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

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Re: In the figure above, points A, B, C, and D are collinear and AB, BC [#permalink]

30 Apr 2020, 05:43

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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.

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Re: In the figure above, points A, B, C, and D are collinear and AB, BC [#permalink]

27 Jun 2020, 08:28

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MentorTutoring wrote:

GDT wrote:

gmatt1476 wrote:

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

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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

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Re: In the figure above, points A, B, C, and D are collinear and AB, BC [#permalink]

05 Jul 2021, 03:22

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

gmatt1476 wrote:

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.

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Re: In the figure above, points A, B, C, and D are collinear and AB, BC [#permalink]

14 Mar 2020, 11:42

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gmatt1476 wrote:

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

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Re: In the figure above, points A, B, C, and D are collinear and AB, BC [#permalink]

27 Jun 2020, 08:19

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GDT wrote:

gmatt1476 wrote:

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

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Re: In the figure above, points A, B, C, and D are collinear and AB, BC [#permalink]

30 Sep 2020, 03:52

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gmatt1476 wrote:

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

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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

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4F164A19-CCA8-4879-A055-556A76039D24.jpeg [ 616.09 KiB | Viewed 14716 times ]

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Re: In the figure above, points A, B, C, and D are collinear and AB, BC [#permalink]

01 May 2020, 02:13

MathRevolution wrote:

gmatt1476 wrote:

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.

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Re: In the figure above, points A, B, C, and D are collinear and AB, BC [#permalink]

27 Jun 2020, 07:02

gmatt1476 wrote:

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

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Re: In the figure above, points A, B, C, and D are collinear and AB, BC [#permalink]

27 Jun 2020, 07:03

gmatt1476 wrote:

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

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Re: In the figure above, points A, B, C, and D are collinear and AB, BC [#permalink]

14 Nov 2020, 10:31

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.

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Re: In the figure above, points A, B, C, and D are collinear and AB, BC [#permalink]

26 Dec 2020, 04:17

gmatt1476 wrote:

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

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Re: In the figure above, points A, B, C, and D are collinear and AB, BC [#permalink]

04 Jul 2021, 23:59

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.

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Re: In the figure above, points A, B, C, and D are collinear and AB, BC [#permalink]

20 Jul 2023, 13:24

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Re: In the figure above, points A, B, C, and D are collinear and AB, BC [#permalink]

20 Jul 2023, 13:24

GMAT Data Sufficiency (DS) Questions

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