Q:
Four girls Robin, Mandy, Stacy, Erica of four families Miller, Jacob, Flure and Clark prepare four salads using the fruits Apples, cherries, bananas, grapes .Each girls uses 3 fruits in her salad. No body have the same combination.
1) Robin not a Miller girl uses apples.
2) Miller and Mandy uses apples and cherries.
3) Clark uses cherries and grapes but Flure uses only one of them.
4) Erica is not Clark nor Flure.
Question :
Give all combinations of Girls with their family and salads ?
Answer
Out of 4 fruits, any 3 are chosen by 4 families.So the combinations are
Apple - A Cherries - C Banana - B Grapes - G
1) ACB
2) ACG
3) BCG
4) GAB
By 2nd condition, Miller family uses either i)ACB or ii)ACG
Now we have Robin, Mandy and Miller who uses apples (ACB,ACG,GAB)
while Miller and Mandy both uses A and C. That leaves GAB for Robin.
By 3rd condition Flure uses either C or G. So if we leave out the terms containing both C and G, we are left with ACB and GAB
Now, for the time being let's suppose Robin is not a Flure.
So ACB is taken by Flure.
So ACG has to be Miller and that leaves BCG to be Clark. So we get Robin - Jacob(GAB).
By 4th and 2nd conditions Erica and Mandy belong to the first two. That leaves Stacy - Clark(BCG).
By 2nd condition Mandy is not a Miller, so we get Mandy - Flure(ACB) and that leaves Erica - Miller(ACG).
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