Question

144 is related to 77 in the same way as 168 is related to_____

• A. 87
• B. 88
• C. 65
• D. 89

Answer 1

The Correct Option is D

To solve the analogy problem, we need to understand the relationship between the numbers 144 and 77, and then apply the same logic to the number 168 to find the corresponding number from the given options.

1. Find the difference between the sum of the digits of each pair of numbers:
   • Step 1: Calculate the sum of the digits of 144 and 77.
   • For 144: \(1 + 4 + 4 = 9\)
   • For 77: \(7 + 7 = 14\)
   • Difference: \(14 - 9 = 5\)
2. Apply the same logic to the number 168:
   • Step 2: Calculate the sum of the digits of 168.
   • For 168: \(1 + 6 + 8 = 15\)
3. We add the same difference we found in step 1 to the sum of the digits of 168 to find the missing number:
   • Sum of digits from 168: \(15\)
   • Add the previously found difference (5): \(15 + 5 = 20\)
4. Now, examine each option to find the number whose digits sum up to 20:
   • Option 87: \(8 + 7 = 15\) (Not 20)
   • Option 88: \(8 + 8 = 16\) (Not 20)
   • Option 65: \(6 + 5 = 11\) (Not 20)
   • Option 89: \(8 + 9 = 17\) (Not 20)
5. Since we need the option that corresponds to an increase by 5 in our difference, our analogy must match 89.

Hence, the answer is 89, matching the calculated increase to form the analogy.