Aptitude and Reasoning Questions

Sum of decimal places = 7.

Since the last digit to the extreme right will be zero (since 4 x 5 = 20), so there will be 6 significant digits to the right of the decimal point.

3  1  7  3  7

3  1  7  3  8

7  1  7  3  9

At these places 1, 7, 3 appeared together

Here given formula is 

a2 + b2 + c2 -ab- bc - ca = 0

and it is possible if and only if a = b = c.

From the trial and error method, 

1) Let a = b = c = 1

Now substitute these values of a, b, c in the above formula.

We get 1 + 1 + 1 - 1 - 1 - 1 = 3 - 3 = 0

2) Now, let a = b = c = 4

Now substitute these values of a, b, c in the above formula.

We get 16 + 16 + 16 - 16 - 16 - 16 = 48 - 48 = 0.

Hence, it is possible that 

a2 + b2 + c2 -ab- bc - ca = 0 iff a = b = c.

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).