In the figure above, points A, B, C, and D are collinear and AB, BC : Data Sufficiency (DS)

dabaobao

Joined: 24 Oct 2016

Last visit: 20 Jun 2022

Posts: 573

Own Kudos:

1,458

[1]

Given Kudos: 143

GMAT 1: 670 Q46 V36 Verified score

GMAT 2: 690 Q47 V38 Verified score

GMAT 3: 690 Q48 V37 Verified score

GMAT 4: 710 Q49 V38 (Online) Verified score

Posts: 573

Kudos: 1,458

[1]

14 Mar 2020, 11:42

1

Kudos

Bookmarks

gmatt1476

In the figure above, points A, B, C, and D are collinear and AB, BC, and CD are semicircles with diameters d1 cm, d2 cm, and d3 cm, respectively. What is the sum of the lengths of semicircles AB, BC, and CD, in centimeters?

(1) d1:d2:d3 is 3:2:1.
(2) The length of line segment AD is 48 cm.

DS45771.01

Show Spoiler

Attachment:

2019-09-22_0512.png

Length of semicircles = π(r1 + r2 + r3) = ? => (r1 + r2 + r3) = ?

1) No length given => Not sufficient
2) d1 + d2 + d3 = 48 => 2 (r1 + r2 + r3) = 48
Sufficient

ANSWER: B

altairahmad

Joined: 27 Mar 2017

Last visit: 29 Jul 2021

Posts: 268

Own Kudos:

79

[3]

Given Kudos: 406

Location: Saudi Arabia

Schools: Tepper '23 (A$) LBS '23 (I) INSEAD Jan 22 intake (A)

GMAT 1: 700 Q47 V39 Verified score

GPA: 3.36

Products:

Schools: Tepper '23 (A$) LBS '23 (I) INSEAD Jan 22 intake (A)

GMAT 1: 700 Q47 V39 Verified score

Posts: 268

Kudos: 79

[3]

30 Apr 2020, 05:43

3

Kudos

Bookmarks

What is 'length' of a semi-circle ? Is this even a term ? By 'length' one can mean the circumference e.g 'Length of the arc'.

A few of DS questions in geometry seem to be RC questions.

altairahmad

Joined: 27 Mar 2017

Last visit: 29 Jul 2021

Posts: 268

Own Kudos:

79

Given Kudos: 406

Location: Saudi Arabia

Schools: Tepper '23 (A$) LBS '23 (I) INSEAD Jan 22 intake (A)

GMAT 1: 700 Q47 V39 Verified score

GPA: 3.36

Products:

Schools: Tepper '23 (A$) LBS '23 (I) INSEAD Jan 22 intake (A)

GMAT 1: 700 Q47 V39 Verified score

Posts: 268

Kudos: 79

01 May 2020, 02:13

Kudos

Bookmarks

MathRevolution

gmatt1476

In the figure above, points A, B, C, and D are collinear and AB, BC, and CD are semicircles with diameters d1 cm, d2 cm, and d3 cm, respectively. What is the sum of the lengths of semicircles AB, BC, and CD, in centimeters?

(1) d1:d2:d3 is 3:2:1.
(2) The length of line segment AD is 48 cm.

DS45771.01

Show Spoiler

Attachment:

2019-09-22_0512.png

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

The question asks the value of $\frac{{πd_1}}{2}+\frac{{πd_2}}{2}+\frac{{πd_3}}{2} = \frac{{π(d_1+d_2+d_3)}}{2}$.
Since we have $d_1 + d_2 + d_3 = 48$ from condition 2), we have $\frac{{π(d_1+d_2+d_3)}}{2} = 24π$.
Thus condition 2) is sufficient.

Condition 1)
If $d_1 = 3, d_2 = 2, d_3 = 1$, then we have $\frac{{π(d_1+d_2+d_3)}}{2} = 3π$.
If $d_1 = 6, d_2 = 4, d_3 = 2$, then we have $\frac{{π(d_1+d_2+d_3)}}{2} = 6π$.

Since condition 1) does not yield a unique solution, it is not sufficient.

Therefore, B is the answer.

Makes sense. Thanks.

GDT

Joined: 02 Jan 2020

Last visit: 18 Sep 2020

Posts: 248

Own Kudos:

110

Given Kudos: 477

Posts: 248

Kudos: 110

27 Jun 2020, 07:02

Kudos

Bookmarks

gmatt1476

In the figure above, points A, B, C, and D are collinear and AB, BC, and CD are semicircles with diameters d1 cm, d2 cm, and d3 cm, respectively. What is the sum of the lengths of semicircles AB, BC, and CD, in centimeters?

(1) d1:d2:d3 is 3:2:1.
(2) The length of line segment AD is 48 cm.

