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If x and y are integers and x + y = 5, which of the following must be true?

A) x and y are consecutive integers.

B) If x < 0, then y > 0.

C) If x > 0, then y < 0.

D) Both x and y are even.

E) Both x and y are less than 5.

x+y = 5, so y = 5 - x. If x is negative, then y is clearly greater than 5, so y must be positive. B must be true.

Certainly A, C and E could be true, but they don't need to be true, while D is absolutely impossible.
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(B) Remember that when you are asked what MUST BE TRUE it is usually easiest to eliminate answer choices by showing that they can be false. Plug in numbers for x and y, so that x + y = 5, but the answer choices are untrue. In other words, show that the conditions aren't always true. Use process of elimination then to eliminate the choices. Choice (A): Let x = 1 and y = 4. x + y = 5, but x and y are not consecutive. Choice (B): If x is less than zero, then y MUST be positive if x + y is to equal 5. If y were negative or zero, x + y would add up to a negative number. It's impossible to find numbers that don't work here. If you didn't see this, you could still have got this as the right answer by running through the rest of the answer choices, as follows.Choice (C): Let x = 2 and y = 3. x + y = 5, x is positive, but y is not less than 0. Eliminate it. (Many students don't see the difference between B and C. If you plug in numbers you see they are entirely different. C requires that x be positive and y be negative, but clearly under these conditions that need not always be true. If x > 0, then y need not be < 0 to get 5 ). Choice (D): Let x = 3 and y = 2. x + y = 5, but x is not even. Eliminate it. Choice (E): Let x = 6 and y = -1, therefore x + y = 5, but x is greater than 5. Eliminate it.

IanStewart wrote:

nitya34 wrote:

If x and y are integers and x + y = 5, which of the following must be true?

A) x and y are consecutive integers.

B) If x < 0, then y > 0.

C) If x > 0, then y < 0.

D) Both x and y are even.

E) Both x and y are less than 5.

x+y = 5, so y = 5 - x. If x is negative, then y is clearly greater than 5, so y must be positive. B must be true.

Certainly A, C and E could be true, but they don't need to be true, while D is absolutely impossible.

No worries Peraspera, it's good that we saw this question here else we would have missed it in main exam. Though I am not happy with myself Dont want to loose a single point in Quanta... It's good in its own way

:beer No worries Peraspera, it's good that we saw this question here else we would have missed it in main exam. Though I am not happy with myself Dont want to loose a single point in Quanta... It's good in its own way

I could not agree more! I was just mad at myself, like you. It seems like at least 50% of the mistakes I make in both quant and verbal are due to inattentiveness.

At any rate, I value the problems I did not solve much more that the ones I did correctly. Hit me more, and I will learn more, and will stand up to fight again.