Multiple choice

Each question contains a statement followed by Quantity I and Quantity II. Read the contents clearly and answer your questions accordingly. Quantity I: How many numbers greater than 3 million can be formed by using the digits 4, 2, 3, 0, 3, 4, 5? Quantity II: How many words can be formed using the letters of the word “CORRESPONDING” if the consonants are always written together?

  1. Quantity II > Quantity I

  2. Quantity I ≥ Quantity II

  3. Quantity I > Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II
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A Correct answer
Explanation

Quantity I: Count 7-digit numbers > 3,000,000 from digits {4,2,3,0,3,4,5}. If first digit is 4 or 5: 2 × 720/2 = 720. If first digit is 3: remaining digits {2,0,3,4,4,5} arranged in 720/2 = 360 ways. Total = 1080. Quantity II: In CORRESPONDING, consonants CRRSPNDNG (9 letters, R repeated) must stay together. Treat consonant block + 4 vowels = 5 units. Vowels OEOI (4 distinct) arrange in 4! = 24. Within block, CRRSPNDNG has 9!/2! = 181440 arrangements. Total = 24 × 181440 = 4354560. Since 4354560 > 1080, Quantity II > Quantity I is correct.

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