Quantitative Aptitude Test

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Quantitative Aptitude Test - 10

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Weekly Quiz Competition

Question 1
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Directions: This problem consists of a question and two statements, labelled (1) and (2), in which certain data are given. Using the information provided and general knowledge, decide whether the information given is sufficient to solve the problem.
In a cricket world cup final match between Sri Lanka and India, Sri Lanka won the toss and chose to bat first. Sri Lankans scored 274 runs, giving a target of 275 runs. India successfully reached the target after losing 4 wickets.
Who was the top scorer in the match?
(1) Only Jayawardene scored a century in the match.
(2) Dhoni, Gambhir and Jayawardene scored 91, 97 and 103 runs respectively.

A
Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.

B
Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.

C
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D
EACH statement ALONE is sufficient.

Solution

From statement 1, Jayawardene has to be the top scorer in the match. So SUFFICIENT
From statement II, we don’t know who is the top scorer. It’s possible that someone else scored more runs than all these three batsmen. So NOT SUFFICIENT.
Hence, the correct option is (a).
Question 2
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Directions For Questions

Read the following information carefully to answer the question that follows:

Profit $\%$ of the company during different quarters in a year

Profit $\%=\frac{\text { Income-cost }}{\text { cost }} \times 100$

...view full instructions

What was the profit of the company in quarter 1?

A
Rs. 9265329

B
Rs. 9433628

C
Rs. 9589369

D
Rs. 9687999

Solution

Let the cost in quarter 1 be Rs. C

So, 13 = $(\frac{(82000000 - C)}{C})$ x 100

Or, C = 72566372

Thus profit = Rs. (82000000 - 72566372) = Rs. 9433628.

Hence, the correct option is (b).
Question 3
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Directions For Questions

Read the following information carefully to answer the question that follows:

Profit $\%$ of the company during different quarters in a year

Profit $\%=\frac{\text { Income-cost }}{\text { cost }} \times 100$

...view full instructions

The total income earned by the company in quarters 3 and 4 was what percent less than the total income earned by the company in first two quarters?

A
38.57%

B
40.27%

C
42.36%

D
43.87%

Solution

The total income earned by the company in first two quarters $=8.2+6.2=14.4$ crore
The total income earned by the company in last two quarters $=8.6$ crore
Percent less $=(14.4-8.6) \times \frac{100}{14.4}=40.27 \%$

Hence, the correct option is (b).
Question 4
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Directions For Questions

Read the following information carefully to answer the question that follows:

Profit $\%$ of the company during different quarters in a year

Profit $\%=\frac{\text { Income-cost }}{\text { cost }} \times 100$

...view full instructions

The profit earned by the company in quarters 2 and 3 is what percent of profit earned by company in quarters 1 and 4?

A
117.58%

B
119.74%

C
42.36%

D
121.54%

Solution

The profit earned by the company in quarters 2 and 3 $=6.2 \times \frac{0.25}{1.25}+5.4 \times \frac{0.15}{1.15}=12400000+$ $7043478$ = Rs. 19443478
The profit earned by the company in quarters 1 and 4
$=8.2 \times \frac{0.13}{1.13}+3.2 \times \frac{0.27}{1.27}=9433628+6803150$ = Rs. 16236778
Required percent $=19443478 \times \frac{100}{16236778}=119.74 \%$

Hence, the correct option is (b).
Question 5
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Directions For Questions

Read the following information carefully to answer the question that follows:

Profit $\%$ of the company during different quarters in a year

Profit $\%=\frac{\text { Income-cost }}{\text { cost }} \times 100$

...view full instructions

What was the profit % of the company for the complete year?

A
17.68%

B
18.36%

C
19.21%

D
20.39%

Solution

The profit of the company in quarters 1,2,3 and 4
$=8.2 \times \frac{0.13}{1.13}+6.2 \times \frac{0.25}{1.25}+5.4 \times \frac{0.15}{1.15}+3.2 \times\frac{0.27}{1.27}$
= $9433628+12400000+7043478+6803150=35680256$
Income of the company in quarters 1,2,3 and 4
$=6.2+8.2+5.4+3.2=230000000$
cost $=$ Rs. 194319744
Profit $\%=35680256 \times \frac{100}{194319744}=18.36 \%$

Hence, the correct option is (b).
Question 6
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A pipe of radius 2 cm can fill a tank in 160 minutes. In how much time will a pipe of radius 4 cm fill a tank of a similar capacity? Assume that the speed with which the water is flowing in the second pipe is twice the speed in the first pipe.

