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Divisibility by 10

P, Q and R ar...

Question

P, Q and R are three natural numbers such that P and Q are primes and Q divides PR Then out of the following the correct statement is

Q divides R

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P divides R

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P divides QR

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P divides PQ

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Solution

The correct options are
A Q divides R
D P divides PQ
Since P and Q are primes and Q divides PR
=> Q divides R as Q divides PR
And P divides PQ as PQ is the product of P and Q

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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.

Question 69

State whether the following statement is true or false:

Let x and y be natural numbers. If x divides y, then $x^{3}$ divides $y^{3}$

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