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Number System: Level 2 Test - 9

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Question 1
A man has 1044 candles. After burning candles, he can make a new candle out of 9 stubs left behind. Find the maximum number of candles that can be made.
A
116
B
120
C
130
D
140
Question 1 Explanation: 
1 candle is made from 9 stubs. Hence, 116 candles will be made from 1044 stubs
From 116 candles, 12 candles can be made. 8 are stubs left.
Now, total stubs left = (12 + 8) = 20 out of which candles can be made with 2 stubs left.
Maximum number of candles that can be m= 116 + 12+ 2= 130
Question 2
A group of 15 women, 7 have nose studs, 8 have ear rings and 3 have neither. How many of these have both nose studs and earrings?
A
0
B
2
C
3
D
7
Question 2 Explanation: 
Let the number of women who have both studs and rings= a
Number of women who only have studs = 7-a
Number of women who only have nose rings = 8-a
Total number of women= Number of women who only have studs + Number of women who only have nose rings + Number of women who only have nose rings and studs + Number of women who only neither have nose rings nor studs 15 = 7 - a + 8 - a + a + 3
a = 3
Question 3
Pintu dealt some cards to Mintu and himself from a full pack of playing cards and laid the rest aside. Pintu then said to Mintu, "If you give me a certain number of your cards, I will have 4 times as many cards as you have. If I give you the same number of cards, I will have thrice as many cards as you have." How many cards did Pintu have?
A
31
B
32
C
29
D
30
Question 3 Explanation: 
Let P and M denote Pintu and Mintu respectively. (P + n) = 4 (M - n) => P - 4M = - 5n ... i) and (P - n) = 3 (M + n) => P - 3M = 4n ... (ii) Solving Equations . I and (ii), we get M = 9n and P = 31n Put n = 1, we get P = 31
Question 4
Students of a class are preparing for a drill and made to stand in a row. If 4 students are extra in Row, then there would be 2 rows less. But would be 4 more rows if 4 students are less in a class.The number of students in the class is
A
96
B
56
C
69
D
86
Question 4 Explanation: 
Let the number of students in the class be x.
Let the number of rows in which they are made to stand is y.
Number of students in each row will be (x/y+4)( y -2) = (x/y – 4 )( y + 4 )
3x - 4y2 - 4y = 0
X = 4 y 2 +4y /3
The least value of y which satisfy the given condition is 8 ie, Y = 8
x= 96
Question 5
A printer prints the pages of a book according to the series starting from 1 and uses 3189 digits in all. How many pages does the book have?
A
1074
B
1075
C
1000
D
None of these
Question 5 Explanation: 
1-digit numbers have 9 digits (9 numbers). 2-digit numbers have 180 digits (90 numbers). 3-digit numbers have 2700 digits (900 numbers). 4-digit numbers have 300 digits (75 numbers). Since, total number of digits = 3189 so number of digit for 4-digit numbers = 3189 - (9 + 180 + 2700) = 300 Total number of pages = 9 + 90 + 900 + 75=1074
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