Test-Series - numerical

Test Number 1/39

Q: Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. 

What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.

P(E) = n(E)/n(S) = 9/20. 
A. 1/2
B. 3/5
C. 9/20
D. 8/15
Solution: Here, S = {1, 2, 3, 4, ...., 19, 20}
The correct answer is: C) 9/20
Q: If 75% of a number is added to 75, then the result is the number itself. The number is :
A. 100
B. 200
C. 300
D. 400
Solution: Let the number be x,

Then  75% of x + 75 = x  => x - 75x/100 =75  => x =  300 .
The correct answer is: C) 300
Q: Today is Monday. After 61 days, it will be :
A. Tuesday
B. Monday
C. Sunday
D. Saturday
Solution: Each day of the week is repeated after 7 days.
So, after 63 days, it will be Monday.  
After 61 days, it will be Saturday.
The correct answer is: D) Saturday
Q: What was the day on 15th august 1947 ?
A. Friday
B. Saturday
C. Sunday
D. Thursday
Solution: 15 Aug, 1947 = (1946 years + Period from 1.1.1947 to 15.8.1947)  
Odd days in 1600 years = 0   
Odd days in 300 years = 1  
46 years = (35 ordinary years + 11 leap years) = (35 x 1 + 11 x 2)= 57 (8 weeks + 1 day) = 1 odd day   
Jan.   Feb.   Mar.   Apr.   May.   Jun.   Jul.   Aug    ( 31 + 28 + 31 + 30 + 31 + 30 + 31 + 15 ) = 227 days = (32 weeks + 3 days) = 3 odd days.  
Total number of odd days = (0 + 1 + 1 + 3) = 5 odd days.     
Hence, as the number of odd days = 5, the given day is Friday.

The correct answer is: A) Friday
Q: 405 sweets were distributed equally among children in such a way that the number of sweets received by each child is 20% of the total number of children. How many sweets did each child recieve ?
A. 9
B. 10
C. 11
D. 12
Solution: Let the total number of children be x. 
Then, x * (20% of x) = 405   => x * 20x/100 = 405  15x2 = 405    => x=45   
 Number of sweets received by each child = 20% of 45 = 9.
The correct answer is: A) 9
Q: The L.C.M of two numbers is 495 and their H.C.F is 5. If the sum of the numbers is 100, then their difference is
A. 10
B. 46
C. 70
D. 90
Solution: Let the numbers be x and (100-x).  Then,
x100-x=5*495    =>  x2-100x+2475=0    =>  (x-55) (x-45) = 0    =>  x = 55 or x=45
The numbers are 45 and 55
Required difference = (55-45) = 10
The correct answer is: A) 10
Q: If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?
A. 1
B. 3
C. 7
D. 14
Solution: Let the required number of days be x.
Less spiders, More days (Indirect Proportion) Less webs, Less days (Direct Proportion)  
Spiders1:7Webs7:1⋮⋮ 7:x  => 1 * 7 * x = 7 * 1 * 7  => x= 7
The correct answer is: C) 7
Q: The speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 35 kms. what was the total distance travelled in 12 hours?
A. 456 kms
B. 482 kms
C. 552 kms
D. 556 kms
Solution: Total distance travelled in 12 hours   =(35+37+39+.....upto 12 terms)
This is an A.P with first term, a=35, number of terms,n= 12,d=2.
Required distance  = 12/2[2 x 35+{12-1) x 2]=6(70+23)= 552 kms.
The correct answer is: C) 552 kms
Q: Simplify:

1.53 + 4.73 + 3.83 - 3 x 1.5 x 4.7 x 3.81.52 + 4.72 + 3.82 - 1.5 x 4.7 - 4.7 x 3.8 - 1.5 x 3.8
A. 6
B. 8
C. 10
D. 12
Solution: Apply:

a3 + b3 + c3 - 3abca2 + b2 + c2 - ab - bc - ca = a + b + c  

Hence, the answer is  1.5 + 4.7 + 3.8 = 10.
The correct answer is: C) 10
Q: If 75% of a number is added to 75, then the result is the number itself. The number is :
A. 100
B. 200
C. 300
D. 400
Solution: Let the number be x,

Then  75% of x + 75 = x  => x - 75x/100 =75  => x =  300 .
The correct answer is: C) 300

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