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Framing and solving equations forms the basis of quants. Get in as much practice as you can in these two topics because the spillover benefits from being good at framing equations can be enormous.
1. ### Counting - Linear Equations

3x + 4|y| = 33. How many integer values of (x, y) are possible?

1. 6
2. 3
3. 4
4. More than 6
More than 6.
• Integer Values; Modulus
• Medium
2. ### Counting - Linear Equations

(|x| - 3) (|y| + 4) = 12. How many pairs of integers (x, y) satisfy this equation?

1. 4
2. 6
3. 10
4. 8
10
• Integer Values; Modulus
• Medium
3. ### Counting - Linear Equations

x + |y| = 8, |x| + y = 6. How many pairs of x, y satisfy these two equations?

1. 2
2. 4
3. 0
4. 1
4. ### Counting - Quadratic Equations

What is the number of real solutions of the equation x2 - 7|x| - 18 = 0?

1. 2
2. 4
3. 3
4. 1
5. ### Counting - Quadratic Equations

x2 - 9x + |k| = 0 has real roots. How many integer values can 'k' take?

1. 40
2. 21
3. 20
4. 41
6. ### Integer Roots

x2 - 11x + |p| = 0 has integer roots. How many integer values can 'p' take?

1. 6
2. 4
3. 8
4. More than 8
More than 8.
• Medium
7. ### Linear Equations - Integer Solutions

2x + 5y = 103. Find the number of pairs of positive integers x and y that satisfy this equation.

1. 9
2. 10
3. 12
4. 20
8. ### Maximum, Minimum

Consider three numbers a, b and c. Max (a,b,c) + Min (a,b,c) = 13. Median (a,b,c) - Mean (a,b,c) = 2. Find the median of a, b, and c.

1. 11.5
2. 9
3. 9.5
4. 12
9.5
• Linear Equations - Median
• Medium
9. ### Unique Solutions

a1x + b1y + c1z = d1, a2x + b2y + c2z = d2, a3x + b3y + c3z = d3.

Which of the following statements if true would imply that the above system of equations does not have a unique solution?
i. ${\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}} \neq \frac{d_{1}}{d_{2}}}$
ii. ${\frac{ a_{1} }{ a_{2} }= \frac{ a_{2} }{ a_{3} }}$ ; ${\frac{ b_{1} }{ b_{2} }= \frac{ b_{2} }{ b_{3} }}$
iii. a1, a2, a3 are integers; b1, b2, b3 are rational numbers, c1, c2, c3 are irrational numbers

• Condition for Unique Soln.
• Hard
10. ### Roots - Quadratic Equation

Equation x2 + 5x – 7 = 0 has roots a and b. Equation 2x2 + px + q = 0 has roots a + 1 and b + 1. Find p + q.

1. 6
2. 0
3. -16
4. 2
11. ### Sum and product of the roots

Sum of the roots of a quadratic equation is 5 less than the product of the roots. If one root is 1 more than the other root, find the product of the roots?

1. 6 or 3
2. 12 or 2
3. 8 or 4
4. 12 or 4
12 or 2
• Sum and product of the roots
• Easy
12. ### Real and imaginary solutions for an equation

How many real solutions are there for the equation x2 – 7|x| - 30 = 0?

1. 3
2. 1
3. 2
4. none
2
• Real and imaginary solutions for an equation
• Easy
13. ### Value of the variables - Quadratic Equation

If (3x+2y-22)2 + (4x-5y+9)2 = 0 and 5x-4y = 0. Find the value of x+y.

1. 7
2. 9
3. 11
4. 13
14. ### Progressions and Equations

Let x3- x2 + bx + c = 0 has 3 real roots which are in A.P. which of the following could be true

1. b=2,c=2
2. b=1,c=1
3. b= -1,c = 1
4. b= -1,c= -1
9
• AP and roots of an equation
• Hard
15. ### Roots of an Equation

(3 + 2√2)(x2 - 3) + (3 - 2√2)(x2 - 3) = b which of the following can be one of the roots of the equation

1. 2
2. √2
3. -√2
4. All of the above
16. ### Real roots

If f(y) = x2 + (2p + 1)x + p2 - 1 and  x is a real number, for what values of ‘p' the function becomes 0?

1. p > 0
2. p > -1
3. p >= -5/4
4. p <= 3/4
17. ### Linear and Quadratic Expressions

A merchant decides to sell off 100 articles a week at a selling price of Rs. 150 each. For each 4% rise in the selling price he sells 3 less articles a week. If the selling price of each article is Rs x, then which of the below expression represents the rupees a week the merchant will receive from the sales of the articles?

1. 175 - x/2
2. x/3 + 156
3. 350 - x2/2
4. x2 - 2x + 75
• Medium

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