What is the total worth of Lakhiram‘s assets? I. Compound interest at 10% on his assets, followed by a tax of 4% on the interest, fetches him Rs. 15000 this year. II. The interest is compounded once every four months.
A :
If both the statements together are insufficient to answer the question.
B :
If any one of the two statements is sufficient to answer the question.
C :
If each statement alone is sufficient to answer the question.
D :
If both the statements together are sufficient to answer the question, but neither statement alone is sufficient.
Answer: D Let Lakhiram‘s assets be worth Rs. X. In the case of compound interest, the period of reckoning or calculation of CI is very important. This information is given in statement (II). The annual CI rate is 10%, so the rate for 4 months is (4/12) 10 = (10/3)%. So the total Cl after one year, in terms of X, may be written as: Cl = X[(1 + ((10/3)/100)]3 , because in a year, there are 3 terms of 4 monthsThis interest is followed by a tax of 4% paid by him which ultimately fetches Lakhiram Rs. 1500. This data helps us to find the value of X, so the answer is (D).
Q. No. 140:
How many different triangles can be formed? I. There are 16 coplanar, straight lines in all. II. No two lines are parallel.
A :
If both the statements together are insufficient to answer the question.
B :
If any one of the two statements is sufficient to answer the question.
C :
If each statement alone is sufficient to answer the question.
D :
If both the statements together are sufficient to answer the question, but neither statement alone is sufficient.
Answer: A Although it is known that none of the lines are parallel to each other, there might be the case wherein all the lines have exactly one point of intersection, or eight lines with one point and the other eight with another point of intersection. Unless something about the relative arrangement of these lines is known, one cannot arrive at a definite answer. So the answer is (A).
Q. No. 141:
The average age of the members in a gymnastic team is 27 with no member having age less than 4 years. The age of all the members in the team is an integer in years. Find the number of possible values of the age of a particular member. I. The new average age of the members in the team is two more than the number of members in the team after that particular member was excluded. II. The new average age of the members in the team is twice the age of that particular member if he is excluded from the team.
A :
If statement (I) alone is sufficient to answer the question.
B :
If statement (II) alone is sufficient to answer the question.
C :
If statement (I) and statement (II) together are sufficient but neither of the two alone is sufficient to answer the question.
D :
If either statement (I) or statement (II) alone is sufficient to answer the question.
Answer: D Using the first statement we have (27n – x) / (n-1)= n+1 For n = 1, x = 27 which is possible. For n = 27, x = 1 which is NOT possible as the age of any member cannot be less than 4 years. So, the maximum value of n is 26 for which x = 27 We can always chose two values a and b for n such that a + b = 27 to yield the same value of x. So the unordered pair (a, b) varies from (1, 26) to (13, 14). Hence 13 different ages are possible. From the second statement we have (27n – x) / (n-1) = 2x x = 27n/(2n-1) For n = 1, 2, 5 and 14, x holds different values. Hence the question can be answered by using either of the statements alone.
Q. No. 142:
Consider a quadratic equation ax2 + bx + c = 0 where a, b, c are real numbers. If ‘k’ is the arithmetic mean of the roots of this equation, then is the value of ax2 + bx + c at x = k greater than 0? I. The expression ax2 + bx + c attains a definite maximum value and both the roots of the equation are real and negative. II. The expression ax2 + bx + c attains a definite minimum value and both the roots of the equation are real and negative.
A :
If statement (I) alone is sufficient to answer the question.
B :
If statement (II) alone is sufficient to answer the question.
C :
If statement (I) and statement (II) together are sufficient but neither of the two alone is sufficient to answer the question.
D :
If either statement (I) or statement (II) alone is sufficient to answer the question.
Answer: D Using statement I we have Two real and distinct roots and with a < 0. So that for any value of x between the two roots the value of
ax2 + bx + c is positive. Using statement II we have Two real and distinct roots and with a > 0. So that for any value of x between the two roots the value of ax2 + bx + c is negative. Hence the question can be answered by using either of the statements alone.
Q. No. 143:
Six characters A, B, C, D, E and F are written from left to right (not necessarily in the same order as given). Which alphabet is to the right of A? I. A does not occupy any of the corner positions and each of C, D and F are to the left of A. II. There is exactly one alphabet between B and F.
A :
If Statement I alone is sufficient to answer the question.
B :
If Statement II alone is sufficient to answer the question.
C :
If Statement I and Statement II together are sufficient but neither of the two alone is sufficient to answer the question.
D :
Both Statement I and Statement II are insufficient to answer the question.
Answer: D From Statement I - C, D and F are to the left of A A is not at rightmost corner So either E or B is to the right of A . Possible cases are - C D F A E B C D F A B E B C D F A E E C D F A B etc. Note: C, D and F can exchange places but that is not of our interest Clearly Statement I is not sufficient alone From Statement II - No information is given about position of A Clearly Statement II is not sufficient alone Combining Statement I and II - Several cases still satisfy this. For example - C D F A B E C F D B A E etc. Clearly Statement I and Statement II when used together are still not sufficient.
Q. No. 144:
Shakuntla Express running at a constant speed of 50 km/hour crosses the Bhatku Bridge in 20 seconds. How long is the Shakuntla Express? I. Indraprasthha Mail is 100 m long and running at a constant speed of ‘v’ km/hour takes 40 seconds to cross the Bhatku Bridge. II. Indraprasthha Mail running at a constant speed of ‘v’ km/hour crosses a 30 m long platform in 20 seconds.
A :
If Statement I alone is sufficient to answer the question.
B :
If Statement II alone is sufficient to answer the question.
C :
If Statement I and Statement II together are sufficient but neither of the two alone is sufficient to answer the question.
D :
If either Statement I or Statement II alone is sufficient to answer the question.
Answer: C Let the length of Shakuntla Express be ‘L’ km. Let the length of the Bhatku Bridge be ‘B’ km. Let the length of the Indraprasthha Mail be ‘P’ km Hence, (L+B)/50 = 20/3600 .........(i) To find the value of L we need the value of B. Using Statement I: Given: P = 0.1 km We can conclude that, (0.1+B)/v = 40/3600 ......(ii) Clearly statement I alone is not sufficient to obtain the value of B (as we don’t know ‘v’) and hence the value of L from (i). Using Statement II: (0.03+P)/v = 20/3600 ....(iii) Clearly statement III when read alone talks only about Indraprastha Mail. So, its not sufficient to answer. Combining Statements I and II together: If we combine the two statements then in equation (iii) the value of ‘P’ will be 0.1. Hence from (ii) and (iii) - 0.1 + B = 2(0.03 + P) = 2(0.13) = 0.26 B = 0.16 km From (i) - L + B = (1000/3600) or L = (1000/3600) – B L = (1000/3600) – 0.16 = 0.118 km or 118 metres So, statement I and II together are sufficient but neither of he two alone is sufficient to answer the question.