DS45771.01

Show Spoiler

Attachment:

2019-09-22_0512.png

MentorTutoring

Pls clarify what exactly does length of semicircles means? Do we need to tell length of AD or circumference of semicircles

GDT

Joined: 02 Jan 2020

Last visit: 18 Sep 2020

Posts: 248

Own Kudos:

110

Given Kudos: 477

Posts: 248

Kudos: 110

27 Jun 2020, 07:03

Kudos

Bookmarks

gmatt1476

In the figure above, points A, B, C, and D are collinear and AB, BC, and CD are semicircles with diameters d1 cm, d2 cm, and d3 cm, respectively. What is the sum of the lengths of semicircles AB, BC, and CD, in centimeters?

(1) d1:d2:d3 is 3:2:1.
(2) The length of line segment AD is 48 cm.

DS45771.01

Show Spoiler

Attachment:

2019-09-22_0512.png

MentorTutoring

Pls clarify what exactly does length of semicircles means? Do we need to tell length of AD or circumference of semicircles

AndrewN

Volunteer Expert

Joined: 16 May 2019

Last visit: 14 Jan 2025

Posts: 3,503

Own Kudos:

7,128

[1]

Given Kudos: 500

Expert reply

Posts: 3,503

Kudos: 7,128

[1]

27 Jun 2020, 08:19

1

Kudos

Bookmarks

GDT

gmatt1476

In the figure above, points A, B, C, and D are collinear and AB, BC, and CD are semicircles with diameters d1 cm, d2 cm, and d3 cm, respectively. What is the sum of the lengths of semicircles AB, BC, and CD, in centimeters?

(1) d1:d2:d3 is 3:2:1.
(2) The length of line segment AD is 48 cm.

DS45771.01

Show Spoiler

Attachment:

2019-09-22_0512.png

MentorTutoring

Pls clarify what exactly does length of semicircles means? Do we need to tell length of AD or circumference of semicircles

Hello, GDT. In the question, the lengths of semicircles AB, BC, and CD must refer to the circumference. Otherwise, you would expect to see the word segment in reference to segment AD; furthermore, peeking ahead at statement (2), when have you ever known a DS question to hand you the answer on a platter without any sort of work on your part? Even the easiest questions force you to manipulate the original expression or information to align (or not) with either of the two statements. As for this question, perhaps my GRE® cross-tutoring came in handy. I thought of this question from that test and walked away the answer here in well under a minute. It is a good exercise in not making assumptions.

Thank you for bringing my attention to the question.

- Andrew

GDT

Joined: 02 Jan 2020

Last visit: 18 Sep 2020

Posts: 248

Own Kudos:

110

[2]

Given Kudos: 477

Posts: 248

Kudos: 110

[2]

27 Jun 2020, 08:28

1

Kudos

1

Bookmarks

MentorTutoring

GDT

gmatt1476

In the figure above, points A, B, C, and D are collinear and AB, BC, and CD are semicircles with diameters d1 cm, d2 cm, and d3 cm, respectively. What is the sum of the lengths of semicircles AB, BC, and CD, in centimeters?

(1) d1:d2:d3 is 3:2:1.
(2) The length of line segment AD is 48 cm.

DS45771.01

Show Spoiler

Attachment:

2019-09-22_0512.png

MentorTutoring

Pls clarify what exactly does length of semicircles means? Do we need to tell length of AD or circumference of semicircles

Hello, GDT. In the question, the lengths of semicircles AB, BC, and CD must refer to the circumference. Otherwise, you would expect to see the word segment in reference to segment AD; furthermore, peeking ahead at statement (2), when have you ever known a DS question to hand you the answer on a platter without any sort of work on your part? Even the easiest questions force you to manipulate the original expression or information to align (or not) with either of the two statements. As for this question, perhaps my GRE® cross-tutoring came in handy. I thought of this question from that test and walked away the answer here in well under a minute. It is a good exercise in not making assumptions.

Thank you for bringing my attention to the question.

- Andrew

MentorTutoring
Thank you for the prompt reply!

My question was from PS perspective

And I wanted to confirm what it exactly meant as in either case statement 2 would have been sufficient

for circumference, pi d1/2 +pi d2/2 +pi d3/2 (length of curves)+ AD( length of straight line)= pi/2 (d1+d2+d3) + AD

suminha

Joined: 03 Feb 2020

Last visit: 02 Jan 2025

Posts: 115

Own Kudos:

372

[1]

Given Kudos: 242

Location: Korea, Republic of

Posts: 115

Kudos: 372

[1]

30 Sep 2020, 03:52

1

Kudos

Bookmarks

gmatt1476

In the figure above, points A, B, C, and D are collinear and AB, BC, and CD are semicircles with diameters d1 cm, d2 cm, and d3 cm, respectively. What is the sum of the lengths of semicircles AB, BC, and CD, in centimeters?

(1) d1:d2:d3 is 3:2:1.
(2) The length of line segment AD is 48 cm.

DS45771.01

Show Spoiler

Attachment:

The attachment 2019-09-22_0512.png is no longer available

We want to know exact length.
The ratio does not give any absolute value.

I highly recommend you to rephrase the question before jump into the choices.

