Quantitative Ability Test

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Quantitative Ability Test - 3

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Weekly Quiz Competition

Question 1
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A vendor has ten 20 litre bottles. He fills bottle 1 with 20 litres of petrol from a barrel containing 120 litres of pure petrol. He then adds 20 litres of kerosene to the barrel. He then fills bottle 2 with 20 litres of the mixture from the barrel and adds 20 litres of kerosene to the barrel. The process is repeated until all the 10 bottles are filled. What is the amount of kerosene in the 5th bottle?

A
3125/324 litres

B
3355/324 litres

C
125/4 litres

D
125/3 litres

Solution

Petrol in 1st bottle = 20 litres.

Petrol in 2nd bottle = 20 x (100/120) = 20 x (5/6) litres.

Petrol in 3rd bottle = 20 x (5/6)² litres.

Petrol in 5th bottle = 20 x (5/6)⁴ = 3125/324 litres.=

Kerosene in the 5th bottle = 20 - (3125/324) = 3355/324 litres Hence, option 2.
Question 2
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Directions For Questions

Answer the following question based on the information given below.

The following bar chart gives the percentage growth in the number of households in the middle, upper middle and high income categories in the four regions for the period from 1987-88 to 1994-95

Additional directions for the last two questions of this set: If the same data as the above were used, with the additional information that the numbers of households in each category were equally distributed in all the regions then

...view full instructions

Which region showed the highest growth rate in the number of households in all the income categories for the period?

A
North

B
South

C
West

D
None of these

Solution

This question can be answered by direct observation.

For the South region, the percentage growth in each category is higher than that for every other region. Thus, the growth in number of households for all income categories is the highest for the South.

Hence, option 2
Question 3
4 / -1

Directions For Questions

Answer the following question based on the information given below.

The following bar chart gives the percentage growth in the number of households in the middle, upper middle and high income categories in the four regions for the period from 1987-88 to 1994-95

Additional directions for the last two questions of this set: If the same data as the above were used, with the additional information that the numbers of households in each category were equally distributed in all the regions then

...view full instructions

What was the total household income in the Northern Region for the upper middle class?

A
50 lakhs

B
500 million

C
Rs. 300 million

D
Indeterminate

Solution

Using the number of households and the average income per household for the upper middle class, the total income for the upper middle class can be found.

However, the region wise distribution of upper middle class households is not known.

Hence, the total household income in the Northern region for the upper middle class cannot be found. Hence, option 4.
Question 4
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Directions For Questions

Answer the following question based on the information given below.

The following bar chart gives the percentage growth in the number of households in the middle, upper middle and high income categories in the four regions for the period from 1987-88 to 1994-95

Additional directions for the last two questions of this set: If the same data as the above were used, with the additional information that the numbers of households in each category were equally distributed in all the regions then

...view full instructions

What is the percentage increase in the total number of households for the Northern Region (upper middle) over the given period?

A
100

B
200

C
240

D
Indeterminate

Solution

This question can be answered by direct observation.

From the bar chart, the percentage increase in the total number of households for the Northern region (upper middles class) is 200%.

Hence, option 2.
Question 5
4 / -1

Directions For Questions

Answer the following question based on the information given below.

The following bar chart gives the percentage growth in the number of households in the middle, upper middle and high income categories in the four regions for the period from 1987-88 to 1994-95

Additional directions for the last two questions of this set: If the same data as the above were used, with the additional information that the numbers of households in each category were equally distributed in all the regions then

...view full instructions

What was the average income of the high-income group in 1987-88?

A
Rs. 75,000

B
Rs. 25,000

C
Rs. 2,25,000

D
Indeterminate

Solution

From the table, the average income of the high income group in 1987-88 was Rs. 75,000.

Hence, option 1.
Question 6
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Directions For Questions

Answer the following question based on the information given below.

The following bar chart gives the percentage growth in the number of households in the middle, upper middle and high income categories in the four regions for the period from 1987-88 to 1994-95

Additional directions for the last two questions of this set: If the same data as the above were used, with the additional information that the numbers of households in each category were equally distributed in all the regions then

...view full instructions

The ratio of total income for the high income category to the upper middle class increased by how much percent in the given period?

A
20

B
36

C
25

D
Indeterminate

Solution

In 1987-88:

The total income for the high income category households = 5000 x 75000 = Rs. 37,50,00,000 The total income for the upper middle class households = 10000 x 50000 = Rs. 50,00,00,000 Thus, the required ratio for 1987-88 = 375000000/500000000 = 3 : 4 = 0.75 It is given that the number of households in each category is equally distributed in all the regions.

Thus, there were 5000/4 = 1250 high income household in each region in 1987-88.

