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Texas Instruments technical mcq question, verified with a worked answer. Free to practise - no sign-up.
Zoey's age** Which of these statements is sufficient to determine the age of Zoey in 2050? Statement I: When Zoey was born her father was 32 years old, who is 4 years older than Zoey's mother. Statement II: Zoey's mother was born in the first leap year that came after 1970.
Show answer & explanation
Statement I provides the age difference between Zoey and her mother, but no absolute dates. Statement II provides the birth year of the mother. Together, they allow for the calculation of Zoey's birth year and subsequently her age in 2050.
Step-by-step Derivation:
Step 1: Analyze Statement I. It states: Father's age at Zoey's birth = 32. Father is 4 years older than Mother. Therefore, Mother's age at Zoey's birth = 32 - 4 = 28. This establishes that Zoey was born 28 years after her mother. However, without a reference year, Zoey's age in 2050 cannot be determined. Statement I is insufficient.
Step 2: Analyze Statement II. It states: Zoey's mother was born in the first leap year after 1970. The leap years after 1970 are 1972, 1976, etc. Thus, the mother was born in 1972. This provides the mother's birth year but gives no information about Zoey's birth date relative to her mother. Statement II is insufficient.
Step 3: Combine Statement I and Statement II. From Statement II, Mother's birth year = 1972. From Statement I, Zoey was born when the mother was 28. Therefore, Zoey's birth year = 1972 + 28 = 2000.
Step 4: Calculate Zoey's age in 2050. Age = 2050 - 2000 = 50 years. Since both statements together provide a unique answer, they are sufficient.