Quantitative Aptitude Test

Result

Quantitative Aptitude Test - 11

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Weekly Quiz Competition

Question 1
4 / -1

Each problem consists of a question followed by 2 statements. Decide whether the data in the statements are sufficient to the answer the question. Choose the option accordingly.

'y' is an odd number and y² + z is even. Is 'x' even?

I. xy + yz + zx = 17

II. x³ - y²z = 3

A
Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.

B
Statement II alone is sufficient, but Statement I alone is not sufficient to answer the question.

C
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.

D
Either statement alone is sufficient.

Solution

We know,

odd * odd = odd; even * odd = even; even * even = eve

odd ± odd = even; odd ± even = odd; even ± even = even

'y' is an odd number.

∴ y² is also odd and given that (y²+ z) is even.

∴ 'z' must be odd.

From Statement I:

xy + yz + zx = 17(Odd)

∴ yz = odd * odd = odd

∴ x(y+z) + odd = odd

x*even = even

so we can not determine whether x is even or odd

So, Statement I alone is not sufficient.

From Statement II:

x³ - y²z = 3(odd)

y² is odd and z is odd.

∴ (y²*z) will be odd.

x³cannot be odd as odd - odd = even but 3 is odd.

∴ x³ is even => x is even.

So, Statement II alone is also sufficient.
Question 2
4 / -1

Each problem consists of a question followed by 2 statements. Check whether the statements are sufficient to answer the question and choose the option accordingly.

In the following triangle, what is the length of AC?

I. ∠BAC = 90° AB = 6 cm

II. BC = 10 cm and area of triangle = 24 cm²

A
Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.

B
Statement II alone is sufficient, but Statement I alone is not sufficient to answer the question.

C
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.

D
Either statement alone is sufficient.

Solution

From Statement I:

ABC is a right-angled triangle.

AB = 6 cm

Length of AC cannot be found out.

From Statement II:

BC = 10 cm Area = 24 cm²

(1/2)*BC*height = 24

Height = 48/10 = 4.8 cm

Length of AC cannot be found out

Using both Statements together:

AB = 6cm, BC = 10 cm and ABC is a right-angled triangle

By Pythagoras' Theorem,

AC²= BC² - AB²= 64

AC = 8 cm
Question 3
4 / -1

Every problem consists of a question followed by 2 statements. Check whether the statements are sufficient to answer to the question and choose the option accordingly.

An article was bought for some money and was sold at some profit. What is the profit?

I. The article was marked up by 40% and sold at a discount of 15%

II. The article was marked at Rs 700 and it was sold at a %profit of 19%.

A
Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.

B
Statement II alone is sufficient, but Statement I alone is not sufficient to answer the question.

C
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.

D
Either statement alone is sufficient.

Solution

Let the C.P of the article = Rs 100x

From Statement I:

M.P of the article = 100x(1 + 40/100) = Rs 140x

S.P of the article = 140x(1 - 15/100) = Rs 119x

Profit = 119x - 100x = Rs 19x

But the value of 'x' is not known

From Statement II:

M.P = Rs 700

Profit% = 19%

Since C.P = Rs 100x

S.P = Rs 119x

Profit = 119x - 100x = Rs 19x

But the value of 'x' is not given.

Using both Statements Together:

%mark-up = 40%, C.P = Rs 100x and M.P = Rs 700

140x = 700

x = 5

Profit = 19x = Rs 95
Question 4
4 / -1

Each problem consists of a question followed by 2 statements. Check whether the statements are sufficient to answer the question. Choose the option accordingly.

What is the value of the principle? Rate of interest is same for both Compound interest and simple interest.

I. The difference between the compound interest and simple interest earned on that principle after 2 years is Rs 150

II. The difference between the compound interest and simple interest earned on that principle after 3 years is Rs 465

A
Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.

B
Statement II alone is sufficient, but Statement I alone is not sufficient to answer the question.

C
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.

D
Either statement alone is sufficient.

Solution

Let the principle be Rs 'P' and the rate of interest be r% respectively.

