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The number 313−310 is divisible by (i)2 and 3 only (ii)3 and 10 only (iii)2,3,and 10 only (iv)all 2,3 and 13

The number 313−310 is divisible by
(i)2 and 3 only
(ii)3 and 10 only
(iii)2,3,and 10 only
(iv)all 2,3 and 13

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 60787 Points
2 years ago
Hint: We need to reduce the expression to a simpler form by taking out the common element 310and then calculate the value of (33−1) and by checking the divisibility of the obtained expression we get our answer Complete step by step answer: The given expression is 313−310 In order to reduce it into its simpler form,lets take 310 as common ⇒310(33−1) Step 2:Now let’s make this expression much simpler. We know that 33=27 Hence we get, ⇒310(27−1)⇒310(26) Step 3:From this it is clearly understood that the expression is divisible by 3. The expression can also be written as 310(2∗13) This shows that it is a multiple of 2 and 13. Hence it is divisible by 2 and 13 also. Therefore the given expression is divisible by 2,3 and 13. The answer is option d. Note: 1)In problems of these kinds, it is enough if we reduce the expression to its simplest form. There is no need to keep calculating the values of 313 and 310. This will take a lot of time and there are chances of making mistakes. 2)You need to read the question more carefully as many students write 313−310=33, which is completely wrong. 3)Many students get distracted by the choices provided and end up choosing that it is divisible by 10 as the expression consists of the term

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