Answer: D From I: X = Y or X = –Y. Hence, I alone is not sufficient. From II: X = –Y. If X is not equal to zero, then X is not equal to Y and if X is equal to zero, X is equal to Y. Hence, statement II is insufficient.
Q. No. 146:
If X ≠ 0 and X2 Z – 4XY + Y = 0, what is the value of Z ? I. Z = 32X. II. Z = 4Y.
A :
If the question can be answered by using any of the statements alone, but not by using
the other statement alone.
B :
If the question can be answered by using either of the statements alone.
C :
If the question can be answered only by using both the statements together.
Answer: D Replacing Z from statement I gives a cubic equation: 32X3 – 4XY + Y = 0. I alone is not sufficient. Replacing Z from statement II gives: 4YX2 – 4YX + Y = 0 or Y(2X – 1)2 = 0. => X = 1/2, Y = 0 and hence Z can take any value. II alone is not sufficient. Both statements together gives us a cubic equation in Z with real roots (if X and Y are replaced with Z): Z3 – 32Z2 + 8 × 32 Z = 0. => Z = 0, Z = 16. Unique value of Z cannot be determined.
Q. No. 147:
Is Y negative? I. X + Y is positive. II. X – Y is positive.
A :
If the question can be answered by using any of the statements alone, but not by using
the other statement alone.
B :
If the question can be answered by using either of the statements alone.
C :
If the question can be answered only by using both the statements together.
Answer: D Consider X = 2 and Y = 1, as well as, X = 2 and Y = –1. Both sets satisfy both the statements. Hence, one cannot say whether Y is positive or negative.
Q. No. 148:
What is the average age of the students in a class? I. Sum of the ages of the students and teacher is 210. II. There are 20 students in the class.
A :
If the question can be answered by using any of the statements alone, but not by using
the other statement alone.
B :
If the question can be answered by using either of the statements alone.
C :
If the question can be answered only by using both the statements together.
Answer: D Age of the teacher is also required in addition to the two statements.
Q. No. 149:
What is the percentage discount? I. The customer get three successive discounts of 20%, 25%, and 10%. II. The customer pays Rs.108 after the discounts for the actual cost of Rs.200.
A :
If the question can be answered by using any of the statements alone, but not by using the other statement alone.
B :
If the question can be answered by using either of the statements alone.
C :
If the question can be answered only by using both the statements together.
Answer: B Statement I gives overall discount and Statement II gives discount = Total discount/ actual price = 92/100 Question can be answered using either statement alone.
Q. No. 150:
If P represents the principal, R the rate of interest and N the number of years, then find the simple interest. I. N = R/2 II. R*N = P/10
A :
If the question can be answered by using any of the statements alone, but not by using
the other statement alone.
B :
If the question can be answered by using either of the statements alone.
C :
If the question can be answered only by using both the statements together.
Answer: D S.I = PNR/100 Statement I gives S.I. = PR2 /200 Statement II gives S.I. = P2 /1000 Both statements together does not answer the question, as P is unknown.