Quantitative Ability Test

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Quantitative Ability Test - 1

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Weekly Quiz Competition

Question 1
4 / -1

In a certain village, 25% of the total number of villagers own a phone and 15% of the total number of villagers own a car. There are 2000 villagers who own both - a car as well as a phone. If 65% of the total number of villagers own neither a car nor a phone, then how many villagers own only a phone?

A
7500

B
6000

C
8000

D
None of these

Solution

Since 65% of the villagers own neither a car nor a phone, 35% of the villagers own atleast one of the two.

Let the percentage of villagers who own a car as well as a phone be x%. 25% of the villagers own a phone and 15% of the villagers own a car. (25 - x) + x + (15 - x) = 35. So x = 5

Hence, 25 - 5 i.e. 20% of the villagers own only a phone.

Since 2000 villagers own both a phone and a car, 5% of the total number of villagers corresponds to 2000.

Hence, the number of villagers who own only a phone (20%) is 4 * 2000 = 8000

Hence, option 3.
Question 2
4 / -1

9 men and 9 women are participating in a tennis tournament. The number of ways in which a mixed double game can be arranged from amongst these 18 players such that no former pair play in the same game is:

A
1512

B
1419

C
756

D
3024

Solution

Out of 9 men players two can be chosen in⁹C₂ ways. Since, no former pair is to play in the same game, so we have to select 2 women from remaining 7 women. This can be done in⁷C₂ ways. If M₁, M₂and W₁, W₂ are chosen, then a team can be constituted in 4 ways viz. M₁, W₂, M₁W₁, M₂W₁, M₂W₂

Thus, the number of ways of arranging the game = ⁹C₂ x ⁷C₂ x 4 = 3024

Option (d) is correct.
Question 3
4 / -1

Two bananas, three cakes, four colas, five books cost Rs. 59.5. Two bananas, four cakes, five colas cost Rs. 39.5. If the difference between the cost of the book and the cost of the cake is Rs. 2 and one of the two costs is some rupees and 50 paisa then find the cost of the cola. (Assume that none of them come free of cost, the cost of any article cannot be greater than 7 and the cost of any book is greater than the cost of cola).

A
2

B
3

C
2.5

D
4

Solution

Let the cost of the banana, cake, cola and book be b, c, a, d respectively.

So,

2b + 3c + 4a + 5d= 59.5 ... (i)

2b + 4c + 5a = 39.5 ... (ii)

Subtracting (i) by (ii) we get,

- c - a + 5d = 20 ... (iii)

We are given that, d - c = 2 ... (iv) And d or c has 50 paisa in it.

So we check all the combination where the difference between the cake and the book.

Also as none of them come free, the cost of anything cannot be greater than 7 and the cost of book is greater than the cost of cake, so using equation (iv) the combinations of the cost of a book and a cake are (2.5, 0.5), (3.5, 1.5), (4.5, 2.5), (5.5, 3.5), (6.5, 4.5).

By substituting each combination of the book and the cake in equation in (iii) we get, the value of the book and the cake to be (5.5, 3.5) and the corresponding value of the cola is Rs. 4 Hence, option 4.
Question 4
4 / -1

If the natural numbers x and y satisfy the equation x² - xy - 101 = 0, then which of the following is a possible value of (x + y)?

A
100

B
101

C
200

D
201

Solution

We simplify the equation x² - xy - 101 = 0 as, x(x- y) = 101 = 1 * 101. As x and y are integers, we have, x = 1 and x - y = 101, or x = 101 and x - y = 1.

If x = 1 , y = 1 - 101 = -100.

If x = 101 , y = 101 - 1 = 100.

As x and y are natural numbers, we must disregard the solution (x, y) = (1, - 100).

There is only one solution: x = 101 and y = 100.

For this set, we have (x + y) = 101 + 100 = 201.

Hence, option 4.
Question 5
4 / -1

Rehaan purchased a bike for Rs.54,000. He sold it at a loss of 8%. With that money he again purchased another bike and sold it at a profit of 10%. What is his overall loss/profit?

