Number System-Test 2

Answer: Option A

Explanation

Here, HCF of two 4-digits numbers=103

∴ Let the numbers be 103a and 103b

And LCM of 103a and 103b=19261

or  103(a×b)=19261

⇒ a×b=187

or a=11 or 17 and b=11 or 17

∴ Numbers =103×11=1133

= 103×17=1751

∴ Sum of these two numbers =2884.

Hence, Option A is correct.

Answer: Option A

Explanation

Here, First of all we have to find the LCM of 2, 3, 4, 5 and 6= 60

Now, 60×5+1=7k

Or 7k=301

K=43

So, sum of the digits of 301=3+0+1=4

Hence, Option A is correct.

Answer: Option B

Explanation

Here, to find out the time after which they meet again at the starting point

= LCM of 18, 24 and 32

=288 s

∴ After 288 s they will meet with one another.

Hence, Option B is correct.

Answer: Option C

Explanation

Here, to find the LCM of fractions,

We find the LCM of numerators and HCF of denominators.

So, $$\begin{gathered} \frac{LCM of 1, 5, 2 and 4}{HCF of 3, 6, 9 and 27} \\ =\frac{20}{3} \end{gathered}$$

Hence, Option C is correct.

Answer: Option C

Explanation

Here, to find out the time after which they will meet one another at the starting point, we have to find LCM of 45s, 36s and 54s

So, LCM of 45,36 and 54= 540s