From Statement I:

P(r/100)² = 150..(i)

There are 2 variables and 1 equation. The value of P cannot be found out.

From Statement II:

P(r/100)²((300 + r)/100) = 465..(ii)

There are 2 variables and 1 equation. The value of P cannot be found out.

Using both Statements together:

(ii)/(i) gives,

(300 + r)/100 = 465/150

=> (300 + r)/100 = 3.1

=> 300 + r = 310

=> r = 10

P(10/100)² = 150

=> P = 15,000
Question 5
4 / -1

Each problem consists of a question followed by 2 statements. Check whether the statements are sufficient to answer the question. Choose the option accordingly.

If a 20% spirit solution is mixed with a x% spirit solution in some ratio, the resultant solution contains 40% spirit. What is the value of x? (x must be greater than 20)

I. 20% spirit solution is mixed with a x% spirit solution in the ratio 1:2

II. If the 20% spirit solution was mixed with a x% spirit solution in the inverse ratio of what it was actually mixed in, the resultant solution would contain 30% spirit.

A
Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.

B
Statement II alone is sufficient, but Statement I alone is not sufficient to answer the question.

C
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.

D
Either statement alone is sufficient.

Solution

From Statement I:

By Alligation Method:

Given, (x - 40)/20 = 1/2

=> x = 50

From Statement II:

Let it be originally mixed in the ratio a:1

By Alligation Method:

Given, (x - 40)/20 = a/1

=> x = 20a + 40..(i)

Now, in reverse case, by Alligation Method:

(x - 30)/10 = 1/a

=> x = 10/a + 30..(ii)

From (i) and (ii),

20a + 40 = 10/a + 30

=> 2a = 1/a - 1

=> 2a² + a - 1 = 0

=> (a + 1)(2a - 1) = 0

=> a ≠ − 1, a = 1/2

x = 20(1/2) + 40 = 50
Question 6
4 / -1

Directions: In a small neighbourhood of a city, in a day, a total of 800 food orders were made online. 75% of the orders were from Zomato, 15% from Swiggy and remaining from Food Panda. The food was characterised in two ways: By Size they were Medium size and Large Size and by type of meal they were Veg and Non-Veg. Following table shows the percentage of total orders for Non-Veg and Medium size food out of total number of orders and also the percentage of food ordered from each vendor.

What is the sum of the number of Veg orders from Zomato and Swiggy?

A
440

B
428

C
468

D
496

Solution

Total orders from Zomato = 0.75*800 = 600

Total orders from Swiggy = 0.15*800 = 120

Total orders from Food Panda = 800 - 600 - 120 = 80

Filling the given table:

Calculating the amount of each type of order for both classifications:

Let the number of Medium Veg Orders from Zomato, Swiggy and Food Panda be 'x', 'y' and 'z' respectively.

From the table,

Required sum = 390 + 78 = 468
Question 7
4 / -1

Directions: In a small neighbourhood of a city, in a day, a total of 800 food orders were made online. 75% of the orders were from Zomato, 15% from Swiggy and remaining from Food Panda. The food was characterised in two ways: By Size they were Medium size and Large Size and by type of meal they were Veg and Non-Veg. Following table shows the percentage of total orders for Non-Veg and Medium size food out of total number of orders and also the percentage of food ordered from each vendor.

What is the difference between the number of Large orders from Swiggy and Food Panda?

A
72

B
68

C
48

D
62

Solution

Total orders from Zomato = 0.75*800 = 600

Total orders from Swiggy = 0.15*800 = 120

Total orders from Food Panda = 800 - 600 - 120 = 80

Filling the given table:

Calculating the amount of each type of order for both classifications:

Let the number of Medium Veg Orders from Zomato, Swiggy and Food Panda be 'x', 'y' and 'z' respectively.

