Maths Section

The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is

• Rs. 3500

• Rs. 3900

• Rs. 3750

• Rs. 3840

Answer explanation

1. 10 chairs = 4 tables

2. 15 chairs + 2 tables = Rs. 4000

First, let's find the price of one chair and one table using the given information.

From the first piece of information, we can write: 10 chairs = 4 tables 1 chair = 4 tables / 10 1 chair = 2 tables / 5

So, the ratio of the price of a chair to the price of a table is 2:5.

Now, let's use the second piece of information: 15 chairs + 2 tables = Rs. 4000

We know the ratio of chair price to table price is 2:5. Let's represent the price of one chair as "2x" and the price of one table as "5x", where "x" is a constant.

So, for 15 chairs and 2 tables, the total price is: 15 2x (for chairs) + 2 5x (for tables) = 30x + 10x = 40x

We are given that this total price is Rs. 4000, so we can set up an equation: 40x = 4000

Solving for x: x = 4000 / 40 x = 100

Now that we have the value of x, we can find the price of 12 chairs and 3 tables:

12 2x (for chairs) + 3 5x (for tables) = 24x + 15x = 39x

Substitute the value of x: 39x = 39 * 100 39x = 3900

So, the total price of 12 chairs and 3 tables is Rs. 3900.

If bx + c = e – ax, then what is x?

• (e+c) / (b+a)

• (b-a) / (e+c)

• (e-c) / (b+a)

• (e-c) / (b-a)

Answer explanation

To solve for x:

bx + c = e – ax

bx + ax = e – c

x(b+a) = e-c

x = (e-c) / (b+a)

√(8y) + 18 = 4
What is y?

• 2

• 24.5

• 14

• -2

Answer explanation

First, simplify the equation:

√(8y) + 18 = 4

√(8y) = -14

Then square both sides

(√8y) ² = -14²

8y = 196

y = 196/8 = 24.5

If 5 + x is 5 more than 5,what is the value of 2x?

• 10

• 5

• 20

• 15

Answer explanation

5 more than 5 = 10

5 + x = 10

Subtract 5 from each side of the equation: x = 5 → 2x = 10

For what value of x does 4(3x – 2) = 12?

• 5/3

• 1

• 2

• 2/3

Answer explanation

We have to solve the equation 4(3x – 2) = 12. First, we can distribute the left side.

4(3x) – 4(2) = 12

12x – 8 = 12

Then we add 8 to both sides.

12x = 20

Divide both sides by 12.

x = 20/12

Simplify 20/12 by dividing the numerator and denominator by 4.

x = 20/12 = 5/3

The answer is 5/3. 

If 2x = 3y = 6z = 48, what is the value of x ×y ×z?

• 1536

• 3072

• 6144

• 1024

Answer explanation

Create 3 separate equations to solve for each variable separately.

1) 2x = 48

2) 3y = 48

3) 6z = 48

x = 24

y = 16

z = 8

x  y z = 3072

What is x?

• 3

• -3

• 4

• -2

• No Solutions.

Answer explanation

Cross multiplying leaves 3x+6=3x, which is not possible.

Michael swam 2,000 yards on each of eighteen days. The scatterplot at left shows his swim time and the corresponding heart rate after each swim. The line of best fit for the data is also shown. For the swim that took 34 minutes, Michaelś actual heart rate was about how many beats per minute less than the rate predicted by the line of best fit?

• 1

• 2

• 3

• 4

Answer explanation

Each point in the scatterplot represents a recorded heart rate at a given swim time. The line of best fit provides the predicted heart rate for the set of times. The question asks us to determine the difference between the expected heart rate at 34 minutes and the actual heart rate at 34 minutes.

We can see that at 34 minutes, Michael’s actual recorded heart rate was 148 BPM, and the line of best fit predicts a heart rate of 150 BPM. The difference, therefore, is 2

Solve for z: 

3(z + 4)³ – 7 = 17

• -2

• 2

• 4

• -8

• 8

Answer explanation

1. Add 7 to both sides

3(z + 4)³ – 7 + 7= 17 + 7

3(z + 4)³ = 24

2. Divide both sides by 3

(z + 4)³ = 8

3. Take the cube root of both sides

z + 4 = 2

4. Subtract 4 from both sides

z = –2

then, what is the value of 3x−z ?

• 4

• 3

• 2

• 1

• 6

Answer explanation

Since the expression we want just involves z and x, but not y, we start by solving yz=12 for y (y=12z).

Then we can plug that expression in for y in the first equation.

14x−16y=16

14x−16(12z)=16

14x−112z=16

Multiply everything by 12 to get rid of fractions.

3x−z=2