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# On the line above, if AB < BC < CD < DE, which of the following must

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Math Expert
Joined: 02 Sep 2009
Posts: 54696
On the line above, if AB < BC < CD < DE, which of the following must  [#permalink]

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12 Jul 2017, 01:55
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5% (low)

Question Stats:

92% (01:25) correct 8% (01:42) wrong based on 83 sessions

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On the line above, if AB < BC < CD < DE, which of the following must be true?

(A) AC < CD

(B) AC < CE

(E) BD < DE

Attachment:

2017-07-12_1253.png [ 3.09 KiB | Viewed 1229 times ]

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On the line above, if AB < BC < CD < DE, which of the following must  [#permalink]

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12 Jul 2017, 03:10
I tried to solve this question by plugging in nos. but really didn't get anything out of it.

Just my best guess:

Is it B?

AC<CE

That's because: AB<BC and BC<CD and DE

So AB is also less than CD and DE.

So the sum of the smaller two nos. would be less than sum of the bigger two nos.

(I am not sure if this correct).

Thanks
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Re: On the line above, if AB < BC < CD < DE, which of the following must  [#permalink]

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12 Jul 2017, 04:43
Bunuel wrote:

On the line above, if AB < BC < CD < DE, which of the following must be true?

(A) AC < CD

(B) AC < CE

(E) BD < DE

Attachment:
2017-07-12_1253.png

Given AB<BC<CD<DE

Please note that all the values which AB, BC, CD or DE take will be positive. Lets assume
AB = a
BC=a+x
CD=a+x+y
DE=a+x+y+z
All a,x,y,z are positive

(A) AC < CD => AB+BC<CD => a+a+x<a+x+y (a could be greater than y) Nope

(B) AC < CE => AB+BC<CD+DE => a+a+x<a+x+y+a+x+y+z => 0<y+x+y+z and since x,y,z is positive..this is our answer

(C) AD < CE => AB+BC+CD<CD+DE => AB+BC<DE => a+a+x<a+x+y+z (a could be greater than y+z) Nope

(D) AD < DE => AB+BC+CD < DE => a+a+x+a+x+y<a+x+y+z (2a+x could be larger than z) Nope

(E) BD < DE => BC+CD<DE => a+x+a+x+y<a+x+y+z (a+x could be larger than z) Nope

Hence B

We can also use smart numbers like a=6, x=2, y=3, z=4
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Re: On the line above, if AB < BC < CD < DE, which of the following must  [#permalink]

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12 Jul 2017, 09:39
1
try to split the inequalities..

AB<BC
BC<CD

BC<CD
CD<DE

from 1 and 2 we get AC<CE..
ans B
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Re: On the line above, if AB < BC < CD < DE, which of the following must  [#permalink]

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12 Jul 2017, 09:43
The addition of 2 smaller quantities will be less than the addition of 2 greater quantities....hence B

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Re: On the line above, if AB < BC < CD < DE, which of the following must  [#permalink]

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06 Aug 2017, 10:44
Bunuel wrote:

On the line above, if AB < BC < CD < DE, which of the following must be true?

(A) AC < CD

(B) AC < CE

(E) BD < DE

Attachment:
2017-07-12_1253.png

AB < CD
BC < DE

AB + BC < CD + DE
AC < CE

Ans B.
Re: On the line above, if AB < BC < CD < DE, which of the following must   [#permalink] 06 Aug 2017, 10:44
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