From the table,

Required difference

= 84 - 36 = 48
Question 8
4 / -1

Directions: In a small neighbourhood of a city, in a day, a total of 800 food orders were made online. 75% of the orders were from Zomato, 15% from Swiggy and remaining from Food Panda. The food was characterised in two ways: By Size they were Medium size and Large Size and by type of meal they were Veg and Non-Veg. Following table shows the percentage of total orders for Non-Veg and Medium size food out of total number of orders and also the percentage of food ordered from each vendor.

If the sum of the number of Large Veg orders from Zomato and Swiggy is 228 and the number of Large Non-Veg orders from Swiggy is 36 more that in Zomato, what is the ratio of Medium Veg orders from Zomato and Swiggy?

A
2:1

B
3:1

C
4:1

D
4:3

Solution

Total orders from Zomato = 0.75*800 = 600

Total orders from Swiggy = 0.15*800 = 120

Total orders from Food Panda = 800 - 600 - 120 = 80

Filling the given table:

Calculating the amount of each type of order for both classifications:

Let the number of Medium Veg Orders from Zomato, Swiggy and Food Panda be 'x', 'y' and 'z' respectively.

Given, 390 - x + 78 - y = 228

=> x + y = 240..(i)

Also, y + 6 = 36 + x - 150

=> x - y = 120..(ii)

(i) + (ii) gives,

x = 180 and y = 60

Required ratio = x:y = 3:1
Question 9
4 / -1

Directions: In a small neighbourhood of a city, in a day, a total of 800 food orders were made online. 75% of the orders were from Zomato, 15% from Swiggy and remaining from Food Panda. The food was characterised in two ways: By Size they were Medium size and Large Size and by type of meal they were Veg and Non-Veg. Following table shows the percentage of total orders for Non-Veg and Medium size food out of total number of orders and also the percentage of food ordered from each vendor.

If the ratio of the number of Medium Non-Veg orders from Swiggy and Food Panda is 1:3 and the average number of Medium Veg orders from Swiggy and Food panda is 28, what is the difference between the number of Large Non-Veg orders from Swiggy and Food Panda?

A
2

B
4

C
6

D
8

Solution

Total orders from Zomato = 0.75*800 = 600

Total orders from Swiggy = 0.15*800 = 120

Total orders from Food Panda = 800 - 600 - 120 = 80

Filling the given table:

Calculating the amount of each type of order for both classifications:

Let the number of Medium Veg Orders from Zomato, Swiggy and Food Panda be 'x', 'y' and 'z' respectively.

Given, (36 - y)/(44 - z) = 1/3

=> 44 - z = 108 - 3y

=> 3y - z = 64..(i)

and, (y + z)/2 = 28

=> y + z = 56..(ii)

(i) + (ii) gives,

4y = 120

=> y = 30

∴ z = 56 - 30 = 26

sum of the number of Large Non-Veg orders from Swiggy and Food Panda

= y + 6 − z - 4

= 6
Question 10
4 / -1

Directions: In a small neighbourhood of a city, in a day, a total of 800 food orders were made online. 75% of the orders were from Zomato, 15% from Swiggy and remaining from Food Panda. The food was characterised in two ways: By Size they were Medium size and Large Size and by type of meal they were Veg and Non-Veg. Following table shows the percentage of total orders for Non-Veg and Medium size food out of total number of orders and also the percentage of food ordered from each vendor.

If, in Food Panda, the ratio of the number of Large Non-Veg orders and Medium Veg orders is 5:4 and the number of Medium Veg orders from Zomato is 10 times that from Food Panda, what is the number of Medium Non-Veg orders from Zomato?

A
160

B
200

C
220

D
180

Solution

Total orders from Zomato = 0.75*800 = 600

Total orders from Swiggy = 0.15*800 = 120

Total orders from Food Panda = 800 - 600 - 120 = 80

Filling the given table:

Calculating the amount of each type of order for both classifications:

Let the number of Medium Veg Orders from Zomato, Swiggy and Food Panda be 'x', 'y' and 'z' respectively.

Given, (z + 4)/z = 5/4

=> 5z = 4z + 16

=> z = 16

x = 10z = 160

number of Medium Non-Veg orders from Zomato

= 360 - x = 200