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

Question

Cathy was born less than 10 years ago and Karen is at least 22 years older than Cathy. How old is Karen?

(1) Last year Karen was 5 times older than Cathy was at that time and next year Karen will be 4 times older than Cathy will be at that time.

(2) Karen is older than 28 but younger than 32.

GMATinsight · Answer

c < 10
k ≥ 22+c

Question: k = ?

Statement 1 : Last year Karen was 5 times older than Cathy was at that time and next year Karen will be 4 times older than Cathy will be at that time.

(k-1) = 5*(c-1) and (k+1) = 4*(c+1)

Solving them we get

-2 = c-9
 i.e. c = 7 and k = 31

SUFFICIENT

Statement 2 : Karen is older than 28 but younger than 32.

28 < k < 32

NOT SUFFICIENT

Answer: Option A

Kinshook · Answer

Given: Cathy was born less than 10 years ago and Karen is at least 22 years older than Cathy. Asked: How old is Karen? Let Cathy's age be c and Karen's age be k years c<10 k > 22 + c k = ? (1) Last year Karen was 5 times older than Cathy was at that time and next year Karen will be 4 times older than Cathy will be at that time. k - 1 = 5 (c-1) k = 5c - 4 k + 1 = 4(c+1) k = 4c + 3 = 5c - 4 c = 7 < 10 k = 4*7 + 3 = 28 + 3 = 31 k = 7 + 24 > 7 + 22 SUFFICIENT (2) Karen is older than 28 but younger than 32. 28 < k < 32 k = {29,30,31} NOT SUFFICIENT IMO A

GMATWhizTeam · Answer

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)   
We need to find the Karen's current age or the value of k.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE 
 Statement 1:  Last year Karen was 5 times older than Cathy was at that time and next year Karen will be 4 times older than Cathy will be at that time.
 • 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.   
Hence, statement 1 is sufficient and we can eliminate answer Options B, C and E.

Statement 2:  Karen is older than 28 but younger than 32.
 • 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.  
Hence, statement 2 is NOT sufficient and we can eliminate answer Option D.
Thus, the correct answer is  Option A.

KaramveerBakshi · Answer

Let Cathy's present age be C.
And Karen's present age be K.

Given:

0<C<10 ---- (A)
K>=C+22 ---(B)

Statements:

(1) - Forming equations:

(K-1) = 5(C-1) AND (K+1) = 4(C+1)

Solving for C and K, we get K=31 and C=7.

Both are acceptable values as they satisfy (A) and (B).

Sufficient.

(2) Karen's Age can be 29, 30, or 31. All are acceptable values according to (A) and (B).

Not Sufficient

Hence, the answer IMO is Option (A).

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

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

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