Find the correct answer If SMART = 96 and MIND = 56, then PRO = ?

Question

Find the correct answer

If SMART = 96 and MIND = 56, then PRO = ?

1. A. 55
2. B. 56
3. C. 57
4. D. 58 (Correct answer)

Correct Answer

Option D — 58

Detailed Solution & Explanation

The correct answer is 58.

Key Points

• The code is the sum of the alphabetical positions of the letters, plus the square of the number of letters.
• Verifying with SMART (5 letters):
  • $S + M + A + R + T = 19 + 13 + 1 + 18 + 20 = 71$
  • $71 + 5^2 = 71 + 25 = \mathbf{96} \;✓$
• Verifying with MIND (4 letters):
  • $M + I + N + D = 13 + 9 + 14 + 4 = 40$
  • $40 + 4^2 = 40 + 16 = \mathbf{56} \;✓$
• Applying it to PRO (3 letters):
  • $P + R + O = 16 + 18 + 15 = 49$
  • $49 + 3^2 = 49 + 9 = \mathbf{58}$

Shortcut Trick

• Since all four options lie between 55 and 58, only the final adjustment needs to be right — the letter sum of 49 is common to every candidate answer. Confirm the rule on the shorter given word (MIND) first, since a 4-letter check is quicker than a 5-letter one.

Additional Information

• Method for number-coding questions:
  • Compute the plain letter-position sum first and compare it with the given code. The gap is the clue.
  • Here SMART gave 71 against a code of 96, a gap of 25; MIND gave 40 against 56, a gap of 16. Recognising 25 and 16 as $5^2$ and $4^2$ — the squares of the word lengths — completes the rule.
  • Always test the rule on both given examples before applying it. A rule that fits only one is usually a coincidence.
• Other frequent number-coding rules: the letter-position sum alone; the sum multiplied by the number of letters; the sum of the reverse positions ($27 - n$); the product of the first and last letter positions; and the sum of the digits of the sum.
• EJOTY — E=5, J=10, O=15, T=20, Y=25 — makes locating any letter's position a matter of counting no more than two steps.