Question Bank  Algebra  Shashank Prabhu, CAT 100 Percentiler

Number of Questions
Topic  Algebra
Answer Key Available ? : Yes
Source : Learningroots forum

Q 2) In a shop, cost of 3 burgers, 7 milkshake and french fries is Rs. 120. In the same shop, cost of 4 burgers, 10 milkshake and french fries is Rs. 164.5. Find the cost of 1 Burger, 1 Milkshake and french fries in the shop.
(1) 41
(2) 21
(3) 31
(4) None of these[OA: Option 3]

Q 3) All the pages of a book starting from page 1 are summed. One of the pages has been added twice, and the total thus obtained is 1000. Which is the page that has been added twice ?
(1) 10
(2) 12
(3) 14
(4) None of these[OA: Option 1]

Q32) The area within the curve x + y = 8 is
a. 32 sq. units
b. 64 sq. units
c. 128 sq. units
d. None of these

Q33) Find a and b such that (x + 1) and (x + 2) are factors of the polynomial x^3 + ax^2  bx + 10
a. 8 and 17
b. 17 and 8
c. 9 and 1
d. None of these

Q34) If the first three numbers of an AP are 3x, 2x + 8, and 6x  4, then what is the sum of the first 10 numbers of that series?
(a) 200
(b) 250
(c) 275
(d) 300

Q42) In an increasing AP, the product of the 5th term and the 6th term is 300. When the 9th term of this AP is divided by the 5th term, the quotient is 5 and the remainder is 4. What is the first term of the AP?
(a) 12
(b) 40
(c) 16
(d) 5

Q48) If the ratio of the roots of the equation x^2 – 2ax + b = 0 is equal to that of the roots x^2 – 2cx + d = 0, then which of the following is true?
a. ba^2 = dc^2
b. ca^2 = db^2
c. da^2 = bc^2
d. bd^2 = ac^2
e. None of these

Q52) If a^x = b^y = c^z, b/a = c/b and a, b and c are not equal, then what is the value of 2z/(x + z)?
a. y/x
b. x/y
c. x/z
d. z/x

Q68) The terms of an arithmetic sequence add up to 715. The first term of the sequence is increased by 1,the second term is increased by 3, the third term is increased by 5, and in general, the kth term is increased by the kth odd positive integer. The terms of the new sequence add to 836. What is the sum of the first, last and middle terms of the original sequence? (in numerical value)

Q75) A real valued function f is such that f(a + b) = a + f[f(b)]. Find the value of f(9).

Q78) A sequence 192, 360, 576……. is formed by multiplying the corresponding terms of two different Arithmetic Progressions. What is the eighth term of the sequence?

Q82) There are five consecutive integers a, b, c, d and e such that a < b < c < d < e and a^2 + b^2 + c^2 = d^2 + e^2. What is the sum of all possible value(s) of b?

Q85) If x and y are natural numbers such that 0 < x < 100 and 0 < y < 100, what is the number of solutions to 3x – 2y = 5?

Q94) Find the number of ordered prime triplets (a, b, c) such that a, b and c are distinct and ab + bc + ca = 316.
a. 0
b. 6
c. 10
d. Infinitely many

Q95) Find the number of non negative integral solutions of the equation 7a + 5b + 35c = 84 such that at least one of a, b or c is zero
a. 3
b. 4
c. 5
d. 7

Q7) If 9x + 15xy + 35y = 100, for all real x, y > 0, then find the minimum value of 3x + 5y.
[OA: 12]

Hint: 3x(3+5y)+7(3+5y)=121
(3x+7)(3+5y)=121
Apply either equal terms logic or AM>=GM

P(getting an electrical contract) = 2/9
So, using basic set theory, 5/6 = 3/4 + 2/9  P(both)
P(both) = 5/36

Take the capacity of tank A to be 120 units.
Find out work done per hour by P, Q and R and then use the cumulative work to find out the total time.