Here are the answer and explanation to yesterday’s problem (thanks for all of your answers!):

Column A

Column B

Length of arc ABC

6

Choose the correct statement: A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

A. is the correct answer.

Video Explanation:

See you next week for another practice question! 🙂

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Actually, the beauty of this problem is it can be solved in 2 seconds, with zero writing. Equilateral triangle, side 6. A curved line that starts and ends at the same point as the the line with length 6. Therefore arc must be longer.

Remember you don’t have to determine the answer mathematically (6.84). You just have to answer which side is larger.

Yes, in this case the right triangle yields the triangle with the maximum area. As soon as you make the right angle more acute, the triangle begins to shrink. Eventually, you would get a triangle with a hypotenuse of 18 and sides of 12 and 6rt5, which would make this triangle, and everything triangle in between, smaller.

Can someone please explain this quantitative comparison question?

The length of two sides of a triangle are 12 and 18 (no other information is provided).

Column A. area of triangle
Column B. 112

A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

The answer is given as B. But potentially the third side x can be anywhere between 6 and 30, so if we take the base as x= 29 or x= 10 and 12 and 18 as opposite sides of triangle or vice versa, the answer will be D.

If we draw out a triangle with legs that are 12, 18 and 29 this triangle is going to be very skinny, and thus have very little area. To maximize a triangle with the following dimensions, 12, 18 (and unknown side) make the triangle into a right triangle with sides 12 and 18, and the unknown side the hypotenuse (which, because it’s a right triangle, would make the hypo. equal to 21.5). However we only care about the base and hight, 12 and 18, so the maximum area is 108. Which is less than 112 (Column B). Thus B has to be the answer.

It’s of “medium” level difficulty. As for solving speed, the more you do practice problems, the more readily you’ll be able to call forward familiar techniques when you’re working on problems. Hope that helps!

I’d use another approach.
If Length of arc ABC were equal 6, then the central angle of the circle would be 1 rad ≅ 57.3 degrees.
The central angle is 60 degrees > 57.3 degrees, hence, A. is the correct answer.

The GRE does not require trig. Also the calculator does not have the tan/sin/cos functions. Anyways, the GRE is not testing an exact answer in QC. Rather your reasoning – a curved line is longer than a straight line; therefore, arc ABC is greater.

No trig, no calculation. Mere using the definition of radian – A unit of angle, equal to an angle at the center of a circle whose arc is equal in length to the radius.
BTW, thank you for the great site!

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Wouldn’t better approach towards this is application of formulla

(Q/360)2pieR

ie

(60/360)X2X3.14X6

(as given 6 is the radius)

=(1/6)X2X3.14X6=6.84>6

Hi Aman :),

Actually, the beauty of this problem is it can be solved in 2 seconds, with zero writing. Equilateral triangle, side 6. A curved line that starts and ends at the same point as the the line with length 6. Therefore arc must be longer.

Remember you don’t have to determine the answer mathematically (6.84). You just have to answer which side is larger.

Hope that helps!

Thanks for the explanation..

Do u mean that a right angled triangle here has the maximum possible area…??

Yes, in this case the right triangle yields the triangle with the maximum area. As soon as you make the right angle more acute, the triangle begins to shrink. Eventually, you would get a triangle with a hypotenuse of 18 and sides of 12 and 6rt5, which would make this triangle, and everything triangle in between, smaller.

Hope that makes sense!

Can someone please explain this quantitative comparison question?

The length of two sides of a triangle are 12 and 18 (no other information is provided).

Column A. area of triangle

Column B. 112

A. The quantity in Column A is greater

B. The quantity in Column B is greater

C. The two quantities are equal

D. The relationship cannot be determined from the information given

The answer is given as B. But potentially the third side x can be anywhere between 6 and 30, so if we take the base as x= 29 or x= 10 and 12 and 18 as opposite sides of triangle or vice versa, the answer will be D.

If we draw out a triangle with legs that are 12, 18 and 29 this triangle is going to be very skinny, and thus have very little area. To maximize a triangle with the following dimensions, 12, 18 (and unknown side) make the triangle into a right triangle with sides 12 and 18, and the unknown side the hypotenuse (which, because it’s a right triangle, would make the hypo. equal to 21.5). However we only care about the base and hight, 12 and 18, so the maximum area is 108. Which is less than 112 (Column B). Thus B has to be the answer.

I got the question right but then you made me realize that I shouldn’t start with fomulas…this reasoning saves a lot of time.

I got the question right, but I didn’t see the super fast way of solving it! Must’ve taken me about 45 seconds versus the 20 really required.

What level of difficulty would you say this question is?

It’s of “medium” level difficulty. As for solving speed, the more you do practice problems, the more readily you’ll be able to call forward familiar techniques when you’re working on problems. Hope that helps!

I’d use another approach.

If Length of arc ABC were equal 6, then the central angle of the circle would be 1 rad ≅ 57.3 degrees.

The central angle is 60 degrees > 57.3 degrees, hence, A. is the correct answer.

The GRE does not require trig. Also the calculator does not have the tan/sin/cos functions. Anyways, the GRE is not testing an exact answer in QC. Rather your reasoning – a curved line is longer than a straight line; therefore, arc ABC is greater.

No trig, no calculation. Mere using the definition of radian – A unit of angle, equal to an angle at the center of a circle whose arc is equal in length to the radius.

BTW, thank you for the great site!