Quantitative Aptitude Test

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Quantitative Aptitude Test - 9

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Weekly Quiz Competition

Question 1
1 / -0.25

Directions For Questions

Directions: Use the following chart, which represents the value of exports and imports (in Rs hundred crore) of a country for a certain period, to answer the given question

...view full instructions

What percentage is the total export in the years 2003, 2006 and 2008 taken together of the total import for the same period?

A
109%

B
110%

C
111%

D
None of these

Solution

Total exports in 2003, 2006 and 2008 = 150 + 300 + 175

= 625

And imports in same year = 75 + 225 +275

= 575

Now, required % = 625 x 100/575

= 108.6%

~ 109%.

Option A is correct.
Question 2
1 / -0.25

If two pipes function together, the tank will be filled in 12 h. One pipe fills the tank in 10 h faster than the other. How many hours does the faster pipe take to fill up the tank?

A
20 hours

B
28 hours

C
32 hours

D
36 hours

Solution

Let one pipe takes m h to fill the tank.

Then, the other pipe takes (m−10)h

According to the question,

Therefore, 1m+1(m−10)=112

=> m−10+mm(m−10)=112

=> 12(m−10+m)=m(m−10)

=> m²−34m+120=0

=> m²−30m−4m+120=0

=> (m−30)(m−4)=0

m = 30 or 4

Faster pipe will take (30−10)h = 20 h to fill the tank.
Question 3
1 / -0.25

Find the sum of the first 20 terms of the sequence S1 where,S1: 3, 15, 35, 63, …

A
8,460

B
11,460

C
19,460

D
22,460

Solution

So, sum is [4n(n+1)(2n+1)/6] - n

Put n=20

$\frac{4 \times 20 \times 21 \times 41}{6} - 20$

=11480-20

Sum = 11460
Question 4
1 / -0.25

A box contains five blocks numbered 1, 2, 3, 4 and 5. Johnnie picks a block and replaces it. Then, Lisa picks a block. What is the probability that the sum of the numbers they picked is even?

A
2/5

B
1/2

C
13/25

D
3/5

Solution

since each person has 5 choices, there are 25 possible pairs of numbers.
The only way the sum can be odd is if one person picks an odd number and the other picks an even number.
Suppose that Johnnie chose the odd number and Lisa the even one.
Johnnie has 3 possible odd numbers to select from, and for each of these, Lisa has 2 possible choices, for a total of $(3) (2) = 6$ possibilities.
However, if Johnnie has to pick an even number and Lisa an odd one, there are 6 ways to do that. Hence, out of 25 possibilities, 12 have an odd total and 13 have an even total.
The probability of an even total is $\frac{13}{25}$
Question 5
1 / -0.25

What is the 4^thdigit from the right of the ternary sum of the decimal numbers 598 and 222?

A
4

B
3

C
2

D
0

Solution

Ternary value of 598 = 211011

Ternary value of 222 = 22020

Ternary sum = 1010101

So, 4th digit from the right is 0.

Option D is correct.
Question 6
1 / -0.25

The area of a square is 1521 sq. m. The breadth of a rectangle is 1/3 times the side of the square and the length of the rectangle is twice the breadth. What is the difference between the areas of the square and the rectangle?

A
1183 m²

B
1300 m²

C
1365.3 m²

D
1452 m²

Solution

Area of the square $= 1521$ sq. $m$
$∴$ Side of the square $= \sqrt{1521} = 39 m$
Breadth of the rectangle $= \frac{1}{3} \times 39 m$
Length of the rectangle $= 2 \times 13 m$
Area of the rectangle $= \frac{1}{3} \times 39 \times 2 \times 13 = 338 m^{2}$
Now, difference between the areas of the square and the rectangle $= 1521 - 338 = 1183 m^{2}$
$∴$ The difference between the areas of the square and the rectangle is $1183 m^{2}$
Question 7
1 / -0.25

Anil grows tomatoes in his backyard which is in the shape of a square. Each tomato takes 1 cm² in his backyard. This year, he has been able to grow 131 more tomatoes than last year. The shape of the backyard remained a square. How many tomatoes did Anil produce this year?

A
4356

B
4225

C
4096

D
Insufficient Data

Solution

Let the area of backyard be x² this year and y² last year

∴ X² - Y² = 131

=> (X+Y)*(X-Y) = 131

Now, 131 is a prime number (a unique one too. Check out its properties on Google). Also, always identify the prime number given in a question. Might be helpful in cracking the solution.

=> (X+Y)*(X-Y) = 131 x 1

=> X+Y = 131

X-Y = 1

=> 2X = 132 => X = 66

and Y = 65

∴ Number of tomatoes produced this year = 66² = 4356
Question 8
1 / -0.25

ABCDE is a regular pentagon. O is a point inside the pentagon such that AOB is an equilateral triangle. What is ∠OEA?

A
$55^{0}$

B
$66^{0}$

C
$70^{0}$

D
$68^{0}$

Solution

Join OE and OD.

Internal angle of regular pentagon = 108°

∠EAB = ∠EDC = 108°

∠OAB = 60°

∠EAO = 48°

AO = OB = AB as the triangle is equilateral.

AB = AE as this is a regular pentagon.

Triangle AEO is isosceles as AO = EA.

∠AEO = ∠AOE = x (say)

In triangle AEO,

∠OAE + 2x = 180°

48° + 2x = 180°

2x = 132°, or x = 66°

∠OEA = 66°
Question 9
1 / -0.25

A fill pipe can fill a tank in 20 hours, a drain pipe can drain a tank in 30 hours. If a system of n pipes (fill pipes and drain pipes put together) can fill the tank in exactly 5 hours, which of the following are possible values of n (More than one option could be correct)?

A
54

B
29

C
Both 54 and 29

D
Neither 54 nor 29

Solution

2 fill pipes cancel out 3 drain pipes. Plus, you need an additional 4 fill pipes to fill the tank in 5 hours. so the answer has to be 5k + 4.

Both 54 and 29 are possible.
Question 10
1 / -0.25

What is the sum of all the even numbers from 1 to 3,400?

A
28,90,000

B
28,91,600

C
28,91,700

D
28,93,301

Solution

3,400/2 =1,700

So, there are 1,700 even numbers.

Sum = 1,700(1,700 + 1)

= 1,700 × 1,701

= 28,91,700.

Option C is correct.

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Quantitative Aptitude Test - 9

Result

Quantitative Aptitude Test - 9

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SHARING IS CARING

Question 1

109%

110%

111%

None of these

Solution

Question 2

20 hours

28 hours

32 hours

36 hours

Solution

Question 3

8,460

11,460

19,460

22,460

Solution

Question 4

2/5

1/2

13/25

3/5

Solution

Question 5

4

3

2

0

Solution

Question 6

1183 m2

1300 m2

1365.3 m2

1452 m2

Solution

Question 7

4356

4225

4096

Insufficient Data

Solution

Question 8

550

660

700

680

Solution

Question 9

54

29

Both 54 and 29

Neither 54 nor 29

Solution

Question 10

28,90,000

28,91,600

28,91,700

28,93,301

Solution

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1183 m²

1300 m²

1365.3 m²

1452 m²

$55^{0}$

$66^{0}$

$70^{0}$

$68^{0}$