**11. Correct answer: (A) **

**Given: **

The figure

**To find: **

The true statement

**Solution: **

Topic(s): supplementary angles

*x* and *y* are supplementary angles

*x* + *y* = 180. If *x* > 90 the *y* < 90

**Answer: (A) y < 90
**

**Given: **

The line with equation *y* = 5*x* – 10

The line crosses the *x*-axis at point (*a*, *b*)

**To find:**

The value of *a*

**Solution: **

Topic(s): Coordinate geometry

At the point where the line crosses the *x*-axis the value of *y* will be 0.

Substitute *y* = 0, and *x* = *a,* into *y* = 5*x* – 10.

0 = 5*a* – 10 ⇒ 5*a* = 10 ⇒ *a* = 2

**Answer: (D) 2**

**13. Correct answer: (E)**

**Given: **

The noon temperature for 7 cities

The median temperature is 40

**To find:**

The temperature (t) that city *D* cannot be

**Solution: **

Topic(s): Statistics

Write out the numbers in increasing order.

27 33 40 44 50 68

In order for 40 to be the median i.e. in the middle, *t* needs to on the left of 40. This means that *t* < 40.

We are required to find the answer that does not fit the criteria.

Only (E) 42 is greater than 40.

**Answer: (E) 42**

**14. Correct answer: (D)**

**Given: **

The figure

**To find: **

Perimeter of the figure

**Solution:**

Topic(s): complementary angles, equilateral triangle, perimeter

To get the perimeter of the figure, we need to know the lengths of

Given the right angles and the lengths of the three sides, we can deduce that* ABCD* is a square. So, we know that the length of *CD* is 6.

Angles *ACP* and *PCD* are complementary angles.

So, angle *PCD* = 90º – angle *ACP* = 90º – 30º = 60º.

In the same way, angles *BDP* and *PDC* are complementary angles.

So, angle *PDC* = 90º – angle *BDP* = 90º – 30º = 60º.

Triangle *PCD *has two angles that are 60º. When a triangle has two 60º angles, it must be an equilateral triangle that has three equal sides. Since the length of CD is 6. We can deduce that the lengths of PC and PD are also 6.

Now, we can calculate the perimeter of the figure = 6 + 6 + 6 + 6 + 6 = 30

**Answer: (D) 30**

**15. Correct answer: (C) **

**Given:**

*m* is the greatest prime factor of 38

*n* is the greatest prime factor of 100

**To find:**

*m* + *n *

**Solution: **

Topic(s): Factors

The factors of 38 are: 1 × 38, 2 × 19.

The greatest prime factor of 38 is 19 = *m*.

The factors of 100 are: 1 × 100, 2 × 50, 4 × 24, 5 × 20, 10 ×10.

The greatest prime factor of 100 is 5 = *n*.

*m* + *n* = 19 + 5 = 24

**Answer: (C) 24**

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