Similarly, there were 10000/4 = 2500 upper middle class households in each region in 1987-88.

In the year 1994-95:

The percentage growth in high income households in the four regions is 245%, 425%, 175% and 150% Thus, the number of high income households throughout the country in 1994-95 is: 1250 x (3.45 + 5.25 + 2.75 + 2.5) i.e. 1250 x 13.95 i.e 17438 households (approx) The percentage growth in upper middle class households in the four regions is 200%, 340%, 120% and 140%

Thus, the number of upper middle class households throughout the country in 1994-95 is: 2500 x (3 + 4.4 + 2.2 + 2.4) i.e. 2500 x 12 i.e 30000 households (approx). Therefore Total income for the high-income households = 17438 x 1.90 x 75000 = Rs. 2,48,49,15,000. Total income for upper middle class = 30000 x 1.6 x 50000 = Rs. 2,40,00,00,000 Thus, the required ratio for 1994-95 = 2484915000/2400000000 = 1.035 Thus, the ratio has increased in absolute terms by 1.035 - 0.75 = 0.285 Hence, the required percentage increase = (0.285/0.75) x 100

= 38%

The closest option is 36%.

Hence, option 2.
Question 7
4 / -1

Directions For Questions

Answer the following question based on the information given below.

The following bar chart gives the percentage growth in the number of households in the middle, upper middle and high income categories in the four regions for the period from 1987-88 to 1994-95

Additional directions for the last two questions of this set: If the same data as the above were used, with the additional information that the numbers of households in each category were equally distributed in all the regions then

...view full instructions

The average income for the Northern region in 1987-88, was _____ .

A
Rs. 37,727

B
Rs. 37,277

C
Rs. 35,000

D
Indeterminate

Solution

The total income for the Northern region in 1987-88 = [(40000 x 30000) + (10000 x 50000) + (5000 x 75000)]/4 = (1200000000 + 500000000 + 375000000)/4

= 2075000000/4

= Rs. 51,87,50,000 The total number of household in the Norther region in 1987-88 = (40000 + 10000 + 5000)/4.

= 55000/4

=13750

Thus, the average income for the Northern region in 1987-88 = 518750000/13750

= Rs. 37,727 (approx) Hence, option 1.
Question 8
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Directions For Questions

Answer the following question based on the information given below.

Analyze the charts given below that show the energy consumption and energy production of XYZ country from various sources. The difference in production and consumption of energy from any source is bridged through external trade (i.e. export or import) of energy from the same source. All the values are given in Terawatt-hours (Twh).

...view full instructions

In which year are the net imports of all the categories taken together the lowest?

A
2009

B
2011

C
2012

D
2014

Solution

Consider the solution to the first question.

Among the given options, net imports are lowest in 2009. Hence, option 1.
Question 9
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Directions For Questions

Answer the following question based on the information given below.

Analyze the charts given below that show the energy consumption and energy production of XYZ country from various sources. The difference in production and consumption of energy from any source is bridged through external trade (i.e. export or import) of energy from the same source. All the values are given in Terawatt-hours (Twh).

...view full instructions

Which of the following statement(s) is/are true?

I. In each year, net exports are always less than the external trade.

II. Coal is always exported.

III. Net import of energy from at least one source is nil from 2009- 2014.

A
Only II

B
II and III

C
I and III

D
I, II and III

Solution

Net exports = - net imports From the table, it is always less than the external trade.

Thus, statement I is true.

Import of coal in 2014 is 150TWh.

Thus, statement II is false.

Net import of nuclear energy = -300 + 0 + 200 + 100 -150 + 150 = 0

Thus, statement III is true.

Hence, option 3.
Question 10
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Hari, Gopi and Sufi enter into a partnership. Gopi contributes one-fourth of the whole capital while Hari contributes twice as much as Gopi and Sufi together contribute. If the profit at the end of the year is Rs. 4800, how much would each receive?

A
Rs. 3200, Rs. 1000 and Rs. 600

B
Rs. 3200, Rs. 1200 and Rs. 400

C
Rs. 3600, Rs. 1000 and Rs. 200

D
Rs. 3600, Rs. 800 and Rs. 400

Solution

Let the total capital be 12x.

Then Gopi contributes 3x.

Hari contributes twice as much as Gopi and Sufi together contribute. If Sufi contributes y, then Hari contributes 2(3x + y). Therefore 3x + y + 2(3x+ y) = 12x.

y = x.

Sufi contributes x and Hari contributes 8x.

Gopi’s, Hari’s and Sufi’s contributions are in the ratio 3 : 8 : 1. Their profits also would be in the same proportion and would be Rs. 1200, Rs. 3200 and Rs. 400.

Hence, option 2.