Choose the correct statements
S1: All the numbers divisible by 10 are also divisible by 5.
S2: A number divisible by 3 is also divisible by 6.
S3: A number is divisible by 7, if the last two digits are divisible by 7.
S4: If a number divides the product of two numbers exactly then it must exactly divide the numbers separately.
S5: If a number exactly divides two numbers separately, and after division, if its difference is taken then this difference will also be exactly divisible by that number.

Only S1 is correct.

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S1, S2 and S5 are correct.

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S4 and S5 are correct.

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All the statements are correct.

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Solution

The correct option is A Only S1 is correct.
A number which is divisible by 10 will have a factor of 5 so for sure it will be divisible by 5.
Secondly, a number divisible by 2 and 3 both will be divisible by 6 and not just 3.
A number which is divisible by 7, we have to remove the last digit, double it, subtract it from the truncated original number and continue doing this until only one digit remains. If this is 0 or 7, then the original number is divisible by 7.
And for the last two cases one can just solve and check and it will be known that the statements written are incorrect.
For example, 24 is divided exactly by 6, 4 × 6 = 24. Now we can see that 6 is exactly divisible by 6 but 4 cannot be exactly divided by 6. Hence the statement is incorrect.
Lastly, 12 is divided by 3 exactly and 6 is also divided by 3 exactly. After division we will get the numbers as 4 and 2, the difference of 4 and 2 is 2, and 2 is not divisible by 3. Hence the statement is incorrect.

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Similar questions

Which of the following statements are true?

(a) If a number is divisible by 3, it must be divisible by 9.

(b) If a number is divisible by 9, it must be divisible by 3.

(d) If a number is divisible by 9 and 10 both, then it must be divisible by 90.

(e) If two numbers are co-primes, at least one of them must be prime.

(f) All numbers which are divisible by 4 must also be divisible by 8.

(g) All numbers which are divisible by 8 must also be divisible by 4.

(h) If a number exactly divides two numbers separately, it must exactly divide their sum.

(i) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.

Question 1

Which of the following statements are true:
(a) If a number is divisible by 3, it must be divisible by 9.
(b) If a number is divisible by 9, it must be divisible by 3.
(c) If a number is divisible by 18, it must be divisible by both 3 and 6.
(d) If a number is divisible by 9 and 10 both, then it must be divisible by 90.
(e) If two numbers are co-primes, at least one of them must be prime.
(f) All numbers which are divisible by 4 must also be divisible by 8.
(g) All numbers which are divisible by 8 must also be divisible by 4.
(h) If a number exactly divides two numbers separately, it must exactly divide their sum.
(i) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.

Q. Write (T) for true and (F) for false against each of the following statements:
(i) If a number is divisible by 4, it must be divisible by 8.
(ii) If a number is divisible by 8, it must be divisible by 4.
(iii) If a number divides the sum of two numbers exactly, it must exactly divide the numbers separately.
(iv) If a number is divisible by both 9 and 10, it must be divisible by 90.
(v) A number is divisible by 18 if it is divisible by both 3 and 6.
(vi) If a number is divisible by 3 and 7, it must be divisible by 21.
(vii) The sum of two consecutive odd numbers is always divisible by 4.
(viii) If a number divides two numbers exactly, it must divide their sum exactly.

Q. Which of the following statements are true?

(i) If a number is divisible by 3, it must be divisible by 9.
(ii) If a number is divisible by 9, it must be divisible by 3.
(iii) If a number is divisible by 4, it must be divisible by 8.
(iv) If a number is divisible by 8, it must be divisible by 4.
(v) A number is divisible by 18, if it is divisible by both 3 and 6.
(vi) If a number is divisible by both 9 and 10, it must be divisible by 90.
(vii) If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.
(viii) If a number divides three numbers exactly, it must divide their sum exactly.
(ix) If two numbers are co-prime, at least one of them must be a prime number
(x) The sum of two consecutive odd numbers is always divisible by 4.

Which of the following statements are true ?
(i) If a number is divisible by 3, it must be divisible by 9.
(ii) If a number is divisible by 9, it must be divisible by 3.
(iii) If a number is divisible by 4, it must be divisible by 8.
(iv) If a number is divisible by 8, it must be divisible by 4.
(v) A number is divisible by 18, if it is divisible by both 3 and 6.
(vi) If a number is bivisible by both 9 and 10, ut nyst be divisible by 90.
(vii) If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.
(viii) If a number divides three numbers exactly, it must divede their sum exactly.
(ix) If two numbers are co-prime , at least one of them must be a prime number.
(x) The sum of two consecutive odd numbers is always divisible by 4.

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