If x is negative and y is positive, which of the following must be

Question

If x is negative and y is positive, which of the following must be positive?

A. x/y
B. xy 
C. 2y + x
D. (x + y)^2 + 1
E. 3x/y

Skywalker18 · Answer

A. x/y 
-ve/+ve=-ve
will be negative
B. xy 
-ve*+ve= -ve
will be negative
C. 2y + x
might be positive or negative . The sign will be depend on the absolute values of x and y . The expression will be positive if 2y>x
D. (x + y)^2 + 1
= (x+y)^2 will be positive irrespective of the absolute values of x and y 
will be positive always
E. 3x/y 
=- ve/ +ve
will be negative

Answer D

BrentGMATPrepNow · Answer

IMPORTANT TIP: To answer this question, we'll need to examine every answer choice. Given this, where would a crafty test-maker place the correct answer? He/she would place it near the bottom, because most people check the answer choices from top to bottom. So, whenever we have such a question, I suggest that we start from the bottom and work our way to the top.

I write about this in the following article - https://www.gmatprepnow.com/articles/han ... -questions

Cheers,
Brent

robu · Answer

Sir i have a query. Can negative integers be even and odd, for example, -4 is even number?

Bunuel · Answer

Yes. 1. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder. 2. An odd number is an integer that is not evenly divisible by 2. 3. According to the above both negative and positive integers can be even or odd. Check more here: number-properties-tips-and-hints-174996.html

BrentGMATPrepNow · Answer

I'd like to add that 0 is also even. 
GMAT questions often test this concept.

Cheers,
Brent

Bunuel · Answer

Yes.

ZERO:

1. 0 is an integer.

2. 0 is an even integer. An even number is an   integer   that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. 0 is neither positive nor negative integer (the only one of this kind).

4. 0 is divisible by EVERY integer except 0 itself.

Shiv2016 · Answer

(negative integer)^2 is always positive.

A negative number raised to an even power is always positive.

BrentGMATPrepNow · Answer

Be careful The part in blue is not correct.

(a negative number)^(odd integer) = some negative number
Example: (-2)^5 = -32

(a negative number)^(even integer) = some positive number
Example: (-2)^6 = 64

RELATED VIDEO
 https://www.youtube.com/watch?v=5JuNf3XEHIQ

Shiv2016 · Answer

Oops. Its a typo. Any negative number raised to an even power is always positive. Thanks for pointing it out.

JeffTargetTestPrep · Answer

Scanning our answer choices, we see that (x + y)^2 must be nonnegative, and then when we add 1 to (x + y)^2, (x + y)^2 + 1 MUST be positive.

Answer: D

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If x is negative and y is positive, which of the following must be

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If x is negative and y is positive, which of the following must be

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