### NTS Quantitative Reasoning Practice Test # 1

**INSTRUCTIONS:**

- This Quiz is related to
**NTS Quantitative Reasoning Practice Test # 1**in this series - The Quiz based on the Topic, “
**Quantitative Reasoning**“ - If you have good understanding about the subject, then you can attempt it
- There will be 10 Multiple Choice Questions (MCQs) in this test
- You have 60 Seconds to answer a single Multiple Choice Question
- Questions will be randomly changed every time you start this test
- You should practice more and more to get high marks
- Passing Criteria is 60 percent for this Quiz
- You can retake this test as many time as you like
- The progress bar at the top of screen will show your progress as well as the time remaining where timed quiz
- After the quiz, You will find Your Test Score and Grade
- If you feel that any Incorrect Answer to a Question, simply Comment us about the Question.

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#### The lengths of sides BA and BC of triangle ABC are equal. Find the measure of angle x.

Since BA and BC have equal lengths, then the triangle is isosceles and the interior angles at A and C have equal measures which may be calculated as follows A + C + 40 = 180 or 2A = 140 or A = 70° The interior angle at A and angle x are supplementary. Hence 70 + x = 180 or x = 110°

#### In the above figure above, does x = 90? (1) The length of AC is less than the length of BC. (2) The length of AB is one-fourth the circumference of the circle.

We need to see the fact statements. Statement (1) says that the length of AC is less than the length of BC. This clearly leads us to nowhere. So BCE. Now the fact statement (2) tells us that the length of AB is one-fourth the circumference of the circle, which clearly leads us to know that it is not the diameter, it is just a chord. So the angle subtended is not equal to 90 deg.

#### (√12 - √3)(-√12 + √3)

Rewrite as (√12 - √3)(-√12 + √3) = - (√12 - √3) (√12 - √3) and simplify = - (12 - 3) = -9

#### Find the area of a right isosceles triangle with hypotenuse equal to 24.

The two legs of a right isosceles triangle have equal lengths; let x be one of these lengths. The area A of the triangle is given by A = (1/2) x * x = (1/2)x2 We now use Pythagora's theorem to find x as follows x2 + x2 = 242 Simplify 2 x2 = 576 x2 = 288 We now calculate the area A as follows A = (1/2)x2 = (1/2) 288 = 144

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#### Solve the equation 2 - (x - 2)2 = - 18 for x.

Subtract 2 from both sides of the equation. - (x - 2)2 = - 20 Multiply both sides of the equation by -1. (x - 2)2 = 20 Solve by extracting the square root. x - 2 = ~+mn~ √20 = ~+mn~ 2 √5 solutions: x = 2 + 2 √5 and x = 2 - 2 √5

#### There are 6 boxes numbered 1, 2,...6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is

#### Find a positive value of the constant k so that the equation x2 + k x + 4 = 0 has only one solution.

For the given equation to have a solution, the left hand side must be a square. Hence x2 + k x + 4 = (x + 2)2 Expand the right hand side x2 + k x + 4 = x2 + 4x + 4 Comparing the left hand side and the right hand sides, the value of k is 4 k = 4

#### Solve the equation (x - 1)(x + 3) = (1 - x) for x.

Rewrite equation with the right hand side equal to 0. (x - 1)(x + 3) - (1 - x) = 0 Rewrite as (x - 1)(x + 3) + (x - 1) = 0 Factor and solve (x - 1) [ (x + 3) + 1 ] = 0 (x - 1)(x + 4) = 0 x - 1 = 0 or x + 4 = 0 Solutions: x = 1 and x = -4

#### A number, K, is a positive integer with the special property that 3 times its unit is equal to 2 times its 10 digit. How many such numbers exist between 10 & 99?

Here’s another smart Question. It appears to be daunting but it’s not that tough. We start with 1 at units place. When multiplied 3 times and then divided by 2 we get 1.5. So it is ruled out. Next we try with 2. When we multiply by 3 we get 6 which when divided by 2 gives us 3.Bingo!! We get the first number 32. Similarly by trying out different numbers at unit place we get other 2 numbers as 64 and 96(which are also multiples of 32 for hint). So we get a total of 3 numbers between 10 and 99.

#### In a drawer of shirts, 8 r blue, 6 r green, and 4 r magenta. If Mason draws 2 shirts at random, what is the probability that at least one of the shirts he draws will be blue?

Remember that at least one is a clue, and when u see phrase, u need to find the probability of getting everything except what u want (in other words, the probability of getting any other color except blue), and then subtract that from 1. The formula for this would be 1-(the probability of getting the other colors). 1-(10/18 * 9/17)=1-5/17=12/17.

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