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An English Language Test Rather Than Maths Test

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by ronnie1985 » Wed May 23, 2012 9:54 am
Bobby and his younger brother Johnny have the same birthday. Johnny's age now is the same as Bobby's age was when Johnny was half as old as Bobby is now. What is Bobby's age now?
(1) Bobby is currently four times as old as he was when Johnny was born.
(2) Bobby was six years old when Johnny was born.

Please help convert the sentences in equations.
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by Anurag@Gurome » Wed May 23, 2012 10:45 pm
ronnie1985 wrote:Bobby and his younger brother Johnny have the same birthday. Johnny's age now is the same as Bobby's age was when Johnny was half as old as Bobby is now. What is Bobby's age now?
(1) Bobby is currently four times as old as he was when Johnny was born.
(2) Bobby was six years old when Johnny was born.

Please help convert the sentences in equations.
Let Johnny's present age be x and Bobby's present age be y.
Half of Bobby's age is y/2.
Johnny must have been y/2 years of age (x-y/2) years ago.
At that time Bobby must have been y - (x - y/2) = 3y/2 - x years of age.
So x = 3y/2 - x
2x = 3y/2
4x = 3y

(1) Bobby is currently four times as old as he was when Johnny was born.
When Johnny was born, Bobby must have been y - x years of age.
4*(y - x) = y
3y = 4x
This is just the same equation as what we get from the main question; NOT sufficient.

(2) Bobby was six years old when Johnny was born implies y - x = 6.
So we have 2 equations, 4x = 3y and y - x = 6.
x = 18 and y is 24.

So Bobby's age now is 24 years; SUFFICIENT.

The correct answer is B.
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by [email protected] » Fri May 25, 2012 2:45 am
Johnny's age now is the same as Bobby's age was when Johnny was half as old as Bobby is now.

This sentence was indeed difficult to identify, could you make it more easier to understand please...

Because of that I am not able to make the equation...
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by patanjali.purpose » Fri May 25, 2012 12:49 pm
[email protected] wrote:Johnny's age now is the same as Bobby's age was when Johnny was half as old as Bobby is now.

This sentence was indeed difficult to identify, could you make it more easier to understand please...

Because of that I am not able to make the equation...
Johnny's age now is the same as Bobby's age was when Johnny was half as old as Bobby is now;

IMO we can start with relative clause first:

MAIN CLAUSE: Johnny's age now is the same as Bobby's age was (B1) WHEN XX

RELATIVE CLAUSE 'XX' = Johnny was half as old as Bobby is now (B) ==> Johnny was half as old as B ==> XX = (B/2)

Bobby's age (B1) was WHEN JONNEY WAS B/2==> B1 = B-(J-B/2)=3B/2-J

Lets go to main clause: Johnny's age now is the same as B1 = Johnny's age now is the same as 3B/2-J ==> J = 3B/2-J

IMO we need to start from END TO START
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