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Number System: Level 2 Test -11

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Question 1
When a number is divided by 2, 3, 4, 5 or 6, remainder in each case is 1. But the number is exactly divisible by 7. If the number lies between 250 and 350, the sum of digits of the number will be
A
4
B
5
C
7
D
10
Question 1 Explanation: 
The LCM of 2,3,4,5,6 is 60.
The required number is 60*5+1 = 301
which is divisible by 7.
Thus the sum of the digits is 3+1=4.
Correct option is (a)
Question 2
HCF of two numbers each of 4 digits is 103 and their LCM is 19261. Sum of the numbers is
A
2884
B
2488
C
4288
D
4882
Question 2 Explanation: 
Since both are 4 digits then the LCM will be of form 103pq
where p and q have almost equal number of digits
and the numbers are 103x and 103y. pq= 187 = 11x17
Thus the two numbers are 103x11 and 103x17
The sum will be 103x(11+17) = 103x28
Correct option is (a)
Question 3
A classroom has equal number of boys and girls. Eight girls left to play Kho-Kho, leaving twice as many boys as girls in the classroom. What was the total number of girls and boys present initially?
A
Cannot be determined
B
16
C
24
D
32
Question 3 Explanation: 
Let the no. of boys and girls each be x.
& 2x-16=x \\ & x=16 \\ \end{align}\]
Therefore total no. of boys and girls present initially in the classroom = 2x= 32
Question 4
The sum of four numbers is 64. lf you add 3 to the first number, 3 is subtracted from the second number, the third is multiplied by 3 and the fourth is divided by three, then all the results are equal. What is the difference between the largest and the smallest of the original numbers?
A
32
B
27
C
21
D
Cannot be determined
Question 4 Explanation: 
Let the 4 numbers be a,b,c,d.
a+b+c+d=64
a+3=b-3=3c=d/3=k(say)
Thus,
$ \begin{array}{l}k-3+k+3+\frac{k}{3}+3k=64\\=>k=12\end{array}$
Thus the numbers are 15,9,4,36.
Thus the difference = 36-4=32.
Question 5
If the digits of a two digit number are interchanged the newly formed number is more than the original number by 18, and sum of the digit is 8 then what was the original number?
A
53
B
26
C
35
D
Cannot be determined
Question 5 Explanation: 
Let the number be of form 10x+y.
x-y=18/9=2.
x+y=8
Solving we get,
x=5 and y=3.
The original number is 35.
Correct option is (c)
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