A started a business with Rs. 50000. After three months, B joins with an investment of Rs. 60000 and A withdraws Rs. 10000 out of his capital. Three months later, B brought in Rs. 20000 more. At the end of the year, what should be the ratio in which they A and B share the profits?
a.
$22: 15$
b.
$13: 22$
c.
$17: 22$
Correct Answer
d.
$15: 22$
Step-by-Step AI Explanation
Verified Method
A's equivalent monthly investment:
For the first 3 months: $\text{Rs. } 50000 \times 3 = \text{Rs. } 150000$
For the remaining 9 months: $(\text{Rs. } 50000 - 10000) \times 9 = \text{Rs. } 40000 \times 9 = \text{Rs. } 360000$
Total for A $= 150000 + 360000 = \text{Rs. } 510000$
B's equivalent monthly investment:
B joins after 3 months with Rs. 60000, and keeps it for 3 months: $\text{Rs. } 60000 \times 3 = \text{Rs. } 180000$
For the next 6 months, B invests Rs. 20000 more: $(\text{Rs. } 60000 + 20000) \times 6 = \text{Rs. } 80000 \times 6 = \text{Rs. } 480000$
Total for B $= 180000 + 480000 = \text{Rs. } 660000$
Ratio of profit sharing $= 510000 : 660000 = 51 : 66 = 17 : 22$.
Q2mcq4 marks
In triangle PQR, PS is perpendicular to QR and S divides QR in the ratio of $3 : 1$ internally. If PQ = 21 and PR = 9, find QR.
a.
$18\sqrt{5}$
b.
$16\sqrt{5}$
c.
$15\sqrt{5}$
d.
$12\sqrt{5}$
Correct Answer
Step-by-Step AI Explanation
Verified Method
Since $PQ = 21$ and $PR = 9$, $PQ > PR$, so $QS > SR$. Hence, $QS : SR = 3 : 1$.
Let $SR = x$ and $QS = 3x$. Then $QR = 4x$.
In right-angled triangle $PSQ$, $PS^2 = PQ^2 - QS^2 = 21^2 - (3x)^2 = 441 - 9x^2$.
In right-angled triangle $PSR$, $PS^2 = PR^2 - SR^2 = 9^2 - x^2 = 81 - x^2$.
Equating the two expressions for $PS^2$:
$$441 - 9x^2 = 81 - x^2$$
$$8x^2 = 360$$
$$x^2 = 45 \implies x = 3\sqrt{5}$$
Therefore, $QR = 4x = 4 \times 3\sqrt{5} = 12\sqrt{5}$.
Q3mcq4 marks
Pipe X can fill a tank in 12 hours and pipe Y can empty the tank in 18 hours. Both pipes are opened at 8 am and after some time Y is closed, and the tank is full at 10 pm on the same day. At what time was pipe Y closed?
a.
1 pm
b.
10 am
c.
11 am
Correct Answer
d.
12 noon
Step-by-Step AI Explanation
Verified Method
Let the capacity of the tank be $\text{LCM}(12, 18) = 36$ units.
Efficiency of pipe X $= +\frac{36}{12} = +3$ units/hour.
Efficiency of pipe Y $= -\frac{36}{18} = -2$ units/hour.
From 8 am to 10 pm is 14 hours. Pipe X was open for the entire 14 hours.
Total work done by X $= 14 \times 3 = 42$ units.
Since the total capacity filled is 36 units, pipe Y emptied $42 - 36 = 6$ units.
Time for which pipe Y was open $= \frac{6}{2} = 3$ hours.
Pipe Y was closed 3 hours after 8 am, which is 11 am.
Q4mcq4 marks
The difference between the compound interest and simple interest for two years on a certain sum at a certain rate of interest is Rs. 64. The compound interest for two years is Rs. 704. The principal is
a.
800
b.
1600
Correct Answer
c.
2400
d.
3200
Step-by-Step AI Explanation
Verified Method
Given $CI - SI = 64$ and $CI = 704$.
So, $SI = 704 - 64 = 640$.
Simple interest for each year is $\frac{640}{2} = \text{Rs. } 320$.
