Answer: A Statement I : siny = 2tanx/ (1+tan2 x) => siny = (2sinx/cosx) / (1+ sin2 x/cos2 x) = 2 sinx cosx = sin2x => siny = sin2x => y = 2x. From statement II : cosy = 2tanx/(1-tan2 x) => cos y = 2(sinx/cosx)/ (1- sin2 x/cos2 x) => cosy = tan2x.
Q. No. 44:
If Beena spent Rs 400 of her earning last month on rent, then how much did Beena earn last month ? Statements : I. Beena saved 1/3 of her earning last month and spend half of the remainder on rent. II. Beena earned this month twice as much as last month.
A :
If statement I alone is sufficient, but statement II alone is not sufficient to answer the given question.
B :
If statement II alone is sufficient, but statement I alone is not sufficient to answer the given question.
C :
If both the statements together are sufficient, but neither statements alone is sufficient to answer the given question.
D :
If each statement alone is sufficient to answer the given question.
Answer: A Statement I : Beena spent on rent = 1/2 * 2/3 of earning = Rs 400.
Q. No. 45:
At a restaurant, Harish left a trip for the waiter equal to 20 percent of his entire dinner check, including tax. What was the amount of the dinner check ? Statements :
I. The sum of the dinner check and the tip was Rs 16.80.
II. Harish's tip consisted of two bills and four coins.
A :
If statement I alone is sufficient, but statement II alone is not sufficient to answer the given question.
B :
If statement II alone is sufficient, but statement I alone is not sufficient to answer the given question.
C :
If both the statements together are sufficient, but neither statements alone is sufficient to answer the given question.
D :
If each statement alone is sufficient to answer the given question.
Answer: A Statement I : Harish spent n dinner check + tip = Rs 16.80 => x + 20% of x = Rs 16.80 => x = Rs 14. and Tip = Rs 2.80.
Q. No. 46:
Paul jogs at a constant rate for 80 minutes along the same route everyday. How long is the route ? Statements :
I. Yesterday, Paul began jogging at 5:00 pm.
II. Yesterday, Paul had jogged 5 miles by 5:40 pm and 8 miles by 6:04pm.
A :
If statement I alone is sufficient, but statement II alone is not sufficient to answer the given question.
B :
If statement II alone is sufficient, but statement I alone is not sufficient to answer the given question.
C :
If both the statements together are sufficient, but neither statements alone is sufficient to answer the given question.
D :
If each statement alone is sufficient to answer the given question.
Answer: C Together with both the statements, In 40 min = 5 miles. In 24 min = 3 miles. Hence, In 80 min = 10 miles
Q. No. 47:
At company R, the average age of executive employees is 54 years old and average age of non-executives employees is 32 years old. What is the average age of all the employees at company R ? Statements :
I. There are 10 executive employees at company R.
II. The number of non-executive employees at company R is four times the number of executive employees at company R.
A :
If statement I alone is sufficient, but statement II alone is not sufficient to answer the given question.
B :
If statement II alone is sufficient, but statement I alone is not sufficient to answer the given question.
C :
If both the statements together are sufficient, but neither statements alone is sufficient to answer the given question.
D :
If each statement alone is sufficient to answer the given question.
Answer: C Statement I : Executive employees = 10. Statement II : Non-executive employees = 40. Thus, S(E.E)/ 10 = 54. And, S(N.E.E)/40 = 32. S(EE) = 540, S(N.EE) = 1280 Average = (S(EE) + S(N.EE) )/ 50 .
Q. No. 48:
At ABC Corporation for a resolution to become policy, a quorum of at least half of the 20 directors must pass the resolution by at least a two third majority. Did resolution pass or fail at a meeting of the Board of Director ? Statements : I. Ten directors voted for the favour of resolution. II. Seven directors voted against the resolution.
A :
If statement I by itself is sufficient to answer the given question.
B :
If statements II by itself is sufficient to answer the given question.
C :
If both the statements I and II taken together are sufficient to answer the given question but neither statement by itself is sufficient.
D :
If both the statements I and II taken together are not sufficient to ans the given question and more data is required.
Answer: C From both the statements it is clear that total 17 directors voted for the resolution in which ten directors voted in favour of resolution and seven director voted against the resolution. Hence we can get the answer by using both the statements together.