Quantitative Aptitude Test

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Quantitative Aptitude Test - 6

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Weekly Quiz Competition

Question 1
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Given that $10^{0.48} = x, 10^{0.70} = y$ and $x^{2} = y^{2}$ , then the value of $z$ is close to:

A
1.45

B
3

C
2.88

D
1.79

Solution
Question 2
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In figure if $∠ A + ∠ B + ∠ C + ∠ D + ∠ E + ∠ F = k$ right angles, then find value of $k$ .

A
$4$

B
$5$

C
$6$

D
$7$

Solution
Question 3
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A person purchased a smartphone for Rs 8,000 and sold it at a profit of 25%. From that amount, he purchased another phone and sold it at a loss of 20%. What is his overall profit or loss?

A
profit of Rs 2,000

B
profit of Rs 1,000

C
loss of Rs 2,000

D
neither profit nor loss

Solution

Selling price of smartphone = 8000 x 1.25 = 10000
CP of 2nd phone = 10000
SP of 2nd phone = 10000 x 0.8 = 8000
Hence, overall the person made no profit or loss.

Hence, the correct option is (d).
Question 4
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Directions: A question is followed by two statements, labelled (1) and (2). Using the information provided and general knowledge, decide whether the information given is sufficient to solve the problem.

For real numbers $x$ and $y,$ is $\frac{x}{y}$ positive?
(1) $\frac{x^{4}}{y^{3}} < 0$
(2) $x^{5} y^{6} < 0$

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 (1) shows that $\frac{x^{4}}{y^{3}}$ is negative. But $x^{4}$ is always positive (irrespective of the fact whether x is positive or negative). Therefore, $\frac{x^{4}}{y^{3}}$ < 0 only when y is negative.

Statement (2) shows that $\frac{x^{5}}{y^{6}}$ is negative. But $y^{6}$ is always positive (irrespective of the fact whether y is positive or negative). Therefore, $\frac{x^{5}}{y^{6}}$ < 0 only when x is negative. Therefore, using Statements (1) and (2), we can conclude that both x and y are negative. Therefore, $\frac{x}{y}$ is positive. Therefore, the question can be answered by using both statements together, but neither statement alone is sufficient to answer the question.

Hence, the correct option is (c).
Question 5
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Find the smallest 4-digit number which, when increased by 8, is divisible by 12, 18, 30 and 45.

A
1,072

B
1,080

C
1,088

D
1,096

Solution

The LCM of 12, 18, 30 and 45 is 180.
Thus, the answer has to be a multiple of (180 – 8). 1080 – 8 = 1072 is the only number that fits and should be the correct answer.

Hence, the correct option is (a).
Question 6
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Directions: A question is followed by two statements, numbered (1) and (2). Using the information provided and general knowledge, decide whether the information given is sufficient to solve the problem.

What is the selling price of the mixture if the ratio of the two qualities of tea mixed is 3:4?

1) Cost price of the first quality of tea is Rs 180 per kg.

2) Cost price of the second quality of tea is Rs 225 per kg.

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.48

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

Solution

The two statements simply give the cost price of the two types of tea. However, from the cost price we cannot get any idea of the selling price. Thus, both the statements together are NOT SUFFICIENT to answer the question asked.

Hence, the correct option is (d).
Question 7
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A tank can be filled by Pipe 1 in 7 hours and by Pipe 2 in 5 hours. There is a waste pipe which is kept open when Pipe 2 is working; the tank then takes 8 hours 30 minutes to fill. What is the time taken to fill the tank if all the three pipes are working?

A
3 hours 20 minutes

B
3 hours 50 minutes

C
4 hours 15 minutes

D
4 hours 50 minutes

Solution

Pipe1 can fill $\frac{1}{7}$ of tank in 1 hour
Pipe2 can fill $\frac{1}{5}$ of tank in 1 hour
Pipe2 and the waste pipe together fill $\frac{1}{8.5}$ of tank in 1 hour
So, waste pipe can empty the tank in 1 hour = ( $\frac{1}{5}$ – $\frac{1}{8.5}$ ) of tank = $\frac{0.7}{8.5}$ of tank
If all the pipes are working together, in 1 hour the tank filled is $\frac{1}{7}$ + $\frac{1}{5}$ -( $\frac{0.7}{8.5}$ ) = $\frac{1}{3.84}$ of tank.
So, the tank will be filled in 3.84 hours = 3 hours 50 minutes.

