Playing with Numbers Test

Result

Playing with Numbers Test - 3

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Weekly Quiz Competition

Question 1
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What is the least number of square sheets of cloth required to cover a land having dimensions 64 m × 32 m?

A
4

B
6

C
8

D
12

Solution

Area of the land = 64 × 32 = 2048 m²

Out of the given numbers, when we divide 2048 by 8, we get a perfect square number.
2048 ÷ 8 = 256

Therefore, the area of each sheet will be 256 m².

Square root of 256 = 16

Therefore, the sheets will have dimensions 16 m × 16 m, and the number of sheets required is 8.
Question 2
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Which of the following statements are true?

A. The divisor can't be greater than the remainder.
B. All prime numbers are odd.
C. The LCM of two even numbers is also even.
D. 1 is a multiple of every number.

A
A and B

B
A and C

C
A, B and C

D
B and C

Solution

A - True - Divisor is the number we divide a number by. Remainder is the amount left over after dividing the number. The divisor can't be greater than the remainder because if the remainder is bigger than the divisor, the divisor can divide the remainder, which is not possible.

B - False - 2 is a prime number and is even.

C - True - LCM is the lowest possible common number in the times table of two numbers, and the numbers in the times table of even numbers are also even.

D - False - 1 is in the times table of 1 only. It doesn't come in the times table of any other number.
Question 3
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Directions For Questions

Read the following statements and choose the correct option.

...view full instructions

Statement 1: If two numbers are divisible by a number, then their product will also be divisible by that number.
Statement 2: The sum of two perfect square numbers can be equal to another perfect square number.

Which of the above is true?

A
Both statements 1 and 2 are true.

B
Only statement 1 is true.

C
Only statement 2 is true.

D
Both statements 1 and 2 are false.

Solution

Statement 1: If two numbers are divisible by a number, then their product will also be divisible by that number. (TRUE)
Let the two numbers be 8 and 12, which are in the table of 4, hence divisible by 4.
Product of 8 and 12 = 96
96 is also in the table of 4, hence divisible by 4.

Statement 2: The sum of two perfect square numbers can be equal to another perfect square number. (FALSE)
Square of 3 = 9
Square of 5 = 25

Square of 3 + Square of 5 = 9 + 25 = 34
34 is not a square number.
Question 4
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Fill in the blanks.

(A) The HCF of two consecutive even numbers below 10 is ________.
(B) The natural numbers which have more than two factors are called ________.
(C) If a number is divisible by 6, it must be divisible by ______.

A
A = 2, B = composite, C = 2

B
A = 2 or 4, B = composite, C = 2

C
A = 2, B = composite, C = 2 and 3

D
A = 2 or 4, B = composite, C = 2 and 3

Solution

Even numbers below 10 are 2, 4, 6 and 8.
The HCF of two numbers could be either 2 or 4.

The numbers which have more than two factors are called composite numbers.
2 and 3 are prime factors of 6. If a number is divisible by 2 and 3, it is also divisible by 6.
Question 5
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Find the values of X, Y and Z, if 24X8 is divisible by 4, 447Y is divisible by 3 and 724Z is divisible by 6.

A
X = 0, Y = 2, Z = 2

B
X = 1, Y = 3, Z = 2

C
X = 0, Y = 3, Z = 2

D
X = 0, Y = 3, Z = 4

Solution

A number is divisible by 4 if the number formed by the last two digits of the number is divisible by 4.
Number formed by the last two digits of 24X8 = X8
Here, the value of X can be 0, 2, 4, 6, or 8 because 08, 28,48,68 and 88 are all in the times table of 4.

A number is divisible by 3 if the sum of its digits is divisible by 3.
Sum of the digits of 447Y = 4 + 4 + 7 + Y
= 15 + Y
Here, the value of Y can be 0, 3, 6, or 9 because 15, 18, 21 and 24 are all in the times table of 3.

A number is divisible by 6 if it is divisible by both 2 and 3.
To be divisible by 2, 724Z has to be an even number.
Therefore, the value of Z can be 0, 2, 4, 6, or 8 because 7240, 7242, 7244, 7246 and 7248 are all even numbers.

A number is divisible by 3 if the sum of its digits is divisible by 3.
Out of these 5 numbers, only the sum of digits of 7242 and 7248 is divisible by 3.
Therefore, the value of Z can be 2 or 8.