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Prime Numbers

The units dig...

Question

The units digit of every prime number (other than $2$ and $5$ ) must be necessarily

A

1, 3

or

5

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B

1, 3, 7

or

9

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C

7

or

9

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D

1

or

7

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Solution

The correct option is D $1, 3, 7$ or $9$
All even numbers (other than $2$ ) are composite, so prime numbers cannot end with any of the digits $0, 2, 4, 6, 8$ .

Also, a number with unit digit $5$ will be divisible by $5.$

Therefore, the unit's digit of every prime number(other than $5$ ) must be necessarily $1, 3, 7$ or $9$ .

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Q. Which ratio is greater?

(i) (5 : 6) or (7 : 9)
(ii) (2 : 3) or (4 : 7)
(iii) (1 : 2) or (4 : 7)
(iv) (3 : 5) or (8 : 13)

Q. Which of the two rational numbers is greater in the given pair?
(i)

\frac{- 4}{3} or \frac{- 8}{7}

\frac{7}{- 9} or \frac{- 5}{8}

\frac{- 1}{3} or \frac{4}{- 5}

\frac{9}{- 13} or \frac{7}{- 12}

\frac{4}{- 5} or \frac{- 7}{10}

\frac{- 12}{5} or - 3

State, true or false :
$(i) \frac{7}{9} = \frac{7 + 5}{9 + 5} (i i) \frac{7}{9} = \frac{7 - 5}{9 - 5} (i i i) \frac{7}{9} = \frac{7 \times 5}{9 \times 5} (i v) \frac{7}{9} = \frac{7 \div 5}{9 \div 5} (v) \frac{- 5}{- 12} is a negative rational number (v i) \frac{- 13}{25} is smaller than \frac{- 25}{13} .$

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