Numbers And Number System Test-1

Result

Numbers And Number System Test-1

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0.25

In a three digit number, the digit in the unit ’s place is twice the digit in the ten ’s place and 1.5 times the digit in the hundred ’s place. If the sum of all the three digits of the number is 13, what is the number?

A
356

B
456

C
436

D
626

E
516

Solution

100a + 10b + c
c = 2b →b = c/2
c = 1.5a →a = c/1.5
c/1.5 + c/2 + c = 13
6.5c = 39
c = 6, b = 3, a = 4 ⇒436
Question 2
1 / -0.25

In a two digit positive number, the digit at the units place is equal to the square of the digit in ten ’s place and the difference between the number and the number obtained by interchanging the digits is 54. What is 40% of the original number?

A
15.6

B
37.2

C
39.4

D
24.8

E
None of the Above
Solution
To solve the problem, follow these steps:

Let the tens digit be x . Then, the units digit is x ² .

The number can be expressed as 10x + x ² .

When digits are interchanged, the new number becomes 10x ²+ x .

The difference between the original number and the number with interchanged digits is 54:

(10x + x ²) - (10x ²+ x) = 54

Simplifying, we get: -9x ²+ 9x = 54

Divide the entire equation by 9:

-x ²+ x = 6
x² -x = -6

Rearrange to form a quadratic equation: x ²- x + 6 = 0

Factorise the equation: (x - 3)(x + 2) = 0

Solutions for x are 3 and -2. Since x must be positive, x = 3 .

Therefore, the original number is 10 ×3 + 3 ²= 39 .

Calculate 40% of the original number:

0.4 ×39 = 15.6
Question 3
1 / -0.25

If the positions of the digits of a two digit number are interchanged, the number obtained is smaller than the original number by 27. If the digits of the number are in the ratio of 1:2, what is the original number?

A
16

B
32

C
63

D
48

E
Can not be determined

Solution

Thus, the original number is 63.
Question 4
1 / -0.25

A certain number of two digits is three times the sum of its digits. If 45 is added to it, the digits are reversed. The number is _______

A
16

B
72

C
63

D
27

E
Can not be determined

Solution
Question 5
1 / -0.25

The number obtained by interchanging the two digits of a two digit number is less than the original number by 27. If the difference between the two digits of the number is 3, then what is the original number?

A
64

B
72

C
65

D
73

E
None of the Above

Solution

original number –10x + y
(10x + y) –(10y + x) = 27
9(x –y) = 27
x –y = 3
All the given options not follow the condition.
Question 6
1 / -0.25

Two numbers such that the sum of twice the first number and thrice the second number is 100 and the sum of thrice the first number and twice the second number is 120. Which is larger number?

A
64

B
72

C
65

D
32

E
None of the Above

Solution
Question 7
1 / -0.25

The ratio of the two numbers is 11 : 4 and the H.C.F is 16, then find the sum of the two numbers.

A
240

B
255

C
480

D
220

E
None of these

Solution

Given:
The ratio of the two numbers is 11 : 4.
The H.C.F is 16
Concept used:
(1) For the two numbers in the ratio y : z.
The value of first number = H.C.F ×y
The value of first number = H.C.F ×z
Calculation:
The value of first number = 16 ×11 = 176
The value of second number = 16 ×4 = 64
The required sum = 176 + 64 = 240
∴The required answer is 240.
Question 8
1 / -0.25

A number is divided by 2, 3, 4, 5 or 6, reminder in each case is one. But the number is exactly divisible by 7. The number lies between 250 and 350, the sum of digits of the number will be

A
4

B
7

C
6

D
10

E
Can not be determined
Solution
To solve this problem, we need to find a number that satisfies the following conditions:

When divided by 2, 3, 4, 5, or 6, the remainder is 1.

The number is divisible by 7.

The number lies between 250 and 350.

Let 's start by finding the least common multiple (LCM) of 2, 3, 4, 5, and 6, which is the smallest number divisible by all of these numbers.

LCM(2, 3, 4, 5, 6) = 60

We need to find a number of the form 7k, where k is an integer, that leaves a remainder of 1 when divided by 60. The numbers in this sequence can be expressed as 60n + 1, where n is an integer.

Now, let 's find the first few numbers of the form 60n + 1 that are divisible by 7 and lie between 250 and 350:

For n = 4: 60(4) + 1 = 241 (not divisible by 7)

For n = 5: 60(5) + 1 = 301 (divisible by 7)

So, the number we 're looking for is 301.

Now, let 's find the sum of its digits: 3 + 0 + 1 = 4

Therefore, the sum of the digits of the number is 4.
Question 9
1 / -0.25

Sum of three consecutive odd numbers &three consecutive even numbers together is 231. Difference between the smallest odd number and the smallest even number is 11. What is the sum of the largest even number and largest odd number?

A
71

B
91

C
101

D
81

E
Can not be determined

Solution

odd numbers –x-2, x, x+2 ; even numbers –y-2, y, y+2
3x + 3y = 231
x + y = 77
(y –2) –(x –2) = 11
y –x = 11
x = 33, y = 44
sum of the largest even number and odd number = 46 + 35 = 81
Question 10
1 / -0.25

Sum of eight consecutive odd numbers is 656. Average of four consecutive even numbers is 87. What is the sum of the largest even number and largest odd number?

A
171

B
191

C
101

D
181

E
179

Solution

odd numbers —x-8, x-6, x-4, x-2, x, x+2, x+4, x+6
x-8 + x-6 + x-4 + x-2 + x + x+2 + x+4 + x+6 = 656
8x –8 =656
x = 83
Even numbers —y-2, y, y+2, y+4
4y + 4 = 87 * 4
y = 86
sum of the largest even number and odd number = 89 + 90 = 179