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algebraic translation

by maus » Wed Jun 08, 2011 5:59 pm
hi folks, please help with this one:

Joan is 2 years younger than Kylie, Kylie is 3 years older than Lillian, and Miriam is one year older than Joan. Which of the following could be the combined age of all four women?

51, 52, 53, 54, 55

The explanation provided was completely useless to me - something about number lines - can anyone provide a shortcut perhaps?
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by smackmartine » Wed Jun 08, 2011 6:19 pm
IMO 54

explaining in a while.
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by Anurag@Gurome » Wed Jun 08, 2011 6:25 pm
maus wrote:hi folks, please help with this one:

Joan is 2 years younger than Kylie, Kylie is 3 years older than Lillian, and Miriam is one year older than Joan. Which of the following could be the combined age of all four women?

51, 52, 53, 54, 55

The explanation provided was completely useless to me - something about number lines - can anyone provide a shortcut perhaps?
Say, age of Kylie is n years.
=> Age of Joan is (n - 2) years
=> Age of Lilian is (n - 3) years
=> Age of Miriam is (n - 1) years

Hence, total age = (4n - 6) years

Hence, the total age must be 6 less than an integer multiple of 4, i.e. 2 less than an integer multiple of 4. Only such option is 54.

Hence, the correct answer is 54.
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by smackmartine » Wed Jun 08, 2011 6:37 pm
IMO 54
Here is the explanation:
Please refer this diagram
Image

When we represent the individual age on a number line, we find that ages are actually consecutive numbers

If age of K is x
age of Joan is (x - 2) years, age of Lilian is (x - 3) years and age of Miriam is (x - 1) years
Total age,T = 4x-6

Only at T= 54 , x is an Integer.
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by cans » Wed Jun 08, 2011 8:18 pm
let L=x years old
thus k=x+3
j=x+1
and m=x+2
total = 4x+6
51-6 = 45 not divisible by 4
52-6 = 46 not divisible by 4
54-6=48 divisible by 4
Thus IMO D
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by phanideepak » Wed Jun 08, 2011 8:28 pm
First we will have to get everything in a single variable in my case i put everything in terms of age of kayla

J + K + L + M = K-2 + K + K-3 + K-1
= 4K-6

So now we know that 4k-6 is even and we have two options 52 and 54 now

4k-6 = 52 ? no coz this gives decimals so 54is the answer.
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by edvhou812 » Wed Jun 08, 2011 10:24 pm
Joan: x+5
Kylie: x+3
Lilian: x
Mirian: x+6

This all comes to 4x+14
Equation has the sum of two even numbers, which must be even, so A,C and E are out.

I tried 4x+14=52, which did not work since 52-14=38 is not a multiple of 4, so I selected D, which gives Lilian's age as 10 and everyone's age adds up nicely to 54.
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