For class P, there are exactly two sections - A and B. What percentage of the boys have passed in both the sections put together ? I. The ratio of the number of boys and girls in the section A is 3:2 and that in the section B is 1:4. 60% of the students have passed in each section. II. 40% of the boys in section A have passed and amng the boys in section B , 60% have failed.
A :
If the question can be answered by using statement I alone but not by using statement II alone.
B :
If the question can be answered by using statement II alone but not by using statement I alone.
C :
If the question can be answered by using either of the statements alone.
D :
If the question can be answered by using both the statements together but not by either of the statements alone.
Answer: B Statement I : In section A say 60x students are boys and 40 x students are girls. If all the girls passed, 20 x boys have passed . if none of the girls passed, all 60x boys. We can't uniquely determine the % of boys who have passed. Statement II : 40% of the boys have passed in section A. And among boys in section B, 40% of the boys have passed. Therefore in both the sections put together, 40% of the boys have passed. Statement II alone is sufficient.
Q. No. 164:
The average age of N men in a group is 20. What is the value of N ? I. If two men aged 22 years and 28 years join the group, the average age of the group increases by a prime number. II. If two men aged 21 years and 26 years join the group, the average age of the group increases by a perfect square.
A :
If the question can be answered by using statement I alone but not by using statement II alone.
B :
If the question can be answered by using statement II alone but not by using statement I alone.
C :
If the question can be answered by using either of the statements alone.
D :
If the question can be answered by using both the statements together but not by either of the statements alone.
Answer: C Total age of N men = 20N. Let the increase in the average, when some men join the group be denoted by K. Statement I : Total age of men is the group when 2 men join the group = 20N +50 20N+50 = (N+2)(20+K), 10 =K(N+2) K and N+2 must be factor of 10. As K is prime it can be 2 or 5. If K = 2 , N = 3. If k =5, N = 0 which is not possible. Hence, N = 3. Statement II : The total age of men in the group when 2 men join the group = 20N+47 20N+47 = (N+2)(20+K) => K(N+2) = 7 = 7*1 K is the perfect square. => K = 1, N = 5
Q. No. 165:
Chintu wrote a test having 50 questions. Each correctly answered question in the test carries, 1 mark. Each wrongly answered and unanswered question in the test lose 1/2 and 1/4 marks respectively.He scored 27 marks in the test. How many questions did he answer correctly ? I. If the number of unanswered questions had doubled and the number of correctly answered questions was only half of what it was, there would be no change in the number of wrongly answered questions, and he would have scored 7 marks in the test. II. If the negative marks for wrong answers and unanswered questions were swapped, he would have scored 23.5 marks in the test.
A :
If the question can be answered by using statement I alone but not by using statement II alone.
B :
If the question can be answered by using statement II alone but not by using statement I alone.
C :
If the question can be answered by using either of the statements alone.
D :
If the question can be answered by using both the statements together but not by either of the statements alone.
Answer: C Let the number of correctly, wrongly and unanswered question be c,w and u respectively. c+w+u = 50 ...............(i) c - w/2 - u/4 = 27........(ii) Statement I : c/2 + w+2u = 50 .........(iii) and c/2 - w/2 - 2u/4 = 7 .................(iv) Thus, from any 3 of 4 equation we can conclude that, c = 32, w=2, u = 16. Statement II : c - w/4 - u/2 = 23.5 ..........(v) On solving (i), (ii) and (v) we get, c = 32 and w= 2 and u =16.
Q. No. 166:
Is the quantity of milk more than 80% of the quantity of solution C ? I. Solution A and B in which milk and water are in the ratio 2:1 and 5:2 are mixed to obtain the solution C. II. Solution A has (3+4x) litres of milk and (7+5x) litres of water. Solution B has (7+2x) litres of milk and (13+7x) litres of water. Solution C is formed by adding solutions A and B.
A :
If the question can be answered by using statement I alone but not by using statement II alone.
B :
If the question can be answered by using statement II alone but not by using statement I alone.
C :
If the question can be answered by using either of the statements alone.
D :
If the question can be answered by using both the statements together but not by either of the statements alone.
Answer: C Statement I : percentage of milk in solution A = 2/3 (100%) = 66.66 % and the percentage of milk in solution C = 500/7 = 71%. When these two solutions are mixed the concentration of milk in the resultant solution lies between 66.66 - 71%. Hence it can't be more than 80% in the solution C. Statement alone is sufficient. Statement II : Milk/total in solution C = > {(3+4x)+(7+2x)}/{(10+9x)+(20+9x)} = 1/3 = 33.33%. Hence, the concentration cannot be more than 80% in solution C.
Q. No. 167:
Among the four siblings - P, Q, R and S, how many males are there ? I. Among them the number of males is different from the number of females . The number of brothers of P is one more than the number of his sisters. II. Among them Q and S are of same gender. R and P are different genders while S is a bachelor.
A :
If the question can be answered by using statement I alone but not by using statement II alone.
B :
If the question can be answered by using statement II alone but not by using statement I alone.
C :
If the question can be answered by using either of the statements alone.
D :
If the question can be answered by using both the statements together but not by either of the statements alone.
Answer: C From I, among them males and females could be 1 and 3 or 3 and 1 It it is 3:1 and P is male, number of brother of P will be 2 and sister of P is 1. Hence 3 males. So, I alone is sufficient. From II : We have Q and S are males and only one among R and P is a male, there are three males. Hence, II alone is sufficient.
Q. No. 168:
Dinesh purchased some pens and pencils from a shop. He spent a total of Rs 280 on his purchase. If the number of pens and pencils he purchased were interchanged, his total expenditure would have been Rs 270. What is the difference between the number of pens and number of pencils he purchased ? (The cost in Rs of a pen and a pencil are integers). I. He purchased a total of 110 pens and pencils. II. The total cost of a pen and a pencil is Rs 5.
A :
If the question can be answered using one of the statements alone, but cannot be answered using the other statements alone.
B :
If the question can be answered using either statement alone.
C :
If the question can be answered using I and II together but not using I or II alone.
D :
If the question cannot be answered even by using I and II together.
Answer: B Let us say Dinesh purchased a pens and b pencils. Let the cost of each pen and pencil he purchased be Rs x and Rs y respectively. xa+yb = 280.........(i) xb+ya = 270.........(ii) Adding equation i and ii. (x+y)(a+b) = 550 Statement I : a+b = 110 => x+y = 5 by substituting x =1 and y = 4, we get non-integral values of a and b. => x = 2 and y = 3, a = 50 and b = 60. Similarly, x = 3, y = 2 => a = 60 and b = 50. These are only two case possible . Whatever be the case |a-b| = 10. So, I alone is sufficient. Statement II : x+y = 5. Also applicable in this case. Hence, II alone is also sufficient.