Three circles with radii of 2 cm, 3 cm and 5 cm, respectively are on

Question

QUANT 4-PACK SERIES Problem Solving Pack 1 Question 3 Three circles with radii...

Three circles with radii of 2 cm, 3 cm and 5 cm, respectively are on the same plane. If the centers of the three circles are all on the same line and each circle is tangent to at least one of the other two circles, then what is the shortest possible distance, in cm, between the center of the largest circle and the center of the smallest circle?

A) 0
B) 1
C) 3
D) 7
E) 13

A) 0
B) 1
C) 3
D) 7
E) 13

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This question is part of the Quant 4-Pack series

ENGRTOMBA2018 · Accepted Answer

As this question asks us to find the smallest value, we will start from the top and keep eliminating answers.

Option A: 0, this is not possible as this would mean that the smallest and largest circles are concentric and hence both can not be tangent to each other or to the 3rd circle. Eliminate.

Option B: 1, The figure above shows 1 possible arrangement. We can clearly see that the distance AB must be less than the radius of the smallest circle (=2), making 1 as the correct answer.

No need to spend time on other options.

B is the correct answer.

camlan1990 · Answer

A) 0 when the center of the largest is that of the smallest => both these circle must be tangent with the second big one => This situation cannot happen => Cross out this ans
B) 1 This situation cannot satisfy the biggest adn the smallest are both tangent with the second one. Hope you can imagine this situation in ur head => Cross out this
C) 3 => the biggest is tangent with the smallest and the smallest is inside the biggest => Both these circle can be tangent with the second one => THIS SITUATION CAN HAPPEN => CHOOSE THIS ANSWER

Because the question asks the shortest distance so I will not check the ans D, E

Ans: C

EMPOWERgmatRichC · Answer

Hi All,

Physically drawing the circles that are described in this prompt will likely help you to visualize the work that needs to be done (the math itself is just arithmetic, but you have to keep track of what the question asks for - the SMALLEST possible distance between the two centers).

We're told that the 3 centers of the 3 circles have to be on the SAME line and that each of the 3 circles is tangent to at least one of the other two circles. Thus, there aren't that many different ways to arrange the 3 circles.

Attachment:

3 circles answer GC.png [ 67.36 KiB | Viewed 12703 times ]

Placing the 2cm circle INSIDE the 3cm circle creates three equal 2cm wide 'pieces.' The two 2cm radii of the smallest circle would take up 4 cm of space on the medium-sized circle's diameter, leaving 2cm of excess space.

Placing the 3cm-with-the-2cm-circle-inside-it INSIDE the 5cm circle now allows us to compare the largest radius (5cm) to the three 2cm 'pieces' in the smaller two circles. The center of the smallest circle is now 4cm from the edge of the largest circle. Since the radius of the largest circle is 5cm, the distance between those 2 centers is 5cm - 4cm = 1cm.

Final Answer:

Show Spoiler

B

GMAT assassins aren't born, they're made,
Rich

Marchewski · Answer

Engr2012 
I'm not sure if this is just one of those days and I'm missing something completely here. But according to your drawing, the smallest circle A would enclose the center of the largest circle B when A is placed inside B and A is tangent to B. I'm wondering how this is possible since the diameter of A is 4 and the radius of B is 5? The center of point B should never be inside circle A when A is tangent to B.

I do agree that the answer is B though.

MathRevolution · Answer

Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

Three circles with radii of 2 cm, 3 cm and 5 cm, respectively are on the same plane. If the centers of the three circles are all on the same line and each circle is tangent to at least one of the other two circles, then what is the shortest possible distance, in cm, between the center of the largest circle and the center of the smallest circle?

A) 0
B) 1
C) 3
D) 7
E) 13

A) 0
B) 1
C) 3
D) 7
E) 13

Let the center of the largest circle be A, that of second large be B and that of the smallest circle be C. 
Since we should find the shortest possible distance between the centers. The smallest circle should be inside of the largest circle, moreover if the smallest circle is tangential to the largest circle, the distance between A and C would be 3.

But let’s consider another possibility : Inside of circle A the circle B is tangential to circle A and inside B the circle C is tangential to circle B at the other side of tangent point of A and B. Then the distance between A and C is 1.

So the answer is (B).

ENGRTOMBA2018 · Answer

Good catch. I drew the figure in a hurry without realising that it is not possible. I have updated the figure. But the answer still remains = 1 as is mentioned by Rich in his post above.

fskilnik · Answer

The correct answer is (B), indeed.

https://preview.ibb.co/dhQD9f/19-Nov18-5z.gif

Regards, 
Fabio.

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Three circles with radii of 2 cm, 3 cm and 5 cm, respectively are on

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