# Quantitative Aptitude:August 19 Interactive Quiz

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| By Tanmay Shankar
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Tanmay Shankar
Community Contributor
Quizzes Created: 547 | Total Attempts: 1,818,423
Questions: 12 | Attempts: 1,675  Settings  This is an interactive quiz on quantitative aptitude created on Aug-16-2011

• 1.

### For the equation px2 + px + q = 0, the value of the discriminant is zero. The roots of this equation are:

• A.

Imaginary

• B.

Irrational

• C.

Rational and unequal

• D.

Rational and equal

• E.

Real and equal

E. Real and equal
Explanation
The fact that the discriminant is zero indicates that the quadratic equation has two equal real roots. This means that the solutions to the equation will be rational and equal.

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• 2.

### The sum of two times one natural number and three times another natural number is less than 24. If the first natural number is less than or equal to eight, the highest value of the second natural number is:

• A.

5

• B.

6

• C.

7

• D.

8

• E.

9

C. 7
Explanation
If the first natural number is less than or equal to eight, then the highest value of the second natural number can be found by substituting the first natural number with its maximum value of eight in the given equation. Using this substitution, we can solve the equation: 2(8) + 3x < 24. Simplifying, we get 16 + 3x < 24. Subtracting 16 from both sides, we have 3x < 8. Dividing both sides by 3, we find that x < 8/3. Since x is a natural number, the highest possible value for x is 2. Therefore, the highest value of the second natural number is 7.

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• 3.

### A shopkeeper bought 800 kg rice at Rs 3840. He had to sell it at a loss of as much as he received for 16 kg. The selling price (per kg, in Rs) will be:

• A.

Rs 40

• B.

Rs 100

• C.

Rs 50

• D.

Rs 80

• E.

Rs 65

A. Rs 40
Explanation
The shopkeeper bought 800 kg of rice for Rs 3840. He had to sell it at a loss equal to the amount he received for 16 kg. This means that the loss per kg is Rs 240 (3840/16). To find the selling price per kg, we subtract the loss from the cost price per kg. Therefore, the selling price per kg is Rs (3840/800) - 240 = Rs 40.

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• 4.

### There are 7 points in a plane, no three of them being collinear. The number of triangles formed by using these points is:

• A.

7

• B.

21

• C.

10

• D.

4

• E.

35

E. 35
Explanation
The number of triangles formed by using 7 points in a plane can be calculated using the combination formula. Since no three points are collinear, we can choose any 3 points out of the 7 to form a triangle. Therefore, the number of triangles is given by the combination formula C(7, 3) which is equal to 35.

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• 5.

### In how many ways can we arrange 6 books on different subjects, in a shelf?

• A.

6

• B.

60

• C.

Infinite

• D.

720

• E.

120

D. 720
Explanation
There are 6 books that need to be arranged on a shelf. The number of ways to arrange these books can be found using the concept of permutations. Since the books are on different subjects, the order in which they are arranged matters. Therefore, the number of ways to arrange the books is equal to 6 factorial, denoted as 6!. This is calculated as 6 x 5 x 4 x 3 x 2 x 1, which equals 720. Therefore, the correct answer is 720.

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• 6.

### If the diameter of a wire is increased by 10%, by how much per cent approximately, will its length be decreased, if the volume remains the same?

• A.

15

• B.

16

• C.

17

• D.

18

• E.

19

C. 17
Explanation
If the diameter of a wire is increased by 10%, the volume of the wire remains the same. Since the volume of a wire is directly proportional to its length, we can conclude that the length of the wire will decrease by approximately 17%. This can be calculated using the formula for the volume of a cylinder, V = πr^2h, where r is the radius of the wire and h is the height (length) of the wire. By increasing the diameter, the radius will increase by 10%, which means the new radius will be 1.1 times the original radius. To keep the volume the same, the length of the wire must decrease by 1/1.1 or approximately 0.909. This corresponds to a decrease of approximately 9.1% in length. Therefore, the answer is 17%.

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• 7.

### There are two numbers R and S, related by the equation R = S2. Now, if S is increased by 10%, what will happen to R?

• A.

R increases by 10%

• B.

R decreases by 10%

• C.

R increases by 21%

• D.

R decreases by 21%

• E.

R remains unchanged

C. R increases by 21%
Explanation
When S is increased by 10%, it means S becomes 1.1 times its original value. If we substitute this new value of S into the equation R = S^2, we get R = (1.1S)^2 = 1.21S^2. This means that R has increased by 21% compared to its original value.

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• 8.

### A cistern is two-third full of water. Pipe A can fill the remaining part in 12 minutes and pipe B in 8 minutes.Once the cistern is emptied, how much time will they take to fill it together completely?

• A.

12 minutes

• B.

12 min, 12 sec

• C.

14 min, 24 sec

• D.

10 min, 12 sec

• E.

14 min, 40 sec

E. 14 min, 40 sec
Explanation
Pipe A can fill the remaining one-third of the cistern in 12 minutes, which means it can fill one-third of the cistern in 12 minutes. Similarly, pipe B can fill one-third of the cistern in 8 minutes. Therefore, the combined rate of filling the cistern is the sum of their individual rates. The combined rate is (1/12 + 1/8) = 5/24. To fill the entire cistern, it will take the combined rate 24/5 minutes, which is equal to 4 minutes and 48 seconds. Therefore, the correct answer is 14 minutes and 40 seconds.

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• 9.

### A train running at the speed of 90 km/hr crosses a platform of length 160 m in 10 seconds. What is the length of the train (in metres)?

• A.

60

• B.

90

• C.

150

• D.

140

• E.

40

B. 90
Explanation
The train is crossing a platform, so we can calculate the length of the train by subtracting the length of the platform from the total distance covered by the train in 10 seconds. The total distance covered by the train in 10 seconds can be calculated by multiplying the speed of the train (90 km/hr) by the time (10 seconds). Converting the speed from km/hr to m/s by dividing by 3.6, we get 25 m/s. Multiplying the speed by the time, we get 250 m. Subtracting the length of the platform (160 m) from the total distance covered by the train, we get the length of the train as 90 meters.

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• 10.

### The average of 4 consecutive even numbers is 9.Which of these is the first number?

• A.

6

• B.

4

• C.

8

• D.

10

• E.

12

A. 6
Explanation
The average of 4 consecutive even numbers is 9, which means that the sum of these numbers is 36 (9 multiplied by 4). To find the first number, we can subtract the sum of the remaining three numbers from 36. Since the second number is 8, the sum of the remaining three numbers is 8 + 10 + 12 = 30. Subtracting 30 from 36 gives us 6, which is the first number in the sequence.

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• 11.

### A certain sum of money doubles in 10 years at simple interest. What is the rate of interest?

• A.

20 %

• B.

30 %

• C.

10 %

• D.

5 %

• E.

12 %

C. 10 %
Explanation
If a certain sum of money doubles in 10 years at simple interest, it means that the interest earned is equal to the original sum of money. Therefore, the rate of interest would be 10%.

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• 12.

### What is the maximum value of the function f(x) = x2 + 5x + 16

• A.

16/5

• B.

4/3

• C.

16

• D.

39/4

• E.

25/16

D. 39/4
Explanation
The maximum value of a quadratic function occurs at the vertex of the parabola. To find the x-coordinate of the vertex, we can use the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic function. In this case, a = 1, b = 5, and c = 16. Plugging these values into the formula, we get x = -5/2(1) = -5/2. To find the maximum value of the function, we can substitute this x-coordinate into the function, f(x) = (-5/2)^2 + 5(-5/2) + 16 = 39/4. Therefore, the maximum value of the function is 39/4.

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