remainder DS ? experts help

[wilson4mba]

When Y is divided by 2, is the remainder 1?
(1) (-1)^(Y+2) = -1
(2) Y is prime.

OA is (A)

Explanation is that using statement 1, Y cannot be even and hence can take odd numbers 1,3,5,,,.

My doubt is that in the question nothing is mentioned whether y is positive integer or negative integer. Hence it can also be -1,-3,-5 .Even then its satisfies the equation and remainder is not 1.

after combining the 2 statements still we cannot solve it hence the answer should be E.

[Rahul@gurome]

You are right, it should be E.

[georgeanand]

When Y is divided by 2, is the remainder 1?
(1) (-1)^(Y+2) = -1
(2) Y is prime.

OA is (A)

Explanation is that using statement 1, Y cannot be even and hence can take odd numbers 1,3,5,,,.

My doubt is that in the question nothing is mentioned whether y is positive integer or negative integer. Hence it can also be -1,-3,-5 .Even then its satisfies the equation and remainder is not 1.

after combining the 2 statements still we cannot solve it hence the answer should be E.

y+2has to be odd, then only the signs remain the same.
y+2 = odd, y can be 1,3,5,7,9..... or -1,-3,-5.-1 divided by 2 gives a remainder of 1,-3 divided by 2 gives a remainder of 1
https://letsgmat.blocked

[wilson4mba]

George anand , through wikipedia i got the following

If a and d are integers, with d non-zero, then a remainder is an integer r such that a = qd + r for some integer q, and with 0 ≤ |r| < |d|.

When defined this way, there are two possible remainders. For example, the division of −42 by −5 can be expressed as either

−42 = 9×(−5) + 3

as is usual for mathematicians,[citation needed] or

−42 = 8×(−5) + (−2).

So the remainder is then either 3 or −2.

This ambiguity in the value of the remainder can be quite serious computationally; for mission critical computing systems, the wrong choice can lead to dangerous consequences. In the case above, the negative remainder is obtained from the positive one just by subtracting 5, which is d. This holds in general. When dividing by d, if the positive remainder is r1, and the negative one is r2, then

r1 = r2 + d.


That means in case of negative numbers we always tend to arrive at 2 remainders.

[Rahul@gurome]

George anand , through wikipedia i got the following

If a and d are integers, with d non-zero, then a remainder is an integer r such that a = qd + r for some integer q, and with 0 ≤ |r| < |d|.

When defined this way, there are two possible remainders. For example, the division of −42 by −5 can be expressed as either

−42 = 9×(−5) + 3

as is usual for mathematicians,[citation needed] or

−42 = 8×(−5) + (−2).

So the remainder is then either 3 or −2.

This ambiguity in the value of the remainder can be quite serious computationally; for mission critical computing systems, the wrong choice can lead to dangerous consequences. In the case above, the negative remainder is obtained from the positive one just by subtracting 5, which is d. This holds in general. When dividing by d, if the positive remainder is r1, and the negative one is r2, then

r1 = r2 + d.


That means in case of negative numbers we always tend to arrive at 2 remainders.

Right. If a = qd + r, then in the present case, -3 = (-1)*(2) + (-1), which clearly shows that the remainder here is -1.