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Q #21
⏰ :

Directions: In each question, you are given certain data followed by two statements. For answering the questions:

  • Mark 1. If both the statements together are insufficient to answer the question.
  • Mark 2. If any one of the two statements is sufficient to answer the question.
  • Mark 3. If each statement alone is sufficient to answer the question.
  • Mark 4. If both the statements together are sufficient to answer the question, but neither statement alone is sufficient.

What is the number of type 2 widgets produced, if the total number of widgets produced is 20,000?

  1. If the production of type - 1 widgets increases by 10% and that of type-2 decreases by 6%, the total production remains the same.
  2. The ratio in which type - 1 and type - 2 widgets are produced is 2 : 1.


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Explanation: If the number of type - 1 widgets produced is A and that of type - 2 widgets is B, then we get the basic equation [A + B = 20,000] from the data in the question. From statement (I), we get [1.1 A + 0.94 B = 20,000]. This is enough to give us the value of B. Similarly from statement (2), we get A = 2B. This is enough to give us the value of B.

Q #22
⏰ :

Directions: In each question, you are given certain data followed by two statements. For answering the questions:

  • Mark 1. If both the statements together are insufficient to answer the question.
  • Mark 2. If any one of the two statements is sufficient to answer the question.
  • Mark 3. If each statement alone is sufficient to answer the question.
  • Mark 4. If both the statements together are sufficient to answer the question, but neither statement alone is sufficient.

How old is Sachin in 1997?

  1. Sachin is 11 years younger than Anil whose age will be prime number in 1998.
  2. Anil’s age was a prime number in 1996.


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Explanation: Anil’s age was a prime number in 1996 and 1998. So Anil’s age in these two yeas can be a pair of such numbers which are prime, and differ by 2. We have many such pairs - (3,5), (5, 7), (11, 13)….. And it is not possible to arrive at a unique answer. So the answer is (1).

Q #23
⏰ :

Directions: In each question, you are given certain data followed by two statements. For answering the questions:

  • Mark 1. If both the statements together are insufficient to answer the question.
  • Mark 2. If any one of the two statements is sufficient to answer the question.
  • Mark 3. If each statement alone is sufficient to answer the question.
  • Mark 4. If both the statements together are sufficient to answer the question, but neither statement alone is sufficient.

What is the total worth of Lakhiram’s assets?

  1. Compound interest at 10% on his assets, followed by a tax of 4% on the interest, fetches him Rs. 15000 this year.
  2. The interest is compounded once every four months.


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Explanation: 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 months. This interest is followed by a tax of 4% paid by him which ultimately fetches LakhiramRs. 1500. This data helps us to find the value of X,.

Q #24
⏰ :

Directions: In each question, you are given certain data followed by two statements. For answering the questions:

  • Mark 1. If both the statements together are insufficient to answer the question.
  • Mark 2. If any one of the two statements is sufficient to answer the question.
  • Mark 3. If each statement alone is sufficient to answer the question.
  • Mark 4. If both the statements together are sufficient to answer the question, but neither statement alone is sufficient.

How many different triangles can be formed?

  1. There are 16 coplanar, straight lines in all.    
  2. No two lines are parallel.


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Explanation: 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 (1).

Q #25
⏰ :

Directions: Each question is followed by two statements. You have to decide whether the information provided the statements is sufficient for answering the question.

  • Mark 1.  If the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.
  • Mark 2. If the question can be answered by using either statement alone.
  • Mark 3. If the question can be answered by using both statements together, but cannot be answered by using either statement alone.
  • Mark 4. If the question cannot be answered even by using both the statements together.

  What is the number of triangles that can be formed?

  1. Each triangle has vertices involving exactly three of the given ten con-cyclic points.
  2. The perimeter of the triangles with integral sides is 14.


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Explanation: From statement A, number of triangles can be determined as 10C3 ? Statement A alone is sufficient From statement B as the sides are integral values and the perimeter is 14 and in a triangles the sum of the two sides is greater than the third side the sides of the triangle can be ? 4, 4, 6 ? 5, 5, 4 ?the number of triangles formed are 2. Statement B alone is sufficient.