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# If x + 3 is positive, then which one of the following must be positive

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Math Expert
Joined: 02 Sep 2009
Posts: 59589
If x + 3 is positive, then which one of the following must be positive  [#permalink]

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02 Apr 2019, 03:57
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Difficulty:

15% (low)

Question Stats:

81% (01:08) correct 19% (01:00) wrong based on 36 sessions

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If x + 3 is positive, then which one of the following must be positive?

(A) x – 3

(B) (x – 3)(x – 4)

(C) (x – 3)(x + 3)

(D) (x – 3)(x + 4)

(E) (x + 3)(x + 6)

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Joined: 13 Feb 2018
Posts: 480
GMAT 1: 640 Q48 V28
Re: If x + 3 is positive, then which one of the following must be positive  [#permalink]

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02 Apr 2019, 04:06
(A) x – 3 --> if x=5 YES, if x=0 NO;

(B) (x – 3)(x – 4) --> If x=7 Yes, If x=3 NO;

(C) (x – 3)(x + 3) --> If x=5 Yes, If x=2 NO;

(D) (x – 3)(x + 4) --> If x=5 Yes, If x=0 NO;

(E) (x + 3)(x + 6) --> As we know x+3 is possitive, then x+3+3 must be possitive as well

IMO
Ans: E
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Joined: 06 Feb 2019
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Re: If x + 3 is positive, then which one of the following must be positive  [#permalink]

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02 Apr 2019, 04:08
(X-3)(X-4) = X2 - 7x + 12
Therefore X = 4 or 3

Both 4 n 3 fulfill the condition of X + 3 = positive

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Joined: 13 Feb 2018
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Re: If x + 3 is positive, then which one of the following must be positive  [#permalink]

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02 Apr 2019, 05:19
justus23 wrote:
(X-3)(X-4) = X2 - 7x + 12
Therefore X = 4 or 3

Both 4 n 3 fulfill the condition of X + 3 = positive

Posted from my mobile device

If x=3 then expression (x-3)(x-4)=0 zero is not possitive
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Re: If x + 3 is positive, then which one of the following must be positive  [#permalink]

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03 Apr 2019, 03:44
Bunuel wrote:
If x + 3 is positive, then which one of the following must be positive?

(A) x – 3

(B) (x – 3)(x – 4)

(C) (x – 3)(x + 3)

(D) (x – 3)(x + 4)

(E) (x + 3)(x + 6)

given x+3 is +ve
so option E (x + 3)(x + 6)
(x+3)*(x+3+3) +ve
IMO E
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Re: If x + 3 is positive, then which one of the following must be positive  [#permalink]

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07 Apr 2019, 18:24
Bunuel wrote:
If x + 3 is positive, then which one of the following must be positive?

(A) x – 3

(B) (x – 3)(x – 4)

(C) (x – 3)(x + 3)

(D) (x – 3)(x + 4)

(E) (x + 3)(x + 6)

Since x + 3 ˃ 0 , then x ˃ -3. Thus, (x + 3)(x + 6) will always be positive.

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Re: If x + 3 is positive, then which one of the following must be positive   [#permalink] 07 Apr 2019, 18:24
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