A
Loss of Rs.657

B
Profit of Rs.567

C
Loss of Rs.648

D
Profit of Rs.648

Solution

Selling price of the second article = 54000 x 92 / 100 × 110 / 100 = Rs. 54648

Thus, Profit = 54648 - 54000 Rs. 648
Question 6
4 / -1

Directions For Questions

Answer the following question based on the information given below.

The three graphs shows the sale of the Hindustan Times newspaper in three different cities of Uttar Pradesh – Agra, Noida and Ghaziabad in a week (from Sunday to Saturday).

The overall weekly sales of the newspaper in the three different cities are the sum of the each day sales in three different cities in the week. All figures in the graphs are in actuals. The total newspaper printed for these three cities is constant at 6000 copies per day. Any newspaper that is not sold is treated as the waste or loss.

...view full instructions

In which day of the week is the highest wastage for the newspaper?

A
Wednesday

B
Thursday

C
Friday

D
Saturday

Solution

Waste = Total Copies Printed – sold copies in (Agra + Noida + Ghaziabad) The wastes for each day are as shown in the table above. Thus, the waste is highest on Thursday.
Question 7
4 / -1

Directions For Questions

Answer the following question based on the information given below.

The three graphs shows the sale of the Hindustan Times newspaper in three different cities of Uttar Pradesh – Agra, Noida and Ghaziabad in a week (from Sunday to Saturday).

The overall weekly sales of the newspaper in the three different cities are the sum of the each day sales in three different cities in the week. All figures in the graphs are in actuals. The total newspaper printed for these three cities is constant at 6000 copies per day. Any newspaper that is not sold is treated as the waste or loss.

...view full instructions

How many times have the sales of the newspaper of all the three different cities increased together as compared to the previous day? Assume that the sales on Saturday of the previous week were same as Sunday of this week

A
1

B
2

C
3

D
4

Solution

All the sales have increased together only on Friday i.e., only once.
Question 8
4 / -1

Directions For Questions

Answer the following question based on the information given below.

The three graphs shows the sale of the Hindustan Times newspaper in three different cities of Uttar Pradesh – Agra, Noida and Ghaziabad in a week (from Sunday to Saturday).

The overall weekly sales of the newspaper in the three different cities are the sum of the each day sales in three different cities in the week. All figures in the graphs are in actuals. The total newspaper printed for these three cities is constant at 6000 copies per day. Any newspaper that is not sold is treated as the waste or loss.

...view full instructions

The overall newspaper sales is said to be “under control” if at least the sales in 2 of the 3 cities do not decrease in value from the previous day. In how many days have the newspaper sales been “under control”?

A
3

B
4

C
5

D
6

Solution

The overall newspaper sales is said to be “under control” if at least the sales in 2 of the 3 cities do not decrease in value from the previous day. In how many days have the newspaper sales been “under control”?
Question 9
4 / -1

Sum of two numbers is equal to sum of square of 11 and cube of 9. Larger number is (5)2 less than square of 25. What is the value of the sum of twice of 24% of the smaller number and half of the larger number?

A
415

B
400

C
410

D
None of these

Solution

Let the two numbers be x and y.

x + y = 11² + 9³

where x = larger number

x + y = 121 + 729 = 850 ....(i)

x = 252 - 52 = (25 + 5) (25 - 5) = 600

y = 850 - 600 = 250

Required sum = 250×24×2 / 100+ 600 / 2 = 420
Question 10
4 / -1

A quadrilateral ABCD circumscribes a circle and AB = 6 cm. CD = 5 cm and AD = 7 cm. The length of side BC is:

A
4 cm

B
5 cm

C
3 cm

D
6 cm

Solution

Let ABCD is a quadrilateral in which a circle is inscribed
Given AB = 6cm; CD = 5cm

By the property of circle, sum of opposite sides are equal
AB + CD = BC + AD
6 + 5 = BC + 7
⇒ BC = 11 - 7 = 4 cm