Online Aptitude Test

Online Aptitude Test - Aptitude

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Total number of questions : 20.
Time alloted : 30 minutes.
Each question carry 1 mark, no negative marks.
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The fourth proportional to 5, 8, 15 is:

	A.	18
	B.	24
	C.	19
	D.	20

Your Answer: Option

Correct Answer: Option B

Explanation:

Let the fourth proportional to 5, 8, 15 be x.

Then, 5 : 8 : 15 : x

5x = (8 x 15)

x =	(8 x 15)	= 24.
	5

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Which of the following are in descending order of their value ?

	A.	1/3 , 2/5 , 3/7 , 4/5 , 5/6 , 6/7
	B.	1/3 , 2/5 , 3/5 , 4/7 , 5/6 , 6/7
	C.	1/3 , 2/5 , 3/5 , 4/6 , 5/7 , 6/7
	D.	6/7 , 5/6 , 4/5 , 3/7 , 2/5 , 1/3

Your Answer: Option

Correct Answer: Option D

Explanation:

No answer description available for this question. Let us discuss.

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Two dice are tossed. The probability that the total score is a prime number is:

	A.	1/6
	B.	5/12
	C.	1/2
	D.	7/9

Your Answer: Option

Correct Answer: Option B

Explanation:

Clearly, n(S) = (6 x 6) = 36.

Let E = Event that the sum is a prime number.

Then E

= { (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3),
(5, 2), (5, 6), (6, 1), (6, 5) }

n(E) = 15.

P(E) =	n(E)	=	15	=	5	.
	n(S)		36		12

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Reduce	128352	to its lowest terms.
Reduce	238368

	A.	3/4
	B.	5/13
	C.	7/13
	D.	9/13

Your Answer: Option

Correct Answer: Option C

Explanation:

128352) 238368 ( 1
         128352
         ---------------
         110016 ) 128352 ( 1
                  110016
                 ------------------  
                   18336 ) 110016 ( 6       
                           110016
                           -------
                                x
                           -------
 So, H.C.F. of 128352 and 238368 = 18336.
 
             128352     128352 � 18336    7
 Therefore,  ------  =  -------------- =  --
             238368     238368 � 18336    13

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Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:

	A.	Rs. 1550
	B.	Rs. 1650
	C.	Rs. 1750
	D.	Rs. 2000

Your Answer: Option

Correct Answer: Option C

Explanation:

C.I.

= Rs.		4000 x		1 +	10		2	- 4000
					100

= Rs.		4000 x	11	x	11	- 4000
			10		10

= Rs. 840.

Sum = Rs.		420 x 100		= Rs. 1750.
		3 x 8

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A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:

	A.	4
	B.	5
	C.	6
	D.	10

Your Answer: Option

Correct Answer: Option B

Explanation:

Let the speed of the stream be x km/hr. Then,

Speed downstream = (15 + x) km/hr,

Speed upstream = (15 - x) km/hr.

	30	+	30	= 4	1
	(15 + x)		(15 - x)		2

	900	=	9
	225 - x²		2

9x² = 225

x² = 25

x = 5 km/hr.

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From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

	A.	564
	B.	645
	C.	735
	D.	756
	E.	None of these

Your Answer: Option

Correct Answer: Option D

Explanation:

We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).

Required number of ways

= (⁷C₃ x ⁶C₂) + (⁷C₄ x ⁶C₁) + (⁷C₅)

=		7 x 6 x 5	x	6 x 5		+ (⁷C₃ x ⁶C₁) + (⁷C₂)
		3 x 2 x 1		2 x 1

= 525 +		7 x 6 x 5	x 6		+		7 x 6
		3 x 2 x 1					2 x 1

= (525 + 210 + 21)

= 756.

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4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?

	A.	35
	B.	40
	C.	45
	D.	50

Your Answer: Option

Correct Answer: Option B

Explanation:

Let 1 man's 1 day's work = x and 1 woman's 1 day's work = y.

Then, 4x + 6y =	1	and 3x + 7y =	1	.
	8		10

Solving the two equations, we get: x =	11	, y =	1
	400		400

1 woman's 1 day's work =	1	.
	400

10 women's 1 day's work =		1	x 10		=	1	.
		400				40

Hence, 10 women will complete the work in 40 days.

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The rational number for recurring decimal 0.125125.... is:

	A.	63/487
	B.	119/993
	C.	125/999
	D.	None of these

Your Answer: Option

Correct Answer: Option C

Explanation:

0.125125... = 0.125 =	125
	999

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10.

Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?

