Quantitative Aptitude Test

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Quantitative Aptitude Test - 14

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Weekly Quiz Competition

Question 1
1 / -0.25

Consider the three circles that touch each other as shown in the figure given below. The radii of all three circles are equal, i.e. 1 cm. Find out the area of the shaded region of the figure.

A
$\left(\frac{2 \sqrt{3}-\pi}{2}\right) \mathrm{cm}^{2}$

B
$\left(\frac{3 \sqrt{2}-\pi}{3}\right) \mathrm{cm}^{2}$

C
$\frac{2 \sqrt{3}}{\pi} \mathrm{cm}^{2}$

D
none of these

Solution

Area of triangle $=\frac{1}{2}bh$
Area of triangle$=\sqrt{3} \mathrm{cm}^{2}=\left(\frac{\sqrt{3}}{4} \times(2)^{2}\right) \mathrm{cm}^{2}$
Area of 3 circles enclosed by the triangle, $= 3 \times \pi \times(1)^{2} \times \frac{60}{360} =\frac{\pi}{2} $
$\therefore$ Area of shaded region
$\Rightarrow \sqrt{3}-\frac{\pi}{2}$
$\Rightarrow \frac{(2 \sqrt{3}-\pi)}{2} \mathrm{cm}^{2}$
Hence, the correct option is (a).
Question 2
1 / -0.25

Compare Quantity A and Quantity B using additional information given above the two quantities, if such information is given, and select the correct alternative accordingly.

Quantity A:Perimeter of triangle ABC

Quantity B:Perimeter of square ABCD

A
Quantity A is greater than Quantity B.

B
Quantity B is greater than Quantity A.

C
Both quantities are equal.

D
Quantity A is less than or equal to Quantity B.

Solution

Quantity A = AB + BC + CA

Quantity B = AB + BC + CD + DA

Also, CD + DA > AC in triangle ACD.

So, Quantity B > Quantity A.

Hence, the correct option is (b).
Question 3
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Compare the two quantities in A and B.

Quantity A

Compoundinterestprincipal amountof $\$ 10000$ at arate of $10 \%$compoundedannually for 2years.

Quantity B

Simple interest onprincipal amountof $\$ 10000$ atrate of $11 \%$ for 2years.

A
Quantity A is greater than quantity B.

B
Quantity B is greater than quantity A.

C
Both quantities are equal.

D
Quantity A is either less than or equal to quantity B.

Solution

Quantity $A: 10000\left(1+\frac{10}{100}\right)^{2}-10000=\$ 2100$

Quantity $B: 10000 \times \frac{11}{100} \times 2=\$ 2200$

Hence, the correct option is (b).
Question 4
1 / -0.25

Shaun surrounds a square-shaped field with an enclosure by erecting 26 poles on each side at a distance of 4 metres from each other. Find out the area of the field?

A
2 hectares

B
1.4 hectares

C
1.3 hectares

D
1 hectare

Solution

According to the question,

Poles on each side are 26 in number.

Total length of each side of square field = (26 – 1) x 4 = 100 m

Therefore,

Area of the field = a²

= (100)2

= 10,000 m²

= 1 hectare

Hence, the correct option is (d).
Question 5
1 / -0.25

The cost price of an article is Rs. 16. The percentage of profit when wrongly calculated on the selling price came out to be numerically equal to the selling price. Then, which of the following denotes the selling price of the article?

A
Rs. 20

B
Rs. 40

C
Rs. 80

D
Either (1) or (3)

Solution

$\frac{\mathrm{SP}-\mathrm{CP}}{\mathrm{SP}} \times 100=\mathrm{SP}$
Putting $\mathrm{CP}=16,$ the below quadratic equation is obtained,
$\mathrm{SP}^{2}-100 \mathrm{SP}+1600=0$
Solving $\mathrm{SP}=20,80$

Hence, the correct option is (d).
Question 6
1 / -0.25

There are 100 students in a class, out of which 70 speak in English and 50 speak in Hindi. Find out how many students can speak both languages, if all the students speak at least one language?

A
30

B
50

C
60

D
20

Solution

$n(E \cup H)=n(E)+n(H)-n(E \cap H)$
$100=70+50-n(E \cap H)$
$n(E \cap H)=120-100$
$n(E \cap H)=20$

Hence, the correct option is (d).
Question 7
1 / -0.25

In how many manners can the word RABBIT be written?

