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

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Math Expert
Joined: 02 Sep 2009
Posts: 60778
If x is negative and y is positive, which of the following must be  [#permalink]

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09 Nov 2015, 00:31
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5% (low)

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97% (00:39) correct 3% (01:28) wrong based on 316 sessions

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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

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Re: If x is negative and y is positive, which of the following must be  [#permalink]

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09 Nov 2015, 01:18
1
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

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Posts: 4235
Re: If x is negative and y is positive, which of the following must be  [#permalink]

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09 Nov 2015, 09:15
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.

Cheers,
Brent
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Re: If x is negative and y is positive, which of the following must be  [#permalink]

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10 Nov 2015, 05:54
Bunuel wrote:
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

Sir i have a query. Can negative integers be even and odd, for example, -4 is even number?
Math Expert
Joined: 02 Sep 2009
Posts: 60778
Re: If x is negative and y is positive, which of the following must be  [#permalink]

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10 Nov 2015, 06:09
robu wrote:
Bunuel wrote:
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

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

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
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Re: If x is negative and y is positive, which of the following must be  [#permalink]

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10 Nov 2015, 09:24
1
1
Bunuel wrote:
robu wrote:
Bunuel wrote:
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

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

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

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

Cheers,
Brent
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Posts: 60778
Re: If x is negative and y is positive, which of the following must be  [#permalink]

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10 Nov 2015, 10:07
GMATPrepNow wrote:
Bunuel wrote:
robu wrote:

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

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

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

Cheers,
Brent

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.
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If x is negative and y is positive, which of the following must be  [#permalink]

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Updated on: 03 Apr 2017, 11:10
(negative integer)^2 is always positive.

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

Originally posted by Shiv2016 on 03 Apr 2017, 10:57.
Last edited by Shiv2016 on 03 Apr 2017, 11:10, edited 1 time in total.
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Posts: 4235
Re: If x is negative and y is positive, which of the following must be  [#permalink]

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03 Apr 2017, 11:05
Top Contributor
Shiv2016 wrote:
(negative integer)^2 is always positive.

A negative number raised to a positive power is always positive.

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

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Re: If x is negative and y is positive, which of the following must be  [#permalink]

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03 Apr 2017, 11:10
GMATPrepNow wrote:
Shiv2016 wrote:
(negative integer)^2 is always positive.

A negative number raised to a positive power is always positive.

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

Oops. Its a typo.

Any negative number raised to an even power is always positive. Thanks for pointing it out.
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Re: If x is negative and y is positive, which of the following must be  [#permalink]

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06 Apr 2017, 09:54
Bunuel wrote:
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

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.

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Re: If x is negative and y is positive, which of the following must be  [#permalink]

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09 Dec 2019, 08:37
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Re: If x is negative and y is positive, which of the following must be   [#permalink] 09 Dec 2019, 08:37
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