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

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

by BTGmoderatorDC » Mon Nov 11, 2019 5:30 pm
Cathy was born less than 10 years ago and Karen is at least 22 years older than Cathy. How old is Karen?

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.

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

OA A

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Source: — Data Sufficiency |
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by deloitte247 » Sat Nov 16, 2019 1:15 am
Cathy's age < 10 years
$$Karen's\ age\ge22\ years+Cathy's\ age$$
How old is Karen?
Let Cathy's age = c
Let Karen's age = 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 = last year for Karen's age
k + 1 = next year for Karen's age
c - 1 = last year for Cathy's age
c + 1 = next year for Cathy's age
k - 1 = 5 (c-1)
k - 1 = 5c - 5
k = 5c - 4 ----- eqn (1)
k + 1 = 4 (c + 1)
k = 4c + 3 ----- eqn (2)
Substituting eqn (1) in eqn (2)
5c - 4 = 4c + 3
c = 7; hence, k = 4c + 3, where c = 7.
k = 31 years ols.
Therefore, statement 1 is SUFFICIENT.

Statement 2: Karen is older than 28 but younger than 32.
28 < k < 32
'k' could be either 29, 30, or 31. Hence, this statement is NOT SUFFICIENT.

Since statement 1 alone is SUFFICIENT, the correct option is A.
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