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 Post subject: Age word problemsPosted: Fri Aug 22, 2014 12:44 pm

Joined: Fri Aug 22, 2014 12:39 pm
Posts: 1
There is a question in the practise papers that is hard to explain the solution for:
David, Gemma, Jane, John and Maria are 12,11,10,10,9 years old but not in that order.
David is 2yrs younger than John
Gemma is 2yrs younger than Jane
Maria is older than David.
Who are twins?

A. David & Maria
B. John & Jane
C. Gemma & David
D. Maria & Gemma
E. John & Maria

Some solutions can be easily eliminated by logic, but I think you are left with B,C and E?
What would the method be to solve this?

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 Post subject: Re: Age word problemsPosted: Fri Aug 22, 2014 2:01 pm

Joined: Sat Feb 16, 2013 12:46 pm
Posts: 32
Hi scon1

Now I don't know whether D. Gemma & Maria is the correct answer but it seems to work if you follow the following:

If David is 2 years younger than John, looking at the ages 12, 11, 10, 10, 9 there are only 2 pairs with that gap i.e. 12&10 or 11&9. Therefore,

- David must be either 9 or 10 years
- John must be either 11 or 12 years

Similarly, if Gemma is 2 years younger than Jane

- Gemma must be either 9 or 10 years
- Jane must be 11 or 12 years

If David is 9, then John must be 11, Gemma must be 10, Jane 12 which would mean that Maria must be 10, which works as we are told that she is older than David. Therefore, the twins are Gemma & Maria.

If you tried out David being 10 first, John would be 12, Gemma 9, Jane 11 and Maria 10 which doesn't work as she needs to be older than David.

I hope the above ramble makes sense!

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 Post subject: Re: Age word problemsPosted: Fri Aug 22, 2014 3:25 pm

Joined: Mon Jan 30, 2006 4:07 pm
Posts: 2668
Children should create a quick table. With this type of question I use 2 columns:

We do not know whether John and David are 12 and 10 or 11 and 9
Additionally we do not know whether Jane and Gemma are 12 and 10 or 11 and 9

D....10.....9

G.....9.....10

Ja....11...12

Jo...12....11

M...10.....10 [Maria has to be 10 as that is the only age not used.]

As we are told Maria is older than David column 1 is incorrect as they are the same age, making column 2 correct.

Maria and Gemma are the twins.

Patricia

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