A
20 minutes

B
40 minutes

C
80 minutes

D
120 minutes

Solution

The total volume of the tank must be Area × speed × time for each pipe
A1 × S1 × T1 = A2 × S2 × T2
As an area of the pipe is A = πr².
So, A1 = π(2)² & A2 = π(4)².
T1 = 160 & S2 = 2 × S1
Hence, π(2)² × S1 × 160 = π(4)² × 2 × S1 × T2
T2 = 20 minutes.
Hence, the correct option is (a).
Question 7
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Directions: This problem consists of a question and two statements, labelled (1) and (2), in which certain data are given. Using the information provided and general knowledge, decide whether the information given is sufficient to solve the problem.
Choose the most suitable option from the given alternatives pertaining to the sufficiency of the data provided. What is $x$?
(1) $x=4 y-4$
(2) $x y=8$

A
Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.

B
Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.

C
EACH statement ALONE is sufficient.

D
Statements (1) and (2) TOGETHER are NOT sufficient.

Solution

(D) Each statement alone is not enough information to solve for x.
Using statements ( 1 ) and ( 2 ) combined, if you substitute the expression for $x$ in the first equation into the second, you get two different answers:
$x=4 y-4$
$x y=(4 y-4) y=8$
$4 y^{2}-4 y=8$
$y^{2}-y-2=0$
$(y+1)(y-2)=0$
$y=\{-1,2\}$
$x=\{-8,4\}$
Statements (1) and (2) TOGETHER are NOT sufficient.
Hence, the correct option is (d).
Question 8
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Directions: This problem consists of a question and two statements, labelled (1) and (2), in which certain data are given. Using the information provided and general knowledge, decide whether the information given is sufficient to solve the problem.
Is x + y > 72?
(1) xy = 72
(2) |x| = 1

A
Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.

B
Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.

C
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D
Statements (1) and (2) TOGETHER are NOT sufficient.

Solution

Statement I:
x and y can be 72 and 1 in which case x + y > 72.
However, x and y can also be 2 and 36 in which case x + y < 72. Thus, NOT SUFFICIENT
Statement II: This tells us nothing about y. So, NOT SUFFICIENT
After combining the two statements, x and y can be -1 and -72 in which case x + y < 72
However, x and y can also be 1 and 72, in which case x + y > 72
Thus, both statements together are also NOT SUFFICIENT.
Hence, the correct option is (d).
Question 9
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It was planned to send 60 tons of relief material to a flood-affected area through a certain number of helicopters. However, due to technical reasons, each helicopter could take 0.5 ton less of relief material than was initially planned. In order to supply all the material, four additional helicopters were required. How many helicopters were initially planned to be used?

A
10

B
12

C
16

D
20

Solution

Let the initial no. of helicopters be x and relief material per helicopter be y.
Then xy = 60 and also xy = (x + 4)(y - 0.5)
4y - 0.5x = 2
Using xy = 60 & so y = $\frac{60}{x}$
$\frac{240}{x}$ – 0.5x = 2
We get a quadratic equation, x² + 4x - 480 = 0
Solving it we get x = -24 or 20.
The value of x must be positive & so x = 20
Hence, there were 20 helicopters which were initially planned.
Hence, the correct option is (d).
Question 10
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Directions: This problem consists of a question and two statements, labelled (1) and (2), in which certain data are given. Using the information provided and general knowledge, decide whether the information given is sufficient to solve the problem.
Anil, Sunil and Vimal are three brothers. What is the ascending order of their ages?
(1) The sum of Anil’s age and Sunil’s age is twice that of Vimal’s age
(2) Five years ago, Sunil was twice as old as Vimal.

A
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.

B
Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.

C
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D
EACH statement ALONE is sufficient.

Solution

Statement I by itself doesn’t tell us anything about the relative ages of the three brothers. So, NOT SUFFICIENT
From statement II, we know that Sunil is older than Vimal, but we still do not know anything about Anil’s age. So, NOT SUFFICIENT
Combining the two statements, we get A + S + 2V.
Note that the sum of Anil and Sunil’s age can only be twice Vimal’s age if Anil is younger than Vimal.
If Anil is older than Vimal, then this sum will be more than twice, which will not be correct.
Thus, on combining the two statements, the order of the ages are Sunil > Vimal > Anil.
Hence, the correct option is (c).