Grade 6 : Mathematics (Ganita Prakash) - Number Play

Question 1

A school librarian has 108 science books and 72 mathematics books. She wishes to stack them on shelves so that each stack contains an equal number of books of only one subject.

What is the greatest possible number of books in each stack?

Accepted Answer

B) 36

Answer

A) 18

Answer

C) 24

Answer

D) 54

Question 2

Assertion (A): The sum of two consecutive prime numbers greater than 2 is always an even number.
Reason (R): Every prime number greater than 2 is odd, and the sum of two odd numbers is always even.

Choose the correct option:

Accepted Answer

A) Both (A) and (R) are true and (R) is the correct explanation of (A).

Answer

B) Both (A) and (R) are true but (R) is not the correct explanation of (A).

Answer

C) (A) is true, but (R) is false.

Answer

D) (A) is false, but (R) is true.

Question 3

A 5-digit secret code is represented as $47X28$. This code must be completely divisible by 9 to unlock a vault.

What single digit must replace $X$?

Accepted Answer

C) 6

Answer

A) 4

Answer

B) 5

Answer

D) 7

Question 4

Which of the following numbers is a perfect number (a number equal to the sum of all its proper divisors)?

Accepted Answer

C) 28

Answer

A) 12

Answer

B) 24

Answer

D) 32

Question 5

Three sports bells ring at intervals of 12 minutes, 15 minutes, and 20 minutes respectively. If all three bells toll together at 9:00 AM, at what time will they next toll together?

Find the next tolling time:

Accepted Answer

B) 10:00 AM

Answer

A) 9:45 AM

Answer

C) 10:15 AM

Answer

D) 10:30 AM

Question 6

Two numbers are called co-prime if their highest common factor is 1. Which pair of numbers is co-prime?

Accepted Answer

D) 15 and 28

Answer

A) 21 and 35

Answer

B) 18 and 27

Answer

C) 26 and 39

Question 7

Using the divisibility rule for 11, determine which digit $P$makes the 6-digit number$8P5412$divisible by 11.

Accepted Answer

A) 6

Answer

B) 4

Answer

C) 3

Answer

D) 8

Question 8

Ravi arranges a collection of 60 square tiles into various rectangular formations. Each formation has dimensions$L imes W$ tiles.

How many distinct factors does the number 60 have?

Accepted Answer

B) 12

Answer

A) 10

Answer

C) 14

Answer

D) 16

Question 9

Twin primes are pairs of prime numbers that differ by exactly 2. Which of the following is NOT a pair of twin primes?

Accepted Answer

D) 21 and 23

Answer

A) 11 and 13

Answer

B) 17 and 19

Answer

C) 29 and 31

Question 10

Assertion (A): If a number is divisible by both 4 and 6, it must always be divisible by 24.
Reason (R): For a number to be divisible by the product of two divisors, the two divisors must be co-prime.

Select the correct choice:

Accepted Answer

A) (A) is false, but (R) is true.

Answer

B) Both (A) and (R) are true and (R) is the correct explanation of (A).

Answer

C) Both (A) and (R) are true but (R) is not the correct explanation of (A).

Answer

D) (A) is true, but (R) is false.

Question 11

A teacher wants to distribute 84 notebooks and 140 pencils equally among a group of students such that every student gets the same number of notebooks and the same number of pencils, with none left over.

What is the maximum number of students who can receive these supplies?

Accepted Answer

C) 28

Answer

A) 14

Answer

B) 21

Answer

D) 42

Question 12

What is the smallest 3-digit number that is completely divisible by 6, 8, and 12?

Accepted Answer

B) 120

Answer

A) 112

Answer

C) 144

Answer

D) 108

Question 13

A student is testing a 6-digit identification number $73A21B$for divisibility by 6. She knows the number must be divisible by both 2 and 3.

If$B = 4$, which of the following values can $A$take?

Accepted Answer

A) 4

Answer

B) 3

Answer

C) 2

Answer

D) 5

Question 14

The product of two numbers is 1800 and their HCF is 15. What is the LCM of the two numbers?

Accepted Answer

C) 120

Answer

A) 60

Answer

B) 90

Answer

D) 150

Question 15

Assertion (A): The HCF of any two consecutive natural numbers is always 1.
Reason (R): Two consecutive natural numbers never share any common factor other than 1.

Choose the correct option:

Accepted Answer

D) Both (A) and (R) are true and (R) is the correct explanation of (A).

Answer

A) (A) is true, but (R) is false.

Answer

B) (A) is false, but (R) is true.

Answer

C) Both (A) and (R) are true, but (R) is not the correct explanation of (A).

Question 16

A shopkeeper has three containers containing 32 litres, 48 litres, and 56 litres of fruit juice. He wants a measuring can of maximum capacity that can measure the juice of all three containers in an exact number of times.

What must be the capacity of this measuring can?

Accepted Answer

B) 8 litres

Answer

A) 4 litres

Answer

C) 12 litres

Answer

D) 16 litres

Question 17

What is the sum of all prime numbers between 20 and 40?

Accepted Answer

B) 120

Answer

A) 118

Answer

C) 122

Answer

D) 143

Question 18

Consider the number 504. A student wants to express it as a product of powers of its prime factors: $504 = 2^a imes 3^b imes 7^c$.

What is the value of $a + b + c$?

Accepted Answer

C) 6

Answer

A) 5

Answer

B) 7

Answer

D) 8

Question 19

Find the least number which when divided by 15, 20, and 25 leaves a remainder of 4 in each case.

Accepted Answer

A) 304

Answer

B) 300

Answer

C) 296

Answer

D) 154

Question 20

A 4-digit number $3K42$is tested for divisibility by 4 and 8.

Which of the following statements about$3K42$is unconditionally true for any single digit$K$?

Accepted Answer

C) It is never divisible by 4.

Answer

A) It is always divisible by 4.

Answer

B) It is always divisible by 8.

Answer

D) It is divisible by 4 only if $K$is even.

Set 3Grade 6 : Mathematics (Ganita Prakash) - Number Play