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

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

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New post 12 Jul 2017, 01:55
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

81% (00:55) correct 19% (00:39) wrong based on 69 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

(C) AD < CE

(D) AD < DE

(E) BD < DE


[Reveal] Spoiler:
Attachment:
2017-07-12_1253.png
2017-07-12_1253.png [ 3.09 KiB | Viewed 695 times ]
[Reveal] Spoiler: OA

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

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New post 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).

Waiting for your method Bunuel.

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

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New post 12 Jul 2017, 04:43
Bunuel wrote:
Image
On the line above, if AB < BC < CD < DE, which of the following must be true?

(A) AC < CD

(B) AC < CE

(C) AD < CE

(D) AD < DE

(E) BD < DE


[Reveal] Spoiler:
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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New post 12 Jul 2017, 09:39
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try to split the inequalities..

AB<BC
BC<CD
add the above equztions...AC<BD....(1)

BC<CD
CD<DE
adding will give BD<CE....(2)

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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New post 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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New post 06 Aug 2017, 10:44
Bunuel wrote:
Image
On the line above, if AB < BC < CD < DE, which of the following must be true?

(A) AC < CD

(B) AC < CE

(C) AD < CE

(D) AD < DE

(E) BD < DE


[Reveal] Spoiler:
Attachment:
2017-07-12_1253.png



AB < CD
BC < DE

AB + BC < CD + DE
AC < CE

Ans B.

Kudos [?]: 10 [0], given: 149

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

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