A
60

B
360

C
300

D
200

Solution

In the given word, there are 6 letters and $B$ occurs two times.
Total number of ways $=\frac{6 !}{2 !}$
$=\frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1}$
$=360$

Hence, the correct option is (b).
Question 8
1 / -0.25

There are 15 male employees and 10 female employees. What will be the probability of selecting 1 female employee and 2 male employees, if three of them are selected randomly?

A

$\frac{1}{2}$

B

$\frac{3}{2}$

C

$\frac{21}{46}$

D

$\frac{3}{25}$

Solution

Let $S$ be the sample space and $E$ be the event of selecting 1 female employee and 2 male employees.
$\therefore \mathrm{n}(\mathrm{S})=$ Number of ways of selecting 3 employees out of 25 $n(S)= {^{25}C_3}$
$=\left(\frac{25 \times 24 \times 23}{3 \times 2 \times 1}\right)$
$=2300$
$n(E)=$ $n(E)=\left({^{10}C_1} \times {^{15}C_{2}}\right)$
$=\left[10 \times \frac{(15 \times 14)}{(2 \times 1)}\right]$
$=1050$
$=P(E)=\frac{n(E)}{n(S)}=\frac{1050}{2300}=\frac{21}{46}$
Hence, the correct option is (c).
Question 9
1 / -0.25

Allen, Brad and Cook participate in a relay race of 1500 m. Allen can beat Brad by 200 m. In another race of 2000 m, Brad can beat Cook by 300 m. Find out the distance by which Allen can beat Cook in a race of 1000 m ?

A
500 m

B
400 m

C
311 m

D
263 m

Solution

According to the question,

Ratio of speeds of Allen and Brad is 15:13 (1500 : 1300).

Ratio of speeds of Brad and Cook is 20:17 (2000 : 1700).

Ratio of speeds of Allen and Cook is 300 : 221.

If in a race of 300 m, Allen beats Cook by 79 m (300 – 221), then in a race of 1000 m, Allen can beat Cook by a distance of 263 m.
= $\frac{(79 \times 100)}{300}$ approximately.

Hence, the correct option is (d).
Question 10
1 / -0.25

If m parallel lines in a plane are intersected by a family of n parallel lines, then the total number of parallelograms so formed is:

A
$\frac{(m-1)(n-1)}{4}$

B
$\frac{m n}{4}$

C
$\frac{m n(m-1)(n-1)}{4}$

D
None of the above

Solution

A parallelogram is formed by choosing two straight lines from the set of m parallel lines and two
straight lines from the set of n parallel lines. Therefore, the required number of ways is
$^{m}{C}_{2} \cdot {^{n}{C}_{2}}=$ $\frac{m n(m-1)(n-1)}{4}$
Hence, the correct option is (c).

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Quantitative Aptitude Test - 14

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Quantitative Aptitude Test - 14

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Question 1

\(\left(\frac{2 \sqrt{3}-\pi}{2}\right) \mathrm{cm}^{2}\)

\(\left(\frac{3 \sqrt{2}-\pi}{3}\right) \mathrm{cm}^{2}\)

\(\frac{2 \sqrt{3}}{\pi} \mathrm{cm}^{2}\)

none of these

Solution

Question 2

Quantity A is greater than Quantity B.

Quantity B is greater than Quantity A.

Both quantities are equal.

Quantity A is less than or equal to Quantity B.

Solution

Question 3

Quantity A is greater than quantity B.

Quantity B is greater than quantity A.

Both quantities are equal.

Quantity A is either less than or equal to quantity B.

Solution

Question 4

2 hectares

1.4 hectares

1.3 hectares

1 hectare

Solution

Question 5

Rs. 20

Rs. 40

Rs. 80

Either (1) or (3)

Solution

Question 6

30

50

60

20

Solution

Question 7

60

360

300

200

Solution

Question 8

\(\frac{1}{2}\)

\(\frac{3}{2}\)

\(\frac{21}{46}\)

\(\frac{3}{25}\)

Solution

Question 9

500 m

400 m

311 m

263 m

Solution

Question 10

\(\frac{(m-1)(n-1)}{4}\)

\(\frac{m n}{4}\)

\(\frac{m n(m-1)(n-1)}{4}\)

None of the above

Solution

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