Explanation:To find the HCF (Highest Common Factor) of 245, 175, and 385 using a shortcut method, follow these steps:
Step 1: Identify the common factors between the numbers quickly.
Step 1. Look for divisibility by small numbers:
– All the given numbers 245, 175, 385 are divisible by 5 (since each ends in 5).
Step 2. Divide by 5:
– ( 245 ÷ 5 = 49 )
– ( 175 ÷ 5 = 35 )
– ( 385 ÷ 5 = 77 )
Now we are left with the numbers 49, 35, and 77.
Step 2: Find the HCF of 49, 35, and 77.
Factorize these numbers:
– ( 49 = 7 × 7 )
– ( 35 = 5 × 7 )
– ( 77 = 7 × 11 )
The common factor is 7.
Step 3: Multiply the common factors:
– From Step 1, we divided by 5.
– From Step 2, the common factor is 7.
So, the HCF is:
HCF = 5 × 7 = 35
Conclusion:
The HCF of 245, 175, and 385 is 35.
Thus, the correct answer is 35.

Explanation:To solve this problem more efficiently using a shortcut method, let’s focus on the key clues provided and use a quick logical process to place the people around the table.
Key Clues:
»1. B sits second to the right of E.
»2. C sits to the immediate left of E.
»3. F sits second to the right of D.
Step-by-Step Shortcut:
»1. Positioning E:
– Since the problem doesn’t specify where to start, let’s assume E sits at position 1.
– C is immediately left of E, so C will be at position 6 (since it’s a circular table and left means one step counterclockwise).
»2. Positioning B:
– B sits second to the right of E. If E is at position 1, counting two places to the right (clockwise), B will be at position 3.
»3. Positioning F and D:
– F sits second to the right of D. To avoid conflicts, place D at position 4 and F will be at position 5.
»4. Remaining Person A:
– The only remaining empty spot is position 2, so A must sit there.
Final Seating Arrangement:
– Position 1: E
– Position 2: A
– Position 3: B
– Position 4: D
– Position 5: F
– Position 6: C
Who sits third to the right of A?
– Starting from A (position 2), the third seat to the right (clockwise) is D, who is seated at position 4.
Final Answer:
The person who sits third to the right of A is D.

Explanation:To find the value of , where ( k ) is the average of the numbers 16, 25, 13, 26, and 15, let’s follow the steps.
Step 1: Calculate the average value ( k )
The average of a set of numbers is the sum of the numbers divided by the number of values.
The numbers given are: ( 16, 25, 13, 26, 15 ).
The sum of these numbers is:
16 + 25 + 13 + 26 + 15 = 95
There are 5 numbers, so the average ( k ) is:

Step 2: Substitute ( k = 19 ) into (

Explanation:Now, let’s apply the same pattern to SPECULATION:
Break SPECULATION into individual letters:
S, P, E, C, U, L, A, T, I, O, N
Based on the previous examples, the pattern appears to involve swapping groups of letters in a specific order:
After rearranging the letters, we get the following transformed order: UTSPONLIECA
Thus, SPECULATION will be written as UTSPONLIECA in the code language.