In the figure above, LM is a lighthouse from the top of which John views object A at an angle of depression of 60o.He then goes down the stairs to another spot in the middle of the lighthouse and views the same object at a different angle of depression. What is the distance between the bottom of the lighthouse and object A?(1) The distance between the top of the lighthouse and object A is 80 feet.(2) The distance between the middle of the lighthouse and object A is 207feet.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'D'. Can you explain this answer?

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In the figure above, LM is a lighthouse from the top of which John views object A at an angle of depression of 60^o.

He then goes down the stairs to another spot in the middle of the lighthouse and views the same object at a different angle of depression. What is the distance between the bottom of the lighthouse and object A?

(1) The distance between the top of the lighthouse and object A is 80 feet.

(2) The distance between the middle of the lighthouse and object A is 20√7 feet.

a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c)
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
d)
EACH statement ALONE is sufficient.
e)
Statements (1) and (2) TOGETHER are NOT sufficient.

Correct answer is option 'D'. Can you explain this answer?

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In the figure above, LM is a lighthouse from the top of which John vie...

Steps 1 & 2: Understand Question and Draw Inferences

In this question, the angle between the horizontal and John’s line of sight when he looks at object A from point L is given to be 60^o.

This means, in right triangle LMA, Angle MAL = 60°

By using the Angle Sum Property, we can find that Angle ALM = 30°

Triangle AML is a 30° -60° -90° triangle. In such a triangle, the sides opposite to the angles 30°, 60°, and 90° respectively are in the ratio 1 : √3 : 2

That is, MA: LM : AL = 1 : √3 : 2

Now, we need to find the distance between the bottom of the lighthouse and object A. That is, we need to find the length of MA.

Let the length of MA be x feet.

Thus,LM=3√x

And, AL=2x

John then moves downstairs to the middle of the lighthouse. Let the middle point be C.

So, MC=LC=√3x/2

Let the angle of depression from Point C to object A be y°

By Applying Pythagoras Theorem in right triangle AMC, we get:

AC²=MC²+AM²

Thus, we have expressed all sides of the right triangles AML and AMC in terms of x. If we know any of these sides, we will be able to find the value of x.

Step 3: Analyze Statement 1

The distance between the top of the lighthouse and object A is 80 feet

AL=80

This means

2x=80

x=40

Thus, Statement 1 alone is sufficient.

Step 4: Analyze Statement 2

The distance between the middle of the lighthouse and object A is 20√7 feet

AC=20√7

This means,

x=40

Thus, Statement 2 alone is sufficient.

Step 5: Analyze Both Statements Together (if needed)

There is no need to analyze further as both statements (1) and (2) are sufficient.

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In the figure above, LM is a lighthouse from the top of which John views object A at an angle of depression of 60o.He then goes down the stairs to another spot in the middle of the lighthouse and views the same object at a different angle of depression. What is the distance between the bottom of the lighthouse and object A?(1) The distance between the top of the lighthouse and object A is 80 feet.(2) The distance between the middle of the lighthouse and object A is 20√7feet.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'D'. Can you explain this answer?

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In the figure above, LM is a lighthouse from the top of which John views object A at an angle of depression of 60o.He then goes down the stairs to another spot in the middle of the lighthouse and views the same object at a different angle of depression. What is the distance between the bottom of the lighthouse and object A?(1) The distance between the top of the lighthouse and object A is 80 feet.(2) The distance between the middle of the lighthouse and object A is 20√7feet.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about In the figure above, LM is a lighthouse from the top of which John views object A at an angle of depression of 60o.He then goes down the stairs to another spot in the middle of the lighthouse and views the same object at a different angle of depression. What is the distance between the bottom of the lighthouse and object A?(1) The distance between the top of the lighthouse and object A is 80 feet.(2) The distance between the middle of the lighthouse and object A is 20√7feet.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the figure above, LM is a lighthouse from the top of which John views object A at an angle of depression of 60o.He then goes down the stairs to another spot in the middle of the lighthouse and views the same object at a different angle of depression. What is the distance between the bottom of the lighthouse and object A?(1) The distance between the top of the lighthouse and object A is 80 feet.(2) The distance between the middle of the lighthouse and object A is 20√7feet.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'D'. Can you explain this answer?.

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