	A.	23 m
	B.	23 2/9 m
	C.	27 7/9 m
	D.	29 m

Your Answer: Option

Correct Answer: Option C

Explanation:

Relative speed = (40 - 20) km/hr =		20 x	5		m/sec =		50		m/sec.
			18				9

Length of faster train =		50	x 5		m =	250	m = 27	7	m.
		9				9		9

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11.

(2² + 4² + 6² + ... + 20²) = ?

	A.	770
	B.	1155
	C.	1540
	D.	385 x 385

Your Answer: Option

Correct Answer: Option C

Explanation:

(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.

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12.

The value of		1	+	1	+	1		is:
		log₃ 60		log₄ 60		log₅ 60

	A.	0
	B.	1
	C.	5
	D.	60

Your Answer: Option

Correct Answer: Option B

Explanation:

Given expression	= log₆₀ 3 + log₆₀ 4 + log₆₀ 5
	= log₆₀ (3 x 4 x 5)
	= log₆₀ 60
	= 1.

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13.

Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?

	A.	3.5
	B.	4.5
	C.	5.6
	D.	6.5

Your Answer: Option

Correct Answer: Option C

Explanation:

Cost Price of 1 toy = Rs.		375		= Rs. 31.25
		12

Selling Price of 1 toy = Rs. 33

So, Gain = Rs. (33 - 31.25) = Rs. 1.75

Profit % =		1.75	x 100	%	=	28	% = 5.6%
		31.25				5

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14.

If m and n are whole numbers such that mn = 121, the value of (m - 1)n + 1 is:

	A.	1
	B.	10
	C.	121
	D.	1000

Your Answer: Option

Correct Answer: Option D

Explanation:

We know that 11² = 121.

Putting m = 11 and n = 2, we get:

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

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15.

What smallest number should be added to 4456 so that the sum is completely divisible by 6 ?

	A.	4
	B.	3
	C.	2
	D.	1
	E.	None of these

Your Answer: Option

Correct Answer: Option C

Explanation:

6) 4456 (742
    42
    ---
     25
     24        Therefore, Required number = (6 - 4) = 2.
     ---
      16
      12
      ---
       4

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16.

Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?

	A.	10
	B.	12
	C.	15
	D.	20

Your Answer: Option

Correct Answer: Option B

Explanation:

Speed of the first train =		120		m/sec = 12 m/sec.
		10

Speed of the second train =		120		m/sec = 8 m/sec.
		15

Relative speed = (12 + 8) = 20 m/sec.

Required time =		(120 + 120)		sec = 12 sec.
		20

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17.

10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?

	A.	3
	B.	5
	C.	7
	D.	Cannot be determined
	E.	None of these

Your Answer: Option

Correct Answer: Option C

Explanation:

1 woman's 1 day's work =	1
	70

1 child's 1 day's work =	1
	140

(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.

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18.

If the number 42573 * is exactly divisible by 72, then the minimum value of * is:

	A.	4
	B.	5
	C.	6
	D.	7
	E.	8

Your Answer: Option

Correct Answer: Option C

Explanation:

72 = 9 x8, where 9 and 8 are co-prime.

The minimum value of x for which 73x for which 73x is divisible by 8 is, x = 6.

Sum of digits in 425736 = (4 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 9.

Required value of * is 6.

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19.

The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?

	A.	69
	B.	78
	C.	96
	D.	Cannot be determined
	E.	None of these

Your Answer: Option

Correct Answer: Option D

Explanation:

Let the ten's digit be x and unit's digit be y.

Then, x + y = 15 and x - y = 3 or y - x = 3.

Solving x + y = 15 and x - y = 3, we get: x = 9, y = 6.

Solving x + y = 15 and y - x = 3, we get: x = 6, y = 9.

So, the number is either 96 or 69.

Hence, the number cannot be determined.

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20.

In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?

	A.	159
	B.	194
	C.	205
	D.	209
	E.	None of these

Your Answer: Option

Correct Answer: Option D

Explanation:

We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).

Required number
of ways

= (⁶C₁ x ⁴C₃) + (⁶C₂ x ⁴C₂) + (⁶C₃ x ⁴C₁) + (⁶C₄)

= (⁶C₁ x ⁴C₁) + (⁶C₂ x ⁴C₂) + (⁶C₃ x ⁴C₁) + (⁶C₂)

= (6 x 4) +

6 x 5

4 x 3

6 x 5 x 4

x 4

6 x 5

2 x 1

3 x 2 x 1

2 x 1

= (24 + 90 + 80 + 15)

= 209.

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