6.3: Analyzing Properties of Mirrored Letters or Sequences

 6.3: Analyzing Properties of Mirrored Letters or Sequences

This type involves analyzing properties (e.g., vowels, palindromes) of the mirrored sequence.

Problem 1

Question: How many vowels are in the mirrored word of "CAT"? (Vowels: A, E, I, O, U)

Solution Process:

• Word: CAT. Positions: C=3, A=1, T=20.
• Mirror each:
  • C: 27-3=24 → X (consonant).
  • A: 27-1=26 → Z (consonant).
  • T: 27-20=7 → I (vowel).
• New word: XZI.
• Vowels: I (1 vowel).

Solution: 1

Detailed Explanation:

• Mirroring "CAT" gives XZI (X=consonant, Z=consonant, I=vowel).
• Only I is a vowel, so the count is 1.
• This tests vowel counting in a mirrored word.

Problem 2

Question: Is the mirrored word of "DEED" a palindrome?

Solution Process:

• Word: DEED. Positions: D=4, E=5, E=5, D=4.
• Mirror each:
  • D: 27-4=23 → W.
  • E: 27-5=22 → V.
  • E: 27-5=22 → V.
  • D: 27-4=23 → W.
• New word: WVVW.
• Check palindrome: Forward = WVVW, Backward = WVVW (matches).

Solution: Yes, palindromic

Detailed Explanation:

• Mirroring "DEED" gives WVVW.
• WVVW reads the same forward and backward, so it’s palindromic.
• This tests symmetry in the mirrored result.

Problem 3

Question: How many consonants are in the mirrored word of "FAN"? (Consonants: all except A, E, I, O, U)

Solution Process:

• Word: FAN. Positions: F=6, A=1, N=14.
• Mirror each:
  • F: 27-6=21 → U (vowel).
  • A: 27-1=26 → Z (consonant).
  • N: 27-14=13 → M (consonant).
• New word: UZM.
• Consonants: Z, M (2 consonants).

Solution: 2

Detailed Explanation:

• Mirroring "FAN" gives UZM (U=vowel, Z=consonant, M=consonant).
• The consonant count is 2.
• This tests consonant counting.

Problem 4

Question: In the mirrored sequence A, B, C, D, how many letters are in the first half of the alphabet (A-M)?

Solution Process:

• Sequence: A=1, B=2, C=3, D=4.
• Mirror each:
  • A: 27-1=26 → Z.
  • B: 27-2=25 → Y.
  • C: 27-3=24 → X.
  • D: 27-4=23 → W.
• New sequence: Z, Y, X, W (positions: 26, 25, 24, 23).
• First half (A-M): Positions 1-13. None of Z, Y, X, W (all >13).
• Count: 0.

Solution: 0

Detailed Explanation:

• Mirroring A, B, C, D gives Z, Y, X, W, all in the second half (N-Z, positions 14-26).
• No letters are in A-M (1-13).
• This tests positional property analysis.

Problem 5

Question: Compare the number of vowels in "KEY" before and after mirroring.

Solution Process:

• Original word: KEY. Positions: K=11, E=5, Y=25.
• Vowels: E (1 vowel).
• Mirror each:
  • K: 27-11=16 → P (consonant).
  • E: 27-5=22 → V (consonant).
  • Y: 27-25=2 → B (consonant).
• New word: PVB.
• Vowels: None (0 vowels).
• Compare: 1 (before) vs. 0 (after).

Solution: 1 vowel before, 0 vowels after.

Detailed Explanation:

• "KEY" has 1 vowel (E). The mirrored word PVB has no vowels.
• The transformation changes the vowel count.
• This tests comparing properties.

Problem 6

Question: Is the mirrored word of "ABA" a palindrome?

Solution Process:

• Word: ABA. Positions: A=1, B=2, A=1.
• Mirror each:
  • A: 27-1=26 → Z.
  • B: 27-2=25 → Y.
  • A: 27-1=26 → Z.
• New word: ZYZ.
• Check palindrome: Forward = ZYZ, Backward = ZYZ (matches).

Solution: Yes, palindromic

Detailed Explanation:

• Mirroring "ABA" gives ZYZ, which is symmetric.
• ZYZ is palindromic, reflecting ABA’s palindromic nature.
• This tests symmetry preservation.

Problem 7

Question: How many vowels are in the mirrored sequence B, D, F? (Vowels: A, E, I, O, U)

Solution Process:

• Sequence: B=2, D=4, F=6.
• Mirror each:
  • B: 27-2=25 → Y (consonant).
  • D: 27-4=23 → W (consonant).
  • F: 27-6=21 → U (vowel).
• New sequence: Y, W, U.
• Vowels: U (1 vowel).

Solution: 1

Detailed Explanation:

• Mirroring B, D, F gives Y, W, U, with U as the only vowel.
• The count is 1.
• This tests vowel counting in a sequence.

Problem 8

Question: In the mirrored word of "HAT", how many letters are consonants?

Solution Process:

• Word: HAT. Positions: H=8, A=1, T=20.
• Mirror each:
  • H: 27-8=19 → S (consonant).
  • A: 27-1=26 → Z (consonant).
  • T: 27-20=7 → I (vowel).
• New word: SZI.
• Consonants: S, Z (2 consonants).

Solution: 2

Detailed Explanation:

• Mirroring "HAT" gives SZI (S=consonant, Z=consonant, I=vowel).
• The consonant count is 2.
• This tests consonant analysis.

Problem 9

Question: In the mirrored word of "GLOW", how many letters have positions greater than 13?

Solution Process:

• Word: GLOW. Positions: G=7, L=12, O=15, W=23.
• Mirror each:
  • G: 27-7=20 → T (20 > 13).
  • L: 27-12=15 → O (15 > 13).
  • O: 27-15=12 → L (12 < 13).
  • W: 27-23=4 → D (4 < 13).
• New word: TOLD.
• Positions > 13: T (20), O (15) → 2 letters.

Solution: 2

Detailed Explanation:

• Mirroring "GLOW" gives TOLD. Check positions: T=20, O=15, L=12, D=4.
• Only T and O are >13, so the count is 2.
• This tests positional property analysis.

Problem 10

Question: Compare the number of consonants in "PAT" before and after mirroring.

Solution Process:

• Original word: PAT. Positions: P=16, A=1, T=20.
• Consonants: P, T (2 consonants).
• Mirror each:
  • P: 27-16=11 → K (consonant).
  • A: 27-1=26 → Z (consonant).
  • T: 27-20=7 → I (vowel).
• New word: KZI.
• Consonants: K, Z (2 consonants).
• Compare: 2 (before) vs. 2 (after).

Solution: 2 consonants before, 2 consonants after.

Detailed Explanation:

• "PAT" has 2 consonants (P, T). The mirrored word KZI has 2 consonants (K, Z).
• The consonant count remains the same.
• This tests property comparison.