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If Carl is 3 times as old as Bea, how old is Bea?

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Source: — Data Sufficiency |

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by Ian Stewart » Sat Aug 10, 2019 5:19 am

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B

C

D

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The stem gives us the equation C = 3B, a line of slope 3. Each Statement will give us a linear equation different from that one, since each will give a line with a slope different from 3, so using either Statement the two lines will meet in a single point and we'll find a unique solution for the two unknowns. So the answer is D.

It's not necessary to write down the equations or to solve them, but if one wanted to, for Statement 1 we have C + 9 = 2(B + 9), a line of slope 2, and for Statement 2 we have C - 6 = 7(B - 6), a line of slope 7. Solving either along with the equation in the stem gives C = 27 and B = 9.
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by deloitte247 » Sun Aug 11, 2019 4:28 am

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C

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Let carl = c
Let Bea = b
c = 3b and b = c/3
Question => how old is Bea ? Find the value of b
Statement 1 => in nine years, carl will be twice as old as Bea
c + 9 = 2 ( b + 9 )
Since c = 3b ; 3b + 9 = 2 ( b + 9 )
3b + 9 = 2b + 18
b = 18 - 9 = 9 ; Bea is 9 years old
Hence, statement 1 is SUFFICIENT
Statement 2 => six years ago, Carl was 7 times as old as Bea
c - 6 = 7 ( b - 6 )
Since c = 3b ; 3b - 6 = 7 ( b - 6 )
3b - 6 = 7b - 42
3b - 7b = - 42 + 6
-4b = -36
Divide both sides by -4
b = 9 ; Bea is 9 years old
Statement 2 is SUFFICIENT
Each statement alone are SUFFICIENT
Therefore, the answer is option D
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