Online Aptitude Test - Aptitude Test - Random

Required numbers are 24, 30, 36, 42, ..., 96

This is an A.P. in which a = 24, d = 6 and l = 96

Let the number of terms in it be n.

Then t_n = 96    a + (n - 1)d = 96

24 + (n - 1) x 6 = 96

(n - 1) x 6 = 72

(n - 1) = 12

n = 13

Required number of numbers = 13.

 19657         Let x - 53651  = 9999
 33994         Then, x = 9999 + 53651 = 63650
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 53651
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For every natural number n, (xⁿ - aⁿ) is completely divisible by (x - a).

36 = 2² x 3²

84 = 2² x 3 x 7

H.C.F. = 2² x 3 = 12.

Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.

So, the numbers 12 and 16.

L.C.M. of 12 and 16 = 48.

Let the numbers be a, b and c.

Then, a² + b² + c² = 138 and (ab + bc + ca) = 131.

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca) = 138 + 2 x 131 = 400.

(a + b + c) = 400 = 20.

Video Explanation: https://youtu.be/qmJ-0X8j_xQ

(0.04)-1.5 =		4		-1.5
		100

=		1		-(3/2)
		25

   = (25)^(3/2)

   = (5²)^(3/2)

   = (5)^{2 x (3/2)}

   = 5³

   = 125.

For managing, A received = 5% of Rs. 7400 = Rs. 370.

Balance = Rs. (7400 - 370) = Rs. 7030.

Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3)

   = 39000 : 42000 : 30000

   = 13 : 14 : 10

B's share = Rs.		7030 x	14		= Rs. 2660.
			37

Suppose the vessel initially contains 8 litres of liquid.

Let x litres of this liquid be replaced with water.

Quantity of water in new mixture =		3 -	3x	+ x		litres
			8

Quantity of syrup in new mixture =		5 -	5x		litres
			8

		3 -	3x	+ x		=		5 -	5x
			8						8

5x + 24 = 40 - 5x

10x = 16

x =	8	.
	5

So, part of the mixture replaced =		8	x	1		=	1	.
		5		8			5

Sum = Rs.		50 x 100		= Rs. 500.
		2 x 5

Amount	= Rs. 500 x 1 + 5 2 100
	= Rs. 500 x 21 x 21 20 20
	= Rs. 551.25

C.I. = Rs. (551.25 - 500) = Rs. 51.25

a^x = b^y

log a^x = log b^y

x log a = y log b

	log a	=	y	.
	log b		x

Capacity = r²h.

I gives, r² = 61600. This gives r.

II gives, h = 1.5 r.

Thus, I and II give the answer.

Again, III gives 2r = 880. This gives r.

So, II and III also give the answer.

Correct answer is (E).

To earn Rs. 135, investment = Rs. 1620.

To earn Rs. 8, investment = Rs.		1620	x 8		= Rs. 96.
		135

Market value of Rs. 100 stock = Rs. 96.

In the word 'MATHEMATICS', we treat the vowels AEAI as one letter.

Thus, we have MTHMTCS (AEAI).

Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.

Number of ways of arranging these letters =	8!	= 10080.
	(2!)(2!)

Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.

Required number of words = (10080 x 12) = 120960.

Total number of balls = (8 + 7 + 6) = 21.

n(E) = 7.

P(E) =	n(E)	=	7	=	1	.
	n(S)		21		3

One of AB, AD and CD must have given.

So, the data is inadequate.

2^nd term = (1^st term) x 1 + 1 = 15 x 1 + 1 = 16.

3^rd term = (2^nd term) x 2 + 2 = 16 x 2 + 2 = 34.

4^th term = (3^th term) x 3 + 3 = 34 x 3 + 3 = 105.

5^th term = (4^th term) x 4 + 4 = 105 x 4 + 4 = 424

6^th term = (5^th term) x 5 + 5 = 424 x 5 + 5 = 2125

6^th term should 2125 instead of 2124.