Cathy was born less than 10 years ago and Karen is at least 22 years

Solution

Step 1: Analyse Question Stem

• Let us assume that Cathy and Karen are currently c and k years old, respectively.

o \(0 < c < 10 ……..(i)\)
o And \(k ≥ c + 22 ………..(ii)\)

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE

• Last year:

o \((k-1) = 5*(c-1) ⟹ k – 5c = -4 ………Eq.(iii)\)
• Next year:

o \((k+1) = 4*(c+1)⟹ k- 4c = 3 ………Eq.(iv)\)
• Subtracting Eq.(iii) from Eq.(iv), we get, \(c = 7\) years, which is less than 10. So, it can be Cathy’s age.

o Therefore, \(k = 3 + 4*7 = 31\), which is exactly 22 more years more that Cathy’s age. So, it can be Karen’s age.

 Thus, Karen’s age is 31 years.

• According to this statement: \(28 < k < 32……(v) \)
• From (i) and (ii) we have, \(0 < c ⟹ 22 < c + 22 ≤ k ⟹ 22 < k……..(vi)\)
• Thus, (v) and (vi), we can say that, \(28 < k < 32 \)

o We cannot determine exact value of k here.