1. Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is: A. 300 m B. 173 m C. 273 m D. 200 m
Assume a triangle with ACD, Let BD be the lighthouse and A and C be the positions of the ships. Then, BD = 100 m, angle BAD = 30° , angle BCD = 45° tan 30° = BD/BA ⇒ 1/√3 = 100/BA ⇒ BA = 100√3 tan 45° = BD/BC ⇒ 1 = 100/BC ⇒ BC = 100 Distance between the two ships = AC = BA + BC = 100√3 + 100 = 100(√3+1) = 100√3+100=100(√3+1) = 100(1.73+1) = 100 × 2.73 = 273 m Answer is Option C
Quantitative Question If a•b≠0, then what is the value of a/b + b/a? (1) a•b=8 (2) a/b=3 A. statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked; B. statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked; C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked; D. EACH statement ALONE is sufficient to answer the question asked; E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Statement 1 alone is not sufficient because by knowing the product a.b we are not sure about the values of a or b There are multiple values of a and b which fits in here a=1, b=8 a=2, b=4 which is why we can not arrive at a unique solution for our problem Now look at Statement 2 alone, a/b=3 With this we can derive the value of b/a which is a/3 Now that we have unique values for a/b and b/a we can solve the problem using statement 2 alone So the answer for this question is B
Evaluate: |5 - 7(3 - 9)| - |4 - 19|
To solve these type of questions, one should keep in mind BODMAS rule Solving math with in brackets first |5-7(-6)|-|-15| Multiplication of 7 & -6 will be next step |5-(-42)|-|-15| = |5+42|-|-15| = |47|-|-15| Solving modulus will modify this equation as = 47-15 = 32 Solution is 32