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# Data Sufficiency Problem 3

 Each question is followed by two statements. You have to decide whether the information provided in the statements is sufficient for answering the question.
 Mark A If the question can be answered by using one of the statements alone, but cannot be answered by using the other statements alone. Mark B If the question can be answered by using either statement alone. Mark C If the question can be answered by using both statements together, but cannot be answered by using the either statement alone. Mark D If the question cannot be answered even by using both the statements together.
 1. What is the number of type-2 widgets produced, if total number of widgets produced is 20,000 ? (I) If the production of type-1 widgets increases by 10% and that of type-2 decreases by 6%, the total production remains the same. (II) The ratio in which type-1 and type-2 widgets are produced is 2 : 1. (a)  A (b) B (c) C (d) D
 2. How old is Sachin in 1997 ? (I)  Sachin is 11 yr  younger than Anil whose age will be a prime number in 1998. (II) Anil’s age was a prime number is 1996. (a) A (b) B (c) C (d) D
 3. What is the total worth of Lakhriram’s assets ? (I) A compound interest at 10% on his assets, followed by a tax of 4% on the interest, fetches him Rs. 1500 this year. (II) The interest is compounded once every four months. (a) A (b) B (c) C (d) D
 4. How many different triangles can be formed ? (I)  There are 16 co-planer straight lines. (II)  No two lines are parallel. (a) A (b) B (c) C (d) D
 5. What is the selling price of the article ? (I)  The profit on sales is 20%. (II) The profit on each unit is 25% and the cost price is Rs 250. (a) A (b) B (c) C (d) D
 6. What is the cost price of the article ? (I)  After selling the article, a loss of 25% on cost price is incurred. (II) The selling price is three-fourths of the cost price. (a) A (b) B (c) C (d) D
 7. If p and q are the roots of the equation (ax2 + bx + c=0) then what is the value of ( p2 + q2 ) ? (I)  p + q = -b/a (II) 2pq = c/a (a) A (b) B (c) C (d) D
 8. If a, b and c are integers, is (a – b + c) > (a + b – c) ? (I)  b is negative. (II) c is positive. (a) A (b) B (c) C (d) D
 9. What is the ratio of the two liquids A and B in the mixture finally, if these two liquids kept in three vessels are mixed together ? (The containers are of equal volume) Assume container volume=volume of liquids (I)  The ratio of liquid A to liquid B in the first and second vessels are 3 : 5, 2 : 3 respectively. (II) The ratio of liquid A to liquid B in vessel 3 is 4 : 3. (a) A (b) B (c) C (d) D
 10 A tractor traveled a distance of 5 M. What is the radius of the rear wheel ? (I)  The front wheels rotates ‘N’ times more than the rear wheel over this distance. (II)The circumference of the rear wheel is ‘t’ times that of the front wheel. (a) A (b) B (c) C (d) D

 1 B 2 D 3 C 4 D 5 A 6 D 7 C 8 C 9 D 10 D

1. Sanket

In sum 9, answer should be c
let k be volume of each vessel.
For vessel 1,
Quantity of A and B are 3x,5x.
3x+5x=8x=k
x=k/8
so, Quantity of A and B are 3k/8, 5k/8
Similary for vessel 2,
Quantities for A and B would be 2k/5, 3k/5
And for vessel 3,
A and B are 4k/7,3k/7.
So now adding A quantites and B Quantities ratio can be found.
Correct me if I am wrong.

2. Amit

The answer to problem 1 should be D,

because it is not mentioned as if ONLY Type 1 and Type 2 products are produced. What if Type 3 is also there ?

& as per your given solution, u have assumed that these are the only two types produced which is not correct.

3. Prabhat Gupta

The answer to problem 10 should be C.

Statement 1 : (N+n)*2*pi*r = n*2*pi*R=5 ;
Statement 2 : r*t = R ;

Solving 1 and 2 ;

R = 5(t-1)/(2*pi*N);

where