6th Grade > Mathematics
PLAYING WITH NUMBERS MCQs
Total Questions : 100
| Page 4 of 10 pages
Answer: Option A. -> 220, 440 and 660
:
A
Common multiples of any given set of numbers will always be the multiples of the LCM of the numbers.
Now, LCM of 4, 5 and 11 can be found as follows.
Hence, LCM = 2×2×5×11=220
The multiples of 220 are 440, 660, 880...
Hence, in the given options, the common multiples of4, 5 and 11 are 220, 440 and660.
:
A
Common multiples of any given set of numbers will always be the multiples of the LCM of the numbers.
Now, LCM of 4, 5 and 11 can be found as follows.
Hence, LCM = 2×2×5×11=220The multiples of 220 are 440, 660, 880...
Hence, in the given options, the common multiples of4, 5 and 11 are 220, 440 and660.
Answer: Option D. -> sum, difference and product
:
D
If two given numbers are divisible by a number, then their sum, difference and product is also divisible by that number.
For example, the numbers 35 and 25 are both divisible by 5 and
their
i)difference (35-25 = 10) is also divisible by 5
ii)sum (35+25 = 60) is also divisible by 5.
iii)product(35×25=875) is also divisible by 5.
:
D
If two given numbers are divisible by a number, then their sum, difference and product is also divisible by that number.
For example, the numbers 35 and 25 are both divisible by 5 and
their
i)difference (35-25 = 10) is also divisible by 5
ii)sum (35+25 = 60) is also divisible by 5.
iii)product(35×25=875) is also divisible by 5.
Answer: Option A. -> 1, 3, 5 and 15
:
A
Factors of 75 are1, 3, 5,15, 25and 75.
Factors of 60 are1, 2, 3, 4, 5, 6, 10, 12, 15, 30and 60.
Factors of 210 are1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105 and 210.
∴Common factors of 75, 60 and 120 are1, 3, 5 and15.
:
A
Factors of 75 are1, 3, 5,15, 25and 75.
Factors of 60 are1, 2, 3, 4, 5, 6, 10, 12, 15, 30and 60.
Factors of 210 are1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105 and 210.
∴Common factors of 75, 60 and 120 are1, 3, 5 and15.
Question 34. Statement 1: If two numbers are co-primes, at least one of them must be prime.
Statement 2: If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.
Statement 3: If a number exactly divides two numbers, then it must also divide the sum of both numbers.
Statement 2: If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.
Statement 3: If a number exactly divides two numbers, then it must also divide the sum of both numbers.
Answer: Option B. -> False,False,True
:
B
Take an example and visualize-
i)9 and 4 are co-prime but none of them are prime.
ii)Now, 14 divides 28, but it does not divide 12 and 16.
iii)4 divides 12 and 16 separately
4 also divides 12+16 = 28
:
B
Take an example and visualize-
i)9 and 4 are co-prime but none of them are prime.
ii)Now, 14 divides 28, but it does not divide 12 and 16.
iii)4 divides 12 and 16 separately
4 also divides 12+16 = 28
Answer: Option D. -> 9648
:
D
If a number is divisible by both 2 and 3, then it will bedivisible by 6 also.
Divisibility by 2
Here all the numbers, 9638, 9640, 9642, 9648 are divisible by 2 as they end with one of these (0, 2, 4, 6, 8) numbers or simply as they are even numbers.
Divisibility by 3
⇒9 + 6 + 3 + 8 = 26
⇒9 +6 + 4 + 0 = 19
⇒9 + 6 + 4 + 2 = 21
⇒9 + 6 + 4 + 8 = 27
Here only 21 and 27 are divisible by 3 hence only9642 and 9648 are divisible by 3.
So, thesetwo numbers are divisible by both 2 and 3 and hence divisible by 6.
Divisibility by 8
A number will bedivisible by 8 only if the last three digits are divisible by 8.
Thelast 3 digits of only9648, i.e. 648 is divisible by 8.
