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Number System: Level 2 Test - 7

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Question 1
If the difference between one-third of a number and one-fourth of the number is 3, then find the value of the number?
A
18
B
24
C
30
D
36
Question 1 Explanation: 
Let the number be x
Then x/3 – x/4 =3
x/12 = 3 so x = 36
Question 2
If one-eighth of length of pencil is black, half of the remaining length is yellow, while the remaining 7/2 cm is blue, find the total length of the pencil is
A
6 cm
B
7 cm
C
8 cm
D
11 cm
Question 2 Explanation: 
1/8 part of pencil is black. Half of remaining, ie,  ½ x 7/8 = 7/16  is yellow.
Now, the part left = 7 / 16 , which  is equal to  7/2 = 3.5
 Therefore, total length of the pencil  3.5/7/16=8cm 
Question 3
In a certain shop, cost of 9 oranges is equal to 5 apples, cost of 5 apples is equal to 3 mangoes, cost of 4 mangoes is equal to 9 lemons. If 3 lemons cost 48 paise, find the price of an orange is
A
12 paise
B
14 paise
C
13 paise
D
15 paise
Question 3 Explanation: 
9 lemons = 144 paise = 4 mangoes
So, 3 mangoes = 144/4x 3 = 108 paise = 5 apples =>
9 oranges = 108 paise 108.
Therefore, One orange = 109/9 = 12 paIse
Question 4
Find the unit's digit of the product 735 x 371 X 1155
A
1
B
3
C
7
D
9
Question 4 Explanation: 
Unit digit in (7)4 = 1, therefore unit digit in (74)8
i.e., 7
^32 will be l.
 Hence, unit digit in (7) ^35 = 1 x 7 x 7 x 7 = 3
Again, unit digit in (3) ^ 4 = 1
Therefore, unit digit in the expansion of (3^4) ^17 =
(3) ^68 = 1: Unit digit in the expansion of (3) ^71 =1 x3x3x3=7
and unit digit in the expansion of (11) ^55 = 1:
Unit digit in the expansion of 7^35 x 3^71   X 11^55 =3x7x1=1
Question 5
The LCM and HCF of two numbers are 84 and 21 respectively. If the ratio of the two numbers is 1 : 4,  Find the largest number of these two numbers
A
12
B
48
C
84
D
108
Question 5 Explanation: 
Let the numbers be x and 4x.  
Then, 84 x 21 = x * 4x
=> 4x^2 = 1764
=> x^2 = 441
=> x = 21
Hence, the larger number is 4x = 84
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