Algebra









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Quiz Begins Here

Q #1
⏰ :

Directions: Read the following information to answer the question.

If two positive numbers a and b are such that a <50 and b >25, then which of the following can never be true?

  1. b > a
  2. 2a – b < 0
  3. III.    3a + 2b > 200

Discuss
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Statement I: Since a can take any value including those less than 25, this statement can be true.

Statement II: By observation, we can make out that 2a-b can be less than zero. 

Statement III : 3a + 2b

=3(50-k) + 2 (25+l) = 200 – 3k + 2l

This can be grater than 200 since there is no restriction on the value if I where as k<50.

 


Q #2
⏰ :

Directions: Read the following information to answer the question.

A candidate takes a test and attempts all the 120 questions therein. If 1/8 of the questions carry 1/8 negative mark, 1/4 of the questions carry 1/4 negative mark and the rest of the questions carry 1/2 negative mark, then what is the difference between the maximum and the minimum marks that he can score given that he gets 1 mark for every correct answer?
Discuss
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Q #3
⏰ :

Directions: Read the following information to answer the question.

Two baskets containing Bananas and Apples respectively are placed adjacent to each other. A man picks up a certain number of Bananas and half that number of Apples from the respective baskets and transfers them to the other basket. If the Banana basket does not have any Bananas left after 20 such operations but has 100 apples in it while the Apples basket has twice the number of Apples as Bananas in it, then find the total number of Apples in both the basket put together.
Discuss
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If he puts x bananas in, he takes out x/2 apples i.e., 100 apples are remaining means 200 bananas were there initially. Therefore the apples basket has 400 apples and local number of apples = 100 + 400 = 500

Q #4
⏰ :

Directions: Read the following information to answer the question.

A family consists of a father, a mother, two sons and a daughter who is the youngest. The present age of the father is four times the present age of the daughter. The age of the eldest son is one and half times the age of the younger son. The age of the father is thrice the age of the younger son. Fifteen years ago, the age of the father was in the ratio of 9 : 7 with that of his wife and the sum of the present ages of the two sons is equal to the sum of the ages of the mother and the elder son fifteen years ago. What was the average age of the family 16 years ago?
Discuss
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Q #5
⏰ :

Directions: Read the following information to answer the question.

A family consists of a father, a mother, two sons and a daughter who is the youngest. The present age of the father is four times the present age of the daughter. The age of the eldest son is one and half times the age of the younger son. The age of the father is thrice the age of the younger son. Fifteen years ago, the age of the father was in the ratio of 9 : 7 with that of his wife and the sum of the present ages of the two sons is equal to the sum of the ages of the mother and the elder son fifteen years ago. It is now know that the elder son got married at the age of 27 years and after two years the couple gave birth to a beautiful girl. Five years after his marriage the average age of the whole family including the new entrants was 31 years. What was age of the elder son’s wife, when their daughter was 3 years old?
Discuss
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