But last three digits of 9642, i.e. 642 is not divisible by 8.
9648 is divisible by both 6 and 8.
:
D
If a number is divisible by both 2 and 3, then it will bedivisible by 6 also.
Divisibility by 2
Here all the numbers, 9638, 9640, 9642, 9648 are divisible by 2 as they end with one of these (0, 2, 4, 6, 8) numbers or simply as they are even numbers.
Divisibility by 3
⇒9 + 6 + 3 + 8 = 26
⇒9 +6 + 4 + 0 = 19
⇒9 + 6 + 4 + 2 = 21
⇒9 + 6 + 4 + 8 = 27
Here only 21 and 27 are divisible by 3 hence only9642 and 9648 are divisible by 3.
So, thesetwo numbers are divisible by both 2 and 3 and hence divisible by 6.
Divisibility by 8
A number will bedivisible by 8 only if the last three digits are divisible by 8.
Thelast 3 digits of only9648, i.e. 648 is divisible by 8.
But last three digits of 9642, i.e. 642 is not divisible by 8.
9648 is divisible by both 6 and 8.
Answer: Option B. -> 105 = 3 × 5 × 7
:
B
72 = 2 × 2 × 2 × 3 × 3
105 = 3 × 5 × 7
625 = 5 × 5 × 5 × 5
162 = 2 × 3 × 3 × 3 × 3
Hence, only the factorisation of 105 is correct
:
B
72 = 2 × 2 × 2 × 3 × 3
105 = 3 × 5 × 7
625 = 5 × 5 × 5 × 5
162 = 2 × 3 × 3 × 3 × 3
Hence, only the factorisation of 105 is correct
Answer: Option B. -> 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72
:
B
72=1×72
=2×36
=3×24
=4×18
=6×12
=8×9
Factors of 72 are1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and72.
:
B
72=1×72
=2×36
=3×24
=4×18
=6×12
=8×9
Factors of 72 are1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and72.
Answer: Option C. -> 19, 13, 11, 7, 3
:
C
Prime numbers have only two factors, 1 and the number itself.
1 is neither prime nor composite.
2 is the only even prime number.
9 and 39 have more than 2 factors, hence they are not prime numbers.
Considering all these, the correctoption is19, 13, 11, 7 and 3.
:
C
Prime numbers have only two factors, 1 and the number itself.
1 is neither prime nor composite.
2 is the only even prime number.
9 and 39 have more than 2 factors, hence they are not prime numbers.
Considering all these, the correctoption is19, 13, 11, 7 and 3.
Answer: Option A. -> a number whose sum of factors is equal to twice the number.
:
A
A perfect number is a number for which the sum of all its factors is equal to twice the number.
For example, 6 is a perfect number since the sum ofits factors 1, 2, 3 and 6 is 12 i.e. twice of 6.
Perfect numbers are also defined as those numbers that equalthe sum of all their factorsincluding 1 butexcluding the number itself.
Taking the same example of 6: sum of its factors excluding the numberitself i.e 6 = 1+2+3 = 6.
:
A
A perfect number is a number for which the sum of all its factors is equal to twice the number.
For example, 6 is a perfect number since the sum ofits factors 1, 2, 3 and 6 is 12 i.e. twice of 6.
Perfect numbers are also defined as those numbers that equalthe sum of all their factorsincluding 1 butexcluding the number itself.
Taking the same example of 6: sum of its factors excluding the numberitself i.e 6 = 1+2+3 = 6.
Answer: Option B. -> 999
:
B
Composite numbers are those numbers which are not prime numbers except 1. 1 is regarded as a unique number.
The largest 3 digit number is 999 and it is a composite number. (divisible by 3, 9 etc)
:
B
Composite numbers are those numbers which are not prime numbers except 1. 1 is regarded as a unique number.
The largest 3 digit number is 999 and it is a composite number. (divisible by 3, 9 etc)
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