Hence, the correct option is (b).
Question 8
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If the roots of the equation ax² + bx + c = 0 are reciprocal of the roots of the equation px² + qx + r = 0, then which of the following represents relation(s) between a, b, c, p, q and r?

A
a = p, c = r and b = 1

B
a = r, c = p and b = q

C
a= $\frac{1}{p}$

D
b= $\frac{1}{q}$

Solution
Question 9
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The average monthly income of Anil and Hemant is Rs 4,025. The average monthly income of Hemant and Chandan is Rs 6,250. The average monthly income of Anil and Chandan is Rs 5,200. What is Hemant's monthly income?

A
Rs 4,590

B
Rs 5,075

C
Rs 5,950

D
Rs 6,075

Solution

Anil + Hemant = 8050
Therefore, Hemant = 8050 – Anil
Hemant + Chandan = 12500
Therefore, Hemant = 12500 – Chandan
8050 – Anil = 12500 – Chandan
Or, Chandan – Anil = 12500 – 8050 = 4450……………i
And, Chandan + Anil = 10400……………………………ii
Adding equations i and ii 2 Chandan = 14850
Therefore, Chandan = 7425
Hemant = 12500 – Chandan = 12500 – 7425 = 5075.

Hence, the correct option is (b).

Question 10

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Directions For Questions

Directions: Go through the given table and solve the question based on it.

Product of Major Crops (tonnes)
	Y1	Y2	Y3	Y4	Y5
Foodgrain (Kharif)	69	78	99	102	111
Foodgrain (Total)	108	130	176	197	217
Cereals (Kharif)	65	74	94	98	106
Cereals (Total)	97	119	162	186	203
Pulses (Kharif)	4	4	5	4	5
Pulses (Total)	12	11	14	11	14
Rice (Kharif)	40	50	66	73	80
Rice (Total)	42	54	74	85	93
Oilseeds (Kharif)	7	5	10	12	14
Oilseeds (Total)	10	9	19	18	24

Total foodgrain production = production of rabi foodgrain + production of kharif foodgrain

...view full instructions

In which year did the production of rabi foodgrains exhibit the highest percentage increase over the preceding year?

Y1

Y2

Y3

Y4

Solution

Let's calculate the total rabi production in each year using the table we have made earlier:
Total rabi production in Y1 = 84
Total rabi production in Y2 = 112
Total rabi production in Y3 = 171
Total rabi production in Y4 = 208
Total rabi production in Y5 = 235
While you can calculate the actual percentage increase for each year, by observation this will clearly be in Y3.
Calculating the actual percentages will take you too much time and you must try to avoid that.

Hence, the correct option is (c).

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Quantitative Aptitude Test - 6

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Quantitative Aptitude Test - 6

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SHARING IS CARING

Question 1

1.45

3

2.88

1.79

Solution

Question 2

4

5

6

7

Solution

Question 3

profit of Rs 2,000

profit of Rs 1,000

loss of Rs 2,000

neither profit nor loss

Solution

Question 4

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

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

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

EACH statement ALONE is sufficient.

Solution

Question 5

1,072

1,080

1,088

1,096

Solution

Question 6

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

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

EACH statement ALONE is sufficient.48

Statements 1) and 2) TOGETHER are NOT sufficient.

Solution

Question 7

3 hours 20 minutes

3 hours 50 minutes

4 hours 15 minutes

4 hours 50 minutes

Solution

Question 8

a = p, c = r and b = 1

a = r, c = p and b = q

a=1p

b=1q

Solution

Question 9

Rs 4,590

Rs 5,075

Rs 5,950

Rs 6,075

Solution

Question 10

Y1

Y2

Y3

Y4

Solution

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$4$

$5$

$6$

$7$

a= $\frac{1}{p}$

b= $\frac{1}{q}$