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CAT workshop- Algebra- Part 2
Question: Question: If p+q+r+s= 30
...
Question: If |𝑥| + |𝑦| = 20
...
-1 < p < 2
2
...
-2 < p < 1
4
...
-1 < p < 2
2
...
-2 < p < 1
4
...
Which of the following is necessarily
true?
Question: |x| ≤ 2 and |y + 3| ≤ 5
...
-4
2
...
-7
4
...
6
2
...
8
4
...
Charge for playing games for one full
time is Rs
...
327
...
Rs
...
6
3
...
210 and Rs
...
Rs
...
12
4
...
210 and Rs
...
Mistake took the
reciprocals of the roots and got the equation of the form x2 - 5x + k1 = 0, whereas Mr
...
What is
the actual equation, which can be formed with the given roots?
Question: How many whole number pairs satisfy both the inequalities 2x + 3y ≤ 12 and 9x +
4y ≤ 72?
1
...
12
3
...
19
Question: If 2y - x > 2x - y, and 0 ≤ y ≤ 20, how many non-negative integer pairs of x and y
satisfy the given inequalities?
1
...
210
3
...
21
Question: What is the sum of all possible values of m in the given inequality?
(m + 2)(m + 3)/(m - 2) > 0, m is an integer, it is known that m < 99
...
4950
2
...
1032
4
...
Find the area enclosed?
Question: How many positive integer pairs (x, y) satisfy the inequality 4x + y - 10(2x + y) +
64 ≤ 10(2x + y)?
1
...
2
3
...
6
Question: If 2x+y+z= 11
...
-16
2
...
1/9
4
...
How many numbers from set S satisfy the
conditions |x - 4| ≤ 6 and |x + 4| < 5?
Question: For the given pair (x, y) of positive integers, 7x + 3y = 123
...
What is the value of (m - n)2?
A
...
16
C
...
4
Question: The number of solutions (x, y, z) to the equation x – y – z = 25, where x, y, and z
are positive integers such that x ≤ 40, y ≤ 12, and z ≤ 12 is
A
...
99
C
...
105
Question: To determine their favourite brand of chocolates in a particular community, a big
chain of retail stores conducted a survey for elementary school kids
...
In all, 400
kids were involved in the survey
...
In the next 200, 40
chose brand C
...
If not more than 25% of kids chose
brand C, then which of the following inequalities best describes the value for k?
A
...
k ≤ 60
C
...
k ≥ 40
Question: p, q and r are three non-negative integers such that p + q + r = 10
...
A
...
≥ 80 and < 90
B
...
≥ 60 and <70
D
...
The difference between the sons' age is 3 years, mother's age exceeds the sum of the sons'
age by 17 years and the difference of age of father and mother is equal to the age of the
elder son
...
While solving, Rocky
commits a mistake in the constant term and finds the roots to be 8 and 2
...
Find the correct roots
...
-9 and 1
B
...
9 and 1
D
...
It is also known that one
factor is (y - k) and k is greater than zero
...
28
B
...
11
D
...
While working together, they
can make 20 pieces per minute
...
The remaining part of the work is done by the
second cook and the third cook, working together
...
46 minutes
B
...
32 minutes
D