Linear Equations and Inequations

Consider the system of equations: 5x + 3y = 19 and bx + 6y = 26. For what value of 'b' will the system have no solution?

1. 10
2. 25
3. 5
4. 15

Answer: (a) 10

Find the solution of the given set -3 < x - 2 ≤ 9 - 2x, the value of x is integers.

1. (1, 2, 3)
2. (1, 2, 3, 4)
3. (0, 1, 2, 3)
4. (0,2,3)

Answer: (c) (0, 1, 2, 3)

What inequality is shown by the region?

1. y < 2x + 1
2. y ≥ 2x + 1
3. y > 2x + 1
4. y > 2x

Answer: (b) y ≥ 2x + 1

Find the value of x for which 9|2x - 5|≤ 80x - 16x2.

1. -1/2 ≤ x ≤ 1/2
2. 1/2 ≤ x ≤ 9/2
3. 1/2 < x < 9/2
4. -1/2 ≤ x < 1/2

Answer: (b) 1/2 ≤ x ≤ 9/2

Find the number of positive integral values of m satisfying the inequalities 8m + 35 > 75 and 5m + 18 < 53.

1. 2
2. 5
3. 6
4. 1

Answer: (c) 6

If a2 + b2 + c2 = 1 and x2 + y2 + z2 = 1, where a, b, c, x, y and z are positive reals, then what is the value of ax + by + cz?

1. ≥ 1
2. ≥ 2
3. ≤ 1
4. ≤ 2

Answer: (c) ≤ 1

For what values of k is the set of equations 2x - 3(2k - 1)y = 10 and 3x + 4(k + 1)y = 20are consistent.

1. R - (1/26)
2. 1/26
3. R - (1/5)
4. 1/5

Answer: (d) 1/5

Read the passage and answer the following question: Aaron is staying at a hotel that charges $99.95 per night plus tax for a room. A tax of 8% is applied to the room rate and an additional one-time untaxed fee of $5.00 is charged by the hotel. For a promotional offer, the hotel decided to decrease the room rate by 5%. What would be the new total charge expression for Aaron staying 10 nights, excluding the $5.00 fee?

1. $2153.2
2. $1054
3. $1126.5
4. $1025.48

Answer: (d) $1025.48

A three-digit number abc is 459 more than the sum of its digits. What is the sum of the 2-digit number ab and the 1-digit number a?

1. 65
2. 15
3. 10
4. 51

Answer: (d) 51

Sam travels 660 km, partly by train and partly by car. If she covers 300 km by train and the rest by car, it takes 13.5 hours. But, if she travels 360 km by train and the rest by car, she takes 30 minutes longer. Find the time taken by Sam if she travels 660 km by car. (in hours)

1. 11 hours
2. 12 hours
3. 15 hours
4. 12 hours

Answer: (a) 11 hours