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# If a < b, is a < c?

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If a < b, is a < c?  [#permalink]

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Updated on: 22 Oct 2019, 23:17
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25% (medium)

Question Stats:

78% (01:23) correct 22% (01:16) wrong based on 101 sessions

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EMPOWERgmat DS Series:
Pack 3, Question 1

If a < b, is a < c?

(1) (a)(c) = 0
(2) a + b = 0

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Originally posted by EMPOWERgmatRichC on 11 Oct 2019, 18:21.
Last edited by EMPOWERgmatRichC on 22 Oct 2019, 23:17, edited 1 time in total.
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Re: If a < b, is a < c?  [#permalink]

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11 Oct 2019, 19:03
If a < b, is a < c?

(1) (a)(c) = 0
This tells us that at least one of the two, a and c, is 0..

(2) a + b = 0
a=-b, and a<b tells us that both cannot be equal, so they cannot be 0.
Now a<b, so b=|a|, that is, a is negative and b is positive...
a<0 and b>0, but nothing about c.

Combined..
a<0, but ac=0 tells us that c=0, so a<c

C
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Re: If a < b, is a < c?  [#permalink]

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11 Oct 2019, 21:29
EMPOWERgmatRichC wrote:
EMPOWERgmat DS Series:
Pack 3, Question 1

If a < b, is a < c?

(1) (a)(c) = 0
(2) a + b = 0

(1) a x c = 0 which means atleast one of them is zero. Insufficient.

(2) a = -b and also a<b which means a is -ve and b is +ve. No relations between a and c is found. Insufficient

(1)+(2) If a is -ve which means c has to be zero. Sufficient

C is correct.
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Re: If a < b, is a < c?  [#permalink]

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09 Nov 2019, 11:12
If a < b, is a < c?

(1) (a)(c) = 0
(2) a + b = 0

Statement 1 : a.c = 0, either a or c is 0. If c is 0 and a is 10, then a > c. again, if a = -2, c= 0, then a < c. so cannot determine whether a < c.

Statement 2: a + b = 0. Since a < b , so a must be a negative number. But we don't know if c is a 0, or positive or negative number. Not sufficient.

Together, a is negative and a*c = 0, so c is 0. Hence, a < c. Sufficient.

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Re: If a < b, is a < c?  [#permalink]

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09 Nov 2019, 11:27
If a < b, is a < c?

(1) (a)(c) = 0
(2) a + b = 0

Let's evaluate each choice.
(i)Given a<b and ac=0. from this we can infer either a can be 0 or c can be 0. If one value is zero then other value can be anything so this one not sufficient.
(ii) a+b=0, a<b from here we can say a=-b; no info about c. So not sufficient.

Let's combine both and check:
ac=0, a+b=0, a<b from these we can say that a cannot be 0, should be -ve and c should be zero so we can conclude that a<c.
Re: If a < b, is a < c?   [#permalink] 09 Nov 2019, 11:27
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