### These CAT Algebra questions/problems with solutions provide you vital practice for the topic. The purpose of these posts is very simple: to help you learn through practice.

Question 1: If one root of x2 + px + 12 = 0 is 4, while the equation x2 + px + q = 0 has equal roots, then the value of q is
(a) 49/4
(b) 4/49
(c) 4
(d) 1/4

The given equation is x2 + px +12 = 0. Since x = 4 is a root of this equation, so it will satisfy it.

Hence, we have 16 + 4p + 12 = 0 => 4p = – 28 => p = -7.

Hence the second equation becomes x2 – 7x + q = 0.

Now the roots of this equation are equal, so its discriminant = (b2 – 4ac) will be 0.

We get:

( -7)2 – 4q = 0 => 4q = 49 => q = 49/4.

Question 2: For the given pair (x, y) of positive integers, such that 4x – 17y = 1 and x < 1,000, how many integer values of y satisfy the given conditions?
(a) 55
(b) 56
(c) 57
(d) 58 Directions for questions 3 – 5: A young girl Roopa leaves home with x flowers, goes to the bank of a nearby river. On the bank of the river, there are four places of worship, standing in a row. She dips all the x flowers into the river, the number of flowers doubles. Then, she enters the first place of worship, offers y flowers to the deity. She dips the remaining flowers into the river, and again the number of flowers doubles. She goes to the second place of worship, offers y flowers to the deity. She dips the remaining flowers into the river, and again the number of flowers doubles. She goes to the third place of worship, offers y flowers to the deity. She dips the remaining flowers into the river, and again the number of flowers doubles. She goes to the fourth place of worship, offers y flowers to the deity. Now she is left with no flowers in hand.

Question 3: If Roopa leaves home with 30 flowers, the number of flowers she offers to each deity is:
(a) 30
(b) 31
(c) 32
(d) 33 Question 4: The minimum number of flowers that could be offered to each deity is:
(a) 10
(b) 15
(c) 16
(d) Cannot be determined  