Online Aptitude Test

On 31^st December, 2005 it was Saturday.

Number of odd days from the year 2006 to the year 2009 = (1 + 1 + 2 + 1) = 5 days.

 On 31^st December 2009, it was Thursday.

Thus, on 1^st Jan, 2010 it is Friday.

Total quantity of petrol consumed in 3 years	= 4000 + 4000 + 4000  litres 7.50 8 8.50
	= 4000 2 + 1 + 2  litres 15 8 17
	= 76700  litres 51

Total amount spent = Rs. (3 x 4000) = Rs. 12000.

Average cost = Rs.		12000 x 51		= Rs.	6120	= Rs. 7.98
		76700			767

Given Exp. =(12)³ x 6⁴=(12)³ x 6⁴= (12)² x 6² = (72)² = 518443212 x 6²

28 May, 2006 = (2005 years + Period from 1.1.2006 to 28.5.2006)

Odd days in 1600 years = 0

Odd days in 400 years = 0

5 years = (4 ordinary years + 1 leap year) = (4 x 1 + 1 x 2)  6 odd days

Jan.  Feb.   March    April    May 
(31 +  28  +  31   +   30   +   28 ) = 148 days

 148 days = (21 weeks + 1 day)  1 odd day.

Total number of odd days = (0 + 0 + 6 + 1) = 7  0 odd day.

Given day is Sunday.

Marking (/) those which are are divisible by 3 by not by 9 and the others by (X), by taking the sum of digits, we get:s

2133  9 (X)

2343  12 (/)

3474  18 (X)

4131  9 (X)

5286  21 (/)

5340  12 (/)

6336  18 (X)

7347  21 (/)

8115  15 (/)

9276  24 (/)

Required number of numbers = 6.

N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)

  = H.C.F. of 3360, 2240 and 5600 = 1120.

Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4

Let C = x.

Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.

So, x + x + 5000 + x + 9000 = 50000

 3x = 36000

 x = 12000

A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.

A's share = Rs.		35000 x	21		= Rs. 14,700.
			50

Let the rate be R% p.a.

Then, 1200 x		1 +	R		2	= 1348.32
			100

		1 +	R		2	=	134832	=	11236
			100				120000		10000

		1 +	R		2	=		106		2
			100					100

1 +	R	=	106
	100		100

 R = 6%

Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.

 Required sale = Rs. [ (6500 x 6) - 34009 ]

   = Rs. (39000 - 34009)

   = Rs. 4991.

We know that 11² = 121.

Putting m = 11 and n = 2, we get:

(m - 1)^{n + 1} = (11 - 1)^{(2 + 1)} = 10³ = 1000.

(2² + 4² + 6² + ... + 20²) = (1 x 2)² + (2 x 2)² + (2 x 3)² + ... + (2 x 10)²

= (2² x 1²) + (2² x 2²) + (2² x 3²) + ... + (2² x 10²)

= 2² x [1² + 2² + 3² + ... + 10²]

	Ref: (12 + 22 + 32 + ... + n2) =	1	n(n + 1)(2n + 1)
		6

=		4 x	1	x 10 x 11 x 21
			6

= (4 x 5 x 77)

= 1540.

Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively.

Then, 14x : 8y : 7z = 5 : 7 : 8.

Now,	14x	=	5	98x = 40y        y =	49	x
	8y		7		20

And,	14x	=	5	112x = 35z        z =	112	x =	16	x.
	7z		8		35		5

x : y : z = x :	49	x	:	16	x	= 20 : 49 : 64.
	20			5

Let their marks be (x + 9) and x.

 25(x + 9) = 14(2x + 9)

 3x = 99

 x = 33

So, their marks are 42 and 33.

A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3.

B's share = Rs.		25000 x	3		= Rs. 7,500.
			10

Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4.

Suppose Tanya takes x days to do the work.

5 : 4 :: 20 : x     x =		4 x 20
		5

 x = 16 days.

Hence, Tanya takes 16 days to complete the work.

We may have(1 black and 2 non-black) or (2 black and 1 non-black) or (3 black).

Required number of ways	= (3C1 x 6C2) + (3C2 x 6C1) + (3C3)
	= 3 x 6 x 5 + 3 x 2 x 6 + 1 2 x 1 2 x 1
	= (45 + 18 + 1)
	= 64.

20 x x = (64 + 36)(64 - 36) = 100 x 28

x =	100 x 28	= 140
	20