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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 **

- 74
- 78
**80**- 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 __**

- 3
- 6
**9**- 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 –**

- 2
- 5
- 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 –**

- 24
- 32
- 40
**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
- 63
**66**- 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-**

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

- 6
- 3
**9**- 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-**

- 3009
- 3010
**3011**- 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-**

- 2850
- 3750
- 2750
**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?**

- 15
**20**- 18
- 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