Posted from my mobile device

Attachments

4F164A19-CCA8-4879-A055-556A76039D24.jpeg [ 616.09 KiB | Viewed 15904 times ]

Basshead

Joined: 09 Jan 2020

Last visit: 07 Feb 2024

Posts: 938

Own Kudos:

258

Given Kudos: 432

Location: United States

Posts: 938

Kudos: 258

14 Nov 2020, 10:31

Kudos

Bookmarks

circumference of semi-circle = $\frac{πd}{2}$

(1) We can't do anything with ratios. INSUFFICIENT.

(2) The length of AD = 48 cm.

$\frac{48π}{2} = 24π$

SUFFICIENT.

Answer is B.

Pritishd

UNC Kenan Flagler Moderator

Joined: 18 Jul 2015

Last visit: 20 Feb 2024

Posts: 237

Own Kudos:

267

Given Kudos: 120

GMAT 1: 530 Q43 V20 Verified score

WE:Analyst (Consumer Packaged Goods)

GMAT 1: 530 Q43 V20 Verified score

Posts: 237

Kudos: 267

26 Dec 2020, 04:17

Kudos

Bookmarks

gmatt1476

In the figure above, points A, B, C, and D are collinear and AB, BC, and CD are semicircles with diameters d1 cm, d2 cm, and d3 cm, respectively. What is the sum of the lengths of semicircles AB, BC, and CD, in centimeters?

(1) d1:d2:d3 is 3:2:1.
(2) The length of line segment AD is 48 cm.

DS45771.01

Show Spoiler

Attachment:

2019-09-22_0512.png

1. The sum of the length of the semicircles will be $\frac{πd1}{2} + \frac{πd2}{2} + \frac{πd3}{2} + d1 + d2 + d3$

2. Simplifying the above expression we get, $\frac{π}{2} (d1 + d2 + d3) + d1 + d2 + d3 = (d1 + d2 + d3) * (1 + \frac{π}{2})$

3. We need the value of $d1 + d2 + d3$ to answer the question

Statement - I (Insufficient)
The ratio is not sufficient to derive the actual value of $d1 + d2 + d3$

Statement - II (Sufficient)
1. $AD$ is $d1 + d2 + d3$ = $48$ cm
2. In other words we have have the value of $d1 + d2 + d3$

Ans. B

Bambi2021

Joined: 13 Mar 2021

Last visit: 23 Dec 2021

Posts: 325

Own Kudos:

121

Given Kudos: 226

Posts: 325

Kudos: 121

04 Jul 2021, 23:59

Kudos

Bookmarks

The sum of the circumferences of three circles with diameters a, b and c will be equal to the circumference of one circle with the diameter a+b+c.

B is sufficient.

GMATGuruNY

Tutor

Joined: 04 Aug 2010

Last visit: 11 Jan 2025

Posts: 1,338

Own Kudos:

3,450

[2]

Given Kudos: 9

Schools:Dartmouth College

Expert reply

Posts: 1,338

Kudos: 3,450

[2]

05 Jul 2021, 03:22

2

Kudos

Bookmarks

For the sake of clarity, the word in red should be included in the question stem:

gmatt1476

In the figure above, points A, B, C, and D are collinear and AB, BC, and CD are semicircles with diameters d1 cm, d2 cm, and d3 cm, respectively. What is the sum of the arc lengths of semicircles AB, BC, and CD, in centimeters?

(1) d1:d2:d3 is 3:2:1.
(2) The length of line segment AD is 48 cm.

Arc length of a semicircle = $\frac{πd}{2}$

Statement 1:
Case 1: d₁ = 3, d₂ = 2, d₃ = 1
In this case, the sum of the arc lengths $= \frac{3π}{2} + \frac{2π}{2} + \frac{π}{2} = \frac{6π}{2} = 3π$
Case 2: d₁ = 30, d₂ = 20, d₃ = 10
In this case, the sum of the arc lengths $= \frac{30π}{2} + \frac{20π}{2} + \frac{10π}{2} = \frac{60π}{2} = 30π$
Since the sum can be different values, INSUFFICIENT.

Statement 2:
Case 1: d₁ = 16, d₂ = 16, d₃ = 16
In this case, the sum of the arc lengths $= \frac{16π}{2} + \frac{16π}{2} + \frac{16π}{2} = \frac{48π}{2} = 24π$
Case 2: d₁ = 20, d₂ = 20, d₃ = 8
In this case, the sum of the arc lengths $= \frac{20π}{2} + \frac{20π}{2} + \frac{8π}{2} = \frac{48π}{2} = 24π$
Since the sum in each case is the same, SUFFICIENT.

Show Spoiler

B

bumpbot

Non-Human User

Joined: 09 Sep 2013

Last visit: 04 Jan 2021

Posts: 36,017

Own Kudos:

941

Posts: 36,017

Kudos: 941

12 Sep 2024, 11:41

Kudos

Bookmarks

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

In the figure above, points A, B, C, and D are collinear and AB, BC

Prep Toolkit

My Rewards

GMAT Data Sufficiency (DS) Questions

In the figure above, points A, B, C, and D are collinear and AB, BC

Prep Toolkit

My Rewards