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Q. The product of 2 numbers is 1575 and their quotient is 9/7. Then the sum of the numbers is

  1. 74
  2. 78
  3. 80
  4. 90

How? See below Solutions

Ans: Let the numbers be x and y.

We know xy = 1575

And x/y = 9/7

We know xy/x/y = 1575/9/7

We know   y2 = 1225

We know y = 35 and x = 45

We know the sum of the numbers = 45+35

= 80

Q.The value of (81)3.6 * (9)2.7/ (81)4.2 * (3) is __

  1. 3
  2. 6
  3. 9
  4. 2

How? See below Solutions

Ans: (81)3.6 * (9)2.7/(81)4.2 * (3) = (3)14.4 * (3)5.4/(3)16.8 * (3)

= 314.4+5.4-16.8-1

= 32

= 9

Q.  √6+√6+√6+… is equal to –

  1. 2
  2. 5
  3. 4
  4. 3

How? See below Solutions

Ans: Let √6+√6+√6+…. be x.

We know x =√6+x

We know x2 = 6+x

We know x2 – x – 6 = 0

We know (x-3) (x+2) = 0

We know x = 3

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

  1. 24
  2. 32
  3. 40
  4. 28

How? See below Solutions

Ans: Let the consecutive odd numbers be x and (x+2)

We know that x2 + (x + 2)2 = 394

We know   x2 + x2 + 4x + 4 = 394

We know   2 x2 +4x – 390 = 0

We know   x2 + 2x – 195 = 0

We know (x +15) (x-13) = 0

We know   x = 13

We know required sum = 13 +15 =28

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

  1. 1
  2. 63
  3. 66
  4. 67

How? See below Solutions

Ans:  (6767+ 67) = 67(6766 + 166)

As 66 is an even number

We know   6766 is an even number

We know   (6766 + 1) is perfectly divisible by (67 + 1)

i.e. 68

We know the remainder = 66

Q. 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-

  1. 4b-a2 /a =3
  2. 4b-2a /a2 =2
  3. (a+1)2 = 4b
  4. a(a+2)/b = 4

Ans: As divisor is a, and dividend is b.

We know    Quotient = a/4

And Remainder = a/2

We know    b = a * a/4 + a/2

We know    4b = a2 + 2a

We know    a (a+2)/b = 4

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

  1. 6
  2. 3
  3. 9
  4. 1

Ans:  As 738A6 A is divisible by 11.

We know    A + A + 3 = 6 + 8 + 7

We know    A = 9

Q. The east positive integer that should be subtracted from 3011 * 3012 so that the difference is perfect square is-

  1. 3009
  2. 3010
  3. 3011
  4. 3012

Ans:  We know that 3011 * 3012 = 3011 (3011 + 1)

= (3011)2 + 3011

We know required least number = 3011

Q. P, Q, R are employed to do a work for Rs. 5750. P and Q together finished 19/23 of work and Q and R together finished 8/23 of work. Wage of Q, in rupees, is-

  1. 2850
  2. 3750
  3. 2750
  4. 1000

Ans:  Work done by Q = 19/23 + 8/23 – 1

4/23

We know   Wage of Q = 4/23 * 5750

= Rs. 1000

Q. A can do a piece of work in 24 day, B in 32 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?

  1. 15
  2. 20
  3. 18
  4. 30

Ans: Work done by A = 6/24 = ¼

Work done by B = (x-6)/32

(Where x is no. of days in which work is completed)

We know that ¼ + x – 6/32 + x/64 = 1

We know 16 + 24 – 12 + x /64 = 1

We know 3x + 4 = 64

We know x = 60/3 = 20 days

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