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If a < b < 0, then which of the following must be true?

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If a < b < 0, then which of the following must be true?  [#permalink]

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New post 23 Jan 2019, 02:56
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

81% (00:54) correct 19% (00:45) wrong based on 51 sessions

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If a < b < 0, then which of the following must be true?

A ab < 0

B a + b > 0

C a/b < 0

D b – a > 0

E a – b > 0
Spoiler: OA

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Re: If a < b < 0, then which of the following must be true?  [#permalink]

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New post 23 Jan 2019, 04:15
a < b < 0 so both a and b are negative.

A ab < 0
-ve·-ve=+ve (x)

B a + b > 0
-ve+-ve=-ve (x)

C a/b < 0
-ve/-ve=positive

D b – a > 0
Substitute numbers to make it easy.
-2<-1<0
-1-(-2)=-1+2=1
1>0 (o)

E a – b > 0
Substitute numbers to make it easy.
-2<-1<0
-2-(-1)=-2+1=-1
-1<0 (x)

D
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Re: If a < b < 0, then which of the following must be true?  [#permalink]

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New post 23 Jan 2019, 06:25
Bunuel wrote:
If a < b < 0, then which of the following must be true?

A ab < 0

B a + b > 0

C a/b < 0

D b – a > 0

E a – b > 0


so we are checking ranges of a & b as both are -ve values

test with a -1 and b = -1/2
we note that only option D is valid
IMO D
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Re: If a < b < 0, then which of the following must be true?  [#permalink]

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New post 23 Jan 2019, 22:00
a < b < 0

Let a = -2, b = -1; -2 < -1 < 0

A) ab < 0
-2(-1) < 0 => Incorrect

B) a + b > 0
-2+(-1) = -3 > 0 => Incorrect

C) a/b < 0
-2/-1 < 0 => Incorrect

D) b – a > 0
-1-(-2) = 1 > 0 => Correct

E) a – b > 0
-2-(-1) > 0 => Incorrect

OPTION: D
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Re: If a < b < 0, then which of the following must be true?  [#permalink]

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New post 27 Jan 2019, 19:32
Bunuel wrote:
If a < b < 0, then which of the following must be true?

A ab < 0

B a + b > 0

C a/b < 0

D b – a > 0

E a – b > 0


Since a and b are both negative, and a is less than b, we see that D must be the answer. Remember:

b - a > 0 is the same as b > a.

Answer: D
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Re: If a < b < 0, then which of the following must be true?  [#permalink]

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New post 27 Jan 2019, 19:47
Bunuel wrote:
If a < b < 0, then which of the following must be true?

A ab < 0

B a + b > 0

C a/b < 0

D b – a > 0

E a – b > 0


Whenever i see such questions, I prefer plugging in ( i learnt a new thing, Always take extreme values as well, Its better to be cautious now rather than be sorry later.)

-2 < -1 < 0 and -5 < -1 < 0

Only D satisfies both

magnitude of a will always be greater than b
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Re: If a < b < 0, then which of the following must be true?   [#permalink] 27 Jan 2019, 19:47
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