Online Aptitude Test - Aptitude Test 7

L.C.M. of 5, 6, 7, 8 = 840.

Required number is of the form 840k + 3

Least value of k for which (840k + 3) is divisible by 9 is k = 2.

Required number = (840 x 2 + 3) = 1683.

  617.00
    6.017
    0.617
 +  6.0017
  --------
  629.6357
  --------- 

Let the average age of the whole team by x years.

11x - (26 + 29) = 9(x -1)

11x - 9x = 46

2x = 46

x = 23.

So, average age of the team is 23 years.

Let their present ages be 4x, 7x and 9x years respectively.

Then, (4x - 8) + (7x - 8) + (9x - 8) = 56

20x = 80

x = 4.

Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.

Let Divya's present age be D years and Shruti's present age b S years

Then, D = 2 x S       D - 2S = 0 ....(i)

From (ii), we get : 5D + 25 = 9S + 45       5D - 9S = 20 ....(iv)

From (iii), we get : D - 10 = 3S - 30       D - 3S = -20 ....(v)

Thus, from (i) and (ii), we get the answer.

Also, from (i) and (iii), we get the answer.

I alone as well as II alone give the answer. Hence, the correct answer is (C).

(256)^0.16 x (256)^0.09 = (256)^{(0.16 + 0.09)}

   = (256)^0.25

   = (256)^(25/100)

   = (256)^(1/4)

   = (4⁴)^(1/4)

   = 4^4(1/4)

   = 4¹

   = 4

Let B's capital be Rs. x.

Then,		3500 x 12	=	2
		7x		3

14x = 126000

x = 9000.

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 us name Ravi, Gagan and Nitin by R, G and N respectively.

 I. R : G : N = 2 : 4 : 7.

II. N = 8750..

From I and II, we get:

When N = 7, then G = 4.

When N = 8750, then G =		4	x 8750		= 5000.
		7

Thus, both I and II are needed to get the answer.

Correct answer is (E).

Let the required number of revolutions made by larger wheel be x.

Then, More cogs, Less revolutions (Indirect Proportion)

14 : 6 :: 21 : x       14 x x = 6 x 21

x =	6 x 21
	14

x = 9.

(5 women + 10 children)'s day's work =		5	+	10		=		1	+	1		=	1
		70		140				14		14			7

5 women and 10 children will complete the work in 7 days.

Work done by the waste pipe in 1 minute =	1	-		1	+	1
	15			20		24

=		1	-	11
		15		120

Volume of	1	part = 3 gallons.
	40

Volume of whole = (3 x 40) gallons = 120 gallons.

Speed of train relative to jogger = (45 - 9) km/hr = 36 km/hr.

=		36 x	5	m/sec
			18

   = 10 m/sec.

Distance to be covered = (240 + 120) m = 360 m.

Time taken =		360	sec	= 36 sec.
		10

Relative speed =	= (45 + 30) km/hr
	= 75 x 5 m/sec 18
	= 125 m/sec. 6

We have to find the time taken by the slower train to pass the DRIVER of the faster train and not the complete train.

So, distance covered = Length of the slower train.

Therefore, Distance covered = 500 m.

Required time =		500 x	6		= 24 sec.
			125

Rate downstream =		1	x 60	km/hr = 6 km/hr.
		10

Rate upstream = 2 km/hr.

Required time =		5	hrs = 1	1	hrs = 1 hr 15 min.
		4		4

Let the quantity of the wine in the cask originally be x litres.

Then, quantity of wine left in cask after 4 operations =		x		1 -	8		4	litres.
					x

		x(1 - (8/x))4		=	16
		x			81

		1 -	8		4	=		2		4
			x					3

		x - 8		=	2
		x			3

3x - 24 = 2x

x = 24.

Total number of balls = (2 + 3 + 2) = 7.

Let S be the sample space.

Let E = Event of drawing 2 balls, none of which is blue.

n(E)	= Number of ways of drawing 2 balls out of (2 + 3) balls.
	= 5C2
	= (5 x 4) (2 x 1)
	= 10.

P(E) =	n(E)	=	10	.
	n(S)		21