Number system questions

Number System

Question 1 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
Two alarm clocks ring their alarms at regular intervals of 50 seconds and 48 seconds. If they first beep together at 12 noon, at what time will they beep again for first time?
A
12:12 PM
B
12:10 PM
C
None of these
D
12:11 PM
Question 1 Explanation: 
They will ring together after,

LCM of 48 and 50 secs.

48 = 2*2*2*2*3;

50 = 2*5*5;

LCM = 2*2*2*2*3*5*5 = 1200 secs

= 20 min.

They will beep together at 12:20.







Question 2 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
In a certain series, each number except the first and second is obtained by adding the previous two numbers. If the first no is 2 and sixth no is 26, then the seventh number is:
A
52
B
46
C
42
D
40
Question 2 Explanation: 
1stt no. = 2

2nd no. = x (let)

3rd no. = x+2

4th no. = x+x+2 = 2x+2

5th no. = x+2 + 2x+2 = 3x+4

Sixth no.,

3x+4 + 2x+2 = 26

5x = 20

x = 4

7th no. = 26 + 3x+4 = 26 + 3*4+4 = 42.

Question 3 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
A string of length 221 metre is cut into two parts such that one part is 9/4th as long as the rest of the string, then the difference between the larger piece and the shorter piece is :
A
53 m
B
85 m
C
76 m
D
58 m
Question 3 Explanation: 
Let one part of string is x.

Now,

x + (9x/4) = 221 m

x = 68 meter

and, (9x/4) = 153 m

Difference between two parts = 153 - 68 = 85m.







Question 4 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
The sum of first five prime numbers is:
A
18
B
11
C
28
D
26
Question 4 Explanation: 
Required sum = (2 + 3 + 5 + 7 + 11) = 28.

Note: 1 is not a prime number.

Definition : A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.

Question 5 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
76n- 66n, where n is an integer >0, is divisible by
A
All of these
B
127
C
13
D
559
Question 5 Explanation: 
For n = 1,

76n-66n = 76 -66

= (73)2-(63)2

= (73-63)( 73+63)

= (343-216)*(343+216)

= 127*559.

= 127 * 13 *43.

Clearly, it is divisible by 127, 13 as well as 559.







Question 6 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
The rightmost non-zero digit of the number 302720 is
A
1
B
3
C
7
D
9
Question 6 Explanation: 

(30)2720, we can write it as[(30)4]680

Or,[(10*3)4]680

The right most non-zero digit depends on the unit digit of [(3)4]680.

Unit digit of [(3)4]680,

Or, (81)680

The unit digit of 81 is 1 so any power of 81 will always give its unit digit as 1.

Thus, required unit digit is 1.

Question 7 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
What is the least number of square tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?
A
814
B
840
C
820
D
841
Question 7 Explanation: 

Length of the room = 15 m 17 cm = 15 *100 +17 = 1517 cm.

Breadth of the room = 9 m 2 cm = 902 cm.

The HCF of the 1517 and 902 will be size of square tiles.

HCF 1517 and 902 = 41 cm.

Area of the room = length * breadth = 1517 * 902 cm2.

Area of tiles = 41 *41 cm21

So, no. of tiles required = (1517 *902) /(41*41) = 814 tiles.







Question 8 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
A magazine publisher publishes a monthly magazine of 84 pages. One I found that in a magazine 4 pages was missing. One out of them was page number 29 it is known that the page number of the last page of the magazine is 84, (including the cover pages). The numbers printed on the missing pages were :
A
28, 52, 53
B
30, 55, 56
C
Cannot determined
D
29, 52, 53
Question 8 Explanation: 

Since, the magazine has 84 pages it means that there are 21 sheets of paper, which are folded in the middle. The pattern of pages will be this way,

Left Right
1, 283,84
3, 481, 82
-

-

-

-

-

-

-

-

29, 30
Question 9 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
If 381A is divisible by 9, find the value of the smallest natural number A?
A
6
B
5
C
9
D
8
Question 9 Explanation: 
A number is divisible by 9 when the sum of its digit is divisible by 9.

So, (3+8+1+A) = must be divisible by 9;

Thus, smallest natural number be 6.

Or, (3+8+1+6) = 18, this is divisible by 9.







Question 10 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
The sum of two numbers is 684 and their HCF is 57. Find all possible pairs of such numbers.
A
(45,495)(30,330)
B
(57,627)(285,399)
C
(37,575)(270,390)
D
(45,575)(280,890)
Question 10 Explanation: 
Since, HCF of two numbers = 57.

Hence, numbers are multiples of 57.

Let, the numbers be 57x and 57y, where x and y are prime to each other.

According to the sum,

57x+57y = 684;

Or, x+y = 12;

Hence, required possible pair of values of x and y which are prime to each other are (1, 11) and (5, 7).

Thus, required pairs of numbers are;

{57*1 = 57 and 57*11 = 627}

{57*5 = 285 and 57*7 = 399 }

There are 10 questions to complete.

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