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Points A, B, C, and D, in that order, lie on a line. If AB = 3 cm, AC = 4 cm, and BD = 6 cm, what is CD, in centimeters?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
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(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
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Putting a value to each point, lets use the following:
A - 0
B - 3 (AB = 3)
C - 4 (AC = 4)
D - 9 (BD = 6)
CD is 9-4 = 5.
Ans E
A - 0
B - 3 (AB = 3)
C - 4 (AC = 4)
D - 9 (BD = 6)
CD is 9-4 = 5.
Ans E
nipunjain14
Joined: 07 May 2015
Last visit: 12 Aug 2017
Posts: 150
Location: India
Schools: ISB '19 Kellogg '20 Yale '20 HEC Dec"18
GMAT 1: 660 Q48 V31
GPA: 3
bc = 4- 3 = 1
cd= 6-1 = 5
Ans:E
cd= 6-1 = 5
Ans:E
leonidbasin1
Joined: 16 Jan 2016
Last visit: 20 Feb 2017
Posts: 18
Location: United States (CA)
Leonid: B
Concentration: Operations, General Management
GPA: 3.6
WE:Operations (Other)
Posts: 18
nipunjain14
How did you get the second part (CD = 6-1 = 5) ?
Thanks,
Leon
nipunjain14
Joined: 07 May 2015
Last visit: 12 Aug 2017
Posts: 150
Location: India
Schools: ISB '19 Kellogg '20 Yale '20 HEC Dec"18
GMAT 1: 660 Q48 V31
GPA: 3
leonidbasin1
BC = AC- AB = 4 - 3 = 1
CD = BD - BC = 6 -1 = 5
Hope this is now clear.
diegocml
Joined: 21 Apr 2016
Last visit: 22 Jun 2018
Posts: 122
Status:On a 600-long battle
Location: Hungary
Concentration: Accounting, Leadership
Schools: Erasmus '19
GMAT 1: 410 Q18 V27
GMAT 2: 490 Q35 V23
Bunuel
Given: The points are in order from A to D.
Given: Distance A to B = 3cm, Distance A to C = 4cm, Distance B to D = 6cm
Just draw a line:
A-----B-----C-----D
A--3--B--1--C--5--D
OA
HasnainAfxal
Joined: 06 Sep 2018
Last visit: 12 Mar 2022
Posts: 124
Location: Pakistan
Concentration: Finance, Operations
GPA: 2.87
WE:Engineering (Other)
Products:
Posts: 124
AC-AB=BS
3-2=1
BD-BC=CD
6-1=5
ANSWER E
3-2=1
BD-BC=CD
6-1=5
ANSWER E
Kinshook
Major Poster
Joined: 03 Jun 2019
Last visit: 10 Sep 2026
Posts: 6,127
Location: India
Schools: HBS '28 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
Bunuel
Points A, B, C, and D, in that order, lie on a line. If AB = 3 cm, AC = 4 cm, and BD = 6 cm, what is CD, in centimeters?
A-----------B-------------C--------------D
----3------- --------------6-------------
-------------4-------------
CD = AB + BD - AC = 3 + 6 -4 = 9 -4 =5
IMO E
Nice as a warm up question, thanks!
Posted from my mobile device
Posted from my mobile device
--------A------B-------C-------D---
mark the values as you read the question:
AB is 3, AC is 4, (BC=AC-AB) meaning BC is 1
BD is 6, (CD=BD-BC) as we know BC is 1, thus, CD is 5.
mark the values as you read the question:
AB is 3, AC is 4, (BC=AC-AB) meaning BC is 1
BD is 6, (CD=BD-BC) as we know BC is 1, thus, CD is 5.
Since points A, B, C, and D lie on a line in that order, you can consider the segments as follows:
AB + BC = AC
3 cm + BC = 4 cm
BC = 4 cm - 3 cm
BC = 1 cm
Now, since points B, C, and D are collinear, you can use the fact that BD = BC + CD:
BD = BC + CD
6 cm = 1 cm + CD
CD = 6 cm - 1 cm
CD = 5 cm
So, CD is 5 centimeters.
AB + BC = AC
3 cm + BC = 4 cm
BC = 4 cm - 3 cm
BC = 1 cm
Now, since points B, C, and D are collinear, you can use the fact that BD = BC + CD:
BD = BC + CD
6 cm = 1 cm + CD
CD = 6 cm - 1 cm
CD = 5 cm
So, CD is 5 centimeters.
charlie-23
Joined: 22 Jul 2023
Last visit: 20 Sep 2024
Posts: 41
Location: India
Concentration: Entrepreneurship, Finance
Posts: 41
Bunuel
BC = 4-3=1
CD = 6 -1 =5
Bunuel
Bunuel question can be tricky if someone ask that A B C D can be in any format in the line, then what is the difference between minimum and maximum possible distance of CD ??
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