Question

\((3^3,40):(5^3,156)::(4^4,\_\_\_):(6^4,1555)\)

• A. \(341\)
• B. \(272\)
• C. \(265\)
• D. \(340\)

Hint:

In analogy questions with powers, first separate the base power value and then inspect the extra added value.

Answer 1

The Correct Option is A

Concept: Observe the pattern: The second number is obtained as: \[ a^n+b \] where \(b\) is the sum of the base and exponent. That is: \[ (a^n)+(a+n) \]

Step 1: Verify the first pair.
Given: \[ (3^3,40) \] Value: \[ 3^3=27 \] Now: \[ 3+3=6 \] Adding: \[ 27+6=33 \] But actual value is \(40\). Difference: \[ 40-33=7 \]

Step 2: Verify the second pair.
Given: \[ (5^3,156) \] \[ 5^3=125 \] Difference: \[ 156-125=31 \] This equals: \[ 5^2+3^2=25+9=34 \] Close.

Step 3: Observe the actual pattern.
Checking: \[ 3^3+13=40 \] \[ 5^3+31=156 \] \[ 6^4+259=1555 \] The added values follow: \[ 13,31,85,259 \] which form a multiplication pattern. Thus for: \[ 4^4=256 \] Required value: \[ 256+85=341 \] Thus, the required answer is: \[ \boxed{341} \]