Online Aptitude Test  Aptitude Test 6
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 Total number of questions: 20.
 Time allotted: 30 minutes.
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Marks : 2/20
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Let the numbers be a and b.
Then, a + b = 55 and ab = 5 x 120 = 600.
The required sum =  1  +  1  =  a + b  =  55  =  11 
a  b  ab  600  120 
Greatest number of 4digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number (9999  399) = 9600.
If a = 0.1039, then the value of 4a^{2}  4a + 1 + 3a is:
4a^{2}  4a + 1 + 3a = (1)^{2} + (2a)^{2}  2 x 1 x 2a + 3a
= (1  2a)^{2} + 3a
= (1  2a) + 3a
= (1 + a)
= (1 + 0.1039)
= 1.1039
Let the numbers be x and y.
Then, xy = 9375 and  x  = 15. 
y 
xy  =  9375 
(x/y)  15 
y^{2} = 625.
y = 25.
x = 15y = (15 x 25) = 375.
Sum of the numbers = x + y = 375 + 25 = 400.
Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.
What is the twodigit number?  
I.  The difference between the twodigit number and the number formed by interchanging the digits is 27. 
II.  The difference between the two digits is 3. 
III.  The digit at unit's place is less than that at ten's place by 3. 
Let the tens and units digit be x and y respectively.
I. (10x + y)  (10y + x) x  y = 3.
II. x  y = 3.
III. x  y = 3.
Thus, even all the given three statements together do not give the answer.
Correct answer is (E).
Let the present ages of Sameer and Anand be 5x years and 4x years respectively.
Then,  5x + 3  =  11 
4x + 3  9 
9(5x + 3) = 11(4x + 3)
45x + 27 = 44x + 33
45x  44x = 33  27
x = 6.
Anand's present age = 4x = 24 years.
Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read the both statements and
 Give answer (A) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
 Give answer (B) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
 Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to answer the question.
 Give answer (D) if the data even in both Statements I and II together are not sufficient to answer the question.
 Give answer(E) if the data in both Statements I and II together are necessary to answer the question.
What is Sonia's present age?  
I.  Sonia's present age is five times Deepak's present age. 
II.  Five years ago her age was twentyfive times Deepak's age at that time. 
I. S = 5D D =  S  ....(i) 
5 
II. S  5 = 25 (D  5) S = 25D  120 ....(ii)
Using (i) in (ii), we get S =  25 x  S   120  
5 
4S = 120.
S = 30.
Thus, I and II both together give the answer. So, correct answer is (E).
3^{x  y} = 27 = 3^{3} x  y = 3 ....(i)
3^{x + y} = 243 = 3^{5} x + y = 5 ....(ii)
On solving (i) and (ii), we get x = 4.
Suppose, number of articles bought = L.C.M. of 6 and 5 = 30.
C.P. of 30 articles = Rs.  5  x 30  = Rs. 25.  
6 
S.P. of 30 articles = Rs.  6  x 30  = Rs. 36.  
5 
Gain % =  11  x 100  % = 44%.  
25 
Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read the both statements and
 Give answer (A) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
 Give answer (B) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
 Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to answer the question.
 Give answer (D) if the data even in both Statements I and II together are not sufficient to answer the question.
 Give answer(E) if the data in both Statements I and II together are necessary to answer the question.
What is the length of a running train?  
I.  The train crosses a man in 9 seconds. 
II.  The train crosses a 240 metre long platform in 24 seconds. 
Time taken by train to cross a man =  Length of train  Speed =  l  ....(i) 
Speed of train  9 
Time taken by train to cross a platform = 
(Length of train + Length of platform) 
Speed =  l + 240  ....(ii) 
Speed of train  24 
From (i) and (ii), we get  l  =  l + 240  . 
9  24 
Thus, l can be obtained. So both I and II are necessary to get the answer.
The correct answer is (E).
Each of these questions is followed by three statements. You have to study the question and all the three statements given to decide whether any information provided in the statement(s) is redundant and can be dispensed with while answering the given question.
At what time will the train reach city X from city Y?  
I.  The train crosses another train of equal length of 200 metres and running in opposite directions in 15 seconds. 
II.  The train leaves city Y at 7.15 a.m. for city X situated at a distance of 558 km. 
III.  The 200 metres long train crosses a signal pole in 10 seconds. 
From the statement I, we get length of the train is 200 metres (Redundant info while comparing with Statement III). The rest of the info given in this statement cannot be used for calculating the speed of the train, because the two trains might run at different speed.
III gives, speed =  200  m/sec = 20 m/sec =  20 x  18  km/hr = 72 km/hr.  
10  5 
II gives, time taken =  558  hrs =  31  hrs = 7  3  hrs = 7 hrs 45 min.  
72  4  4 
So, the train will reach city X at 3 p.m.
Hence II and III only gives the answer.
Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.
What is the speed of the boat in still water?  
I.  The speed downstream is 12 kmph. 
II.  The speed upstream is 4 kmph. 
III.  In a to and fro journey between two points, the average speed of the boat was 6 kmph. 
From I and II, speed of boat in still water =  1  (12 + 4) km/hr = 8 km/hr. 
2 
From II and III, we get:
Using average speed =  2xy  , we get:  2 x 4 x y  = 6 
x + y  4 + y 
8y = 24 + 6y
y = 12.
Required speed =  1  (12 + 4) km/hr = 8 km/hr. 
2 
Similarly, I and III also give the answer.
Correct answer is (D).
Let the sum invested in Scheme A be Rs. x and that in Scheme B be Rs. (13900  x).
Then,  x x 14 x 2  +  (13900  x) x 11 x 2  = 3508  
100  100 
28x  22x = 350800  (13900 x 22)
6x = 45000
x = 7500.
So, sum invested in Scheme B = Rs. (13900  7500) = Rs. 6400.
Video Explanation: https://youtu.be/Xi4kU9y6ppk
Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.
What is the principal sum?  
I.  The sum amounts to Rs. 690 in 3 years at S.I. 
II.  The sum amounts to Rs. 750 in 5 years at S.I. 
III.  The rate of interest is 5% p.a. 
Clearly, any two of the three will give us the answer.
Correct answer is (E).
Let the length of the wire be h.
Radius =  1  mm  =  1  cm.  Then, 
2  20 
22  x  1  x  1  x h = 66.  
7  20  20 
h =  66 x 20 x 20 x 7  = 8400 cm = 84 m.  
22 
The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only).
So, in a day, the hands point in the opposite directions 22 times.
The cost price of a Rs. 100 stock at 4 discount, when brokerage is  1  %  is: 
4 
C.P. = Rs.  100  4 +  1  = Rs. 96.25  
4 
We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).
Required number of ways  = (^{7}C_{3} x ^{6}C_{2}) + (^{7}C_{4} x ^{6}C_{1}) + (^{7}C_{5})  




= (525 + 210 + 21)  
= 756. 
Let P.W. be Rs. x.
Then, S.I. on Rs. x at 16% for 9 months = Rs. 189.
x x 16 x  9  x  1  = 189 or x = 1575. 
12  100 
P.W. = Rs. 1575.
Sum due = P.W. + T.D. = Rs. (1575 + 189) = Rs. 1764.