The difference between CI and SI for 2 years is the interest earned on the first year's simple interest:
Interest on Rs. 320 for 1 year $= 64$.
Rate of interest $R = \left(\frac{64}{320}\right) \times 100 = 20\%$.
Since the first year's simple interest is 320:
$$\frac{P \times 20}{100} = 320 \implies P = 320 \times 5 = 1600$$.
Q5mcq4 marks
In a 1000 metre race, Rahul reaches the finishing line 5 seconds before than Raj and beats Raj by 50 metre. What is Rahul's speed (in m/s)?
a.
$11\frac{9}{19}$
b.
$9\frac{9}{19}$
c.
$10\frac{10}{19}$
Correct Answer
d.
$9\frac{10}{19}$
Step-by-Step AI Explanation
Verified Method
When Rahul finishes the 1000 m race, Raj has covered $1000 - 50 = 950$ m.
Raj reaches the finish line 5 seconds later, meaning Raj covers the remaining 50 m in 5 seconds.
Raj's speed $= \frac{50}{5} = 10\text{ m/s}$.
Total time taken by Raj to complete 1000 m $= \frac{1000}{10} = 100\text{ seconds}$.
Rahul finishes 5 seconds earlier, so Rahul's time $= 100 - 5 = 95\text{ seconds}$.
Rahul's speed $= \frac{1000}{95} = \frac{200}{19} = 10\frac{10}{19}\text{ m/s}$.
Q6mcq4 marks
During the next year, the probability that a Company A releases a mobile is 0.7. The probability that mobile is a success, given that it is released by the Company A is 0.8. The probability that a mobile is a success and released by a Company B is 0.28. A mobile released by either Company A or Company B during the next one year is a success. Find the probability that it is released by Company A.
a.
1/3
b.
1/2
c.
2/3
Correct Answer
d.
3/4
Step-by-Step AI Explanation
Verified Method
Let $S$ denote the event that the mobile is a success.
$P(\text{Success and from Company A}) = P(A) \times P(S|A) = 0.7 \times 0.8 = 0.56$.
$P(\text{Success and from Company B}) = 0.28$.
Given that a successful mobile was released by either Company A or Company B, the probability that it was released by Company A is:
$$P(A|S) = \frac{P(S \cap A)}{P(S \cap A) + P(S \cap B)} = \frac{0.56}{0.56 + 0.28} = \frac{0.56}{0.84} = \frac{2}{3}$$.
Q7mcq4 marks
In a company there are 252 engineers, in which the ratio of the number of electronics engineers and computer engineers is 2 : 1. The ratio of the number of electronics engineers and computer engineers becomes 1 : 1 after recruitment of some more computer engineers. The average age of all the engineers is now 22 years and the average age of the computer engineers is 2 years less than the average age of electronics engineers.
(A) The average age (in years) of electronics engineers is 21
(B) The average age (in years) of computer engineers is 21
(C) The average age (in years) of electronics engineers is 23
(D) The average age (in years) of electronics engineers is 25
(E) The average age (in years) of computer engineers is 23
Choose the correct answer from the options given below:
a.
(A) and (E) only
b.
(B) and (C) only
Correct Answer
c.
(D) and (E) only
d.
(E) only
Step-by-Step AI Explanation
Verified Method
Initially, total engineers $= 252$.
Ratio of Electronics to Computer engineers $= 2 : 1$.
Number of Electronics engineers $= \frac{2}{3} \times 252 = 168$.
Number of Computer engineers initially $= \frac{1}{3} \times 252 = 84$.
After recruiting more computer engineers, the ratio becomes $1 : 1$. Since the number of electronics engineers remains 168, the new number of computer engineers is also 168.
Since the numbers of electronics and computer engineers are now equal (168 each), the overall average age is simply the mean of their individual average ages.
Let $E$ be the average age of electronics engineers and $C$ be the average age of computer engineers.
Given $C = E - 2$ and $\frac{E + C}{2} = 22$.
$$\frac{E + (E - 2)}{2} = 22 \implies 2E - 2 = 44 \implies E = 23$$
Thus, $C = 23 - 2 = 21$.
Statements (B) and (C) are correct.
Q8mcq4 marks
A vