parenthesis straight x plus straight y right parenthesis space left parenthesis straight x squared minus xy plus straight y squared right parenthesis
              = (9) (41 - 20) = 9 x 21 = 189

Question
SSCCGLENQA12043325
Wired Faculty App

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

  • 60

  • 75

  • 90

  • 100

Solution

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

Question
SSCCGLENQA12042848
Wired Faculty App

The least positive integer that should be subtracted from 3011 x 3012 so that the difference is a perfect square is

  • 3009

  • 3010

  • 3011

  • 3012

Solution

C.

3011

The expression is:
 = 3011 x 3012
 = 3011 (3011 + 1)
 = (3011)2 + 3011
∴ Required answer = 3011

Question
SSCCGLENQA12042852
Wired Faculty App

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

  • 74

  • 78

  • 80

  • 90

Solution

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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