# Linear Equations

### Consider the system of linear equation: x1 + 2x2 + x3 = 3

Consider the system of linear equation

x1 + 2x2 + x3 = 3

2x1 + 3x2 + x3 = 3

3x1 + 5x2 + 2x3 = 1

The system has

1. Infinite no. of solutions
2. No solution
3. Unique solution
4. Exactly 3 solutions

### The number of solutions of the equation 2x + y = 40 where both x and y

The number of solutions of the equation 2x + y = 40 where both x and y are positive integers and x ≤ y is:

1. 7
2. 13
3. 14
4. 18

### Three times the first of three consecutive odd integers is 3 more than twice

Three times the first of three consecutive odd integers is 3 more than twice the third. What is the third integer?

1. 5
2. 9
3. 11
4. 15

### Which one of the following conditions must p, q and r satisfy so that the following system

Which one of the following conditions must p, q and r satisfy so that the following system of linear simultaneous equations has at least one solution, such that p + q + r ≠ 0?

• x + 2y - 3z = p
• 2x + 6y - 11z = q
• x - 2y + 7z = r
1. 5p - 2q - r = 0
2. 5p + 2q + r = 0
3. 5p + 2q - r = 0
4. 5p - 2q + r = 0

### If x and y are integers, then the equation 5x + 19y = 64 has

If x and y are integers, then the equation 5x + 19y = 64 has

1. A solution for -59 < y < -56
2. No solution for x > 250 and y > -100
3. A solution for 250 < x < 300
4. No solution for x < 300 and y < 0

### Using only 2, 5, 10, 25, and 50 paisa coins, what will be the minimum number of coins

Using only 2, 5, 10, 25, and 50 paisa coins, what will be the minimum number of coins required to pay exactly 78 paise, 69 paise and Rs. 1.01 to three different persons?

1. 17
2. 18
3. 19
4. 20

### What is the value of k for which the following system of equations has no solution: 2x - 8y = 3 and kx + 4y = 10

What is the value of k for which the following system of equations has no solution: 2x - 8y = 3 and kx + 4y = 10.

1. 2
2. -2
3. -1
4. 1

### Two oranges, three bananas and four apples cost Rs.15. Three oranges, two bananas

Two oranges, three bananas and four apples cost Rs.15. Three oranges, two bananas and one apple cost Rs.10. I bought 3 oranges, 3 bananas and 3 apples. How much did I pay?

1. Rs 8
2. Rs 10
3. Rs 12
4. Rs 15

### In 2004, Rohini was thrice as old as her brother Arvind

In 2004, Rohini was thrice as old as her brother Arvind. In 2014, Rohini was only six years older than her brother. In which year was Rohini born?

1. 1984
2. 1986
3. 1995
4. 2000

### A firm is thinking of buying a printer for its office use for the next one year

A firm is thinking of buying a printer for its office use for the next one year. The criterion for choosing is based on the least per-page printing cost. It can choose between an inkjet printer which costs Rs. 5000 and a laser printer which costs Rs. 8000. The per-page printing cost for an inkjet is Rs. 1.80 and that for a laser printer is Rs. 1.50. The firm should purchase the laser printer, if the minimum number of a pages to be printed in the year exceeds

1. 5000
2. 10000
3. 15000
4. 18000

### Hari’s family consisted of his younger brother (Chari), younger sister (Gouri)

Hari’s family consisted of his younger brother (Chari), younger sister (Gouri), and their father and mother. When Chari was born, the sum of the ages of Hari, his father and mother was 70 years. The sum of the ages of four family members, at the time of Gouri’s birth, was twice the sum of ages of Hari’s father and mother at the time of Hari’s birth. If Chari is 4 years older than Gouri, then find the difference in age between Hari and Chari.

1. 5 years
2. 6 years
3. 7 years
4. 8 years
5. 9 years

### The captain of a cricket team of 11 members is 26 years old and the wicket keeper

The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

1. 22 years
2. 23 years
3. 24 years
4. 25 years

### The number of positive integer valued pairs (x, y) satisfying 4x - 17y = 1 and x ≤ 1000 is

The number of positive integer valued pairs (x, y) satisfying 4x - 17y = 1 and x ≤ 1000 is

1. 55
2. 57
3. 58
4. 59

### Consider a triangle drawn on the X-Y plane with its three vertices of (41, 0), (0, 41) and (0, 0)

Consider a triangle drawn on the X-Y plane with its three vertices of (41, 0), (0, 41) and (0, 0), each vertex being represented by its (X, Y) coordinates. The number of points with integer coordinates inside the triangle (excluding all the points on the boundary) is

1. 741
2. 780
3. 800
4. 820

### A shop, which sold same marked price shirts, announced an offer

A shop, which sold same marked price shirts, announced an offer - if one buys three shirts then the fourth shirt is sold at a discounted price of ₹100 only. Patel took the offer. He left the shop with 20 shirts after paying ₹20,000. What is the marked price of a shirt?

1. ₹1260
2. ₹1300
3. ₹1350
4. ₹1400
5. ₹1500