Sequence x1, x2, x3, ...x10 and y1, y2, y3, ... y10 where Yn

Question

Sequence x1, x2, x3, ...x10 and y1, y2, y3, ... y10 where Yn is the remainder when Xn is divided by 2. What is the sum of y1+...+y10?
1) Six of the numbers in sequence Xn are even.
2) The sum of the numbers in sequence Xn is 100


Please explain answer choice.

rthothad · Answer

I am going to assume that the numbers in the different sequences are integers.

yn = xn Mod 2, so yn is odd when xn is odd and yn is zero when xn is even.

From statement1: The sum of 6 numbers is zero so the sum of other 4 numbers should be 4, I am assuming that the other 4 numbers in xn are odd.
From statement2: Inconclusive.

so I will go with 'A'

pb_india · Answer

From statement1: The sum of 6 numbers is zero so the sum of other 4 numbers should be 4, I am assuming that the other 4 numbers in xn are odd. 

=> rthothad, how did u get this??

Tyr · Answer

y1, ... , y10 - remainders after dividing by 2 - that means a sequence of 0 and 1. 0 for each even x and 1 for each odd.

1. we have 6 even numbers out of 10 - that means 4 odd. We can count out even numbers from the sum y1+..+y10 because even numbers give us 0es, we will have four ones in there so the sum is 4.

2. x1 + ... + x10 = 100

Pick x1 = x2 = ... = x9 = 2, x10= 82
y1 = y2 = ... = y10 = 0, sum is 0
Now pick x1 = x2 = ... = x8 = 2, x9 = 1, x10 = 83
y1 = y2 = ... = y8 = 0, y9 = 1, y10 = 1, sum is 2

MA · Answer

guys, do we know that all numbers in the sequences are integers?
i think it should be E.

emilem · Answer

If the problem states that Yn is the remainder of Xn/2, then how can non-integer numbers have remainders? As far as I know, only integers can have remainders. MA, could you please correct be if I'm wrong.

1st statement is sufficient. The remaining 4 are odd, therefore, the remainders will be 1 and the sum 4.

2nd statement is insufficient. Say, Xn=2p+Yn, where p is a whole number. We can express all Xs by this equation and summing up all those 10 equations we'll left with 2 unknowns, p and sum of Ys. Insufficient

Answer is A. Please post OA.

Sequence x1, x2, x3, ...x10 and y1, y2, y3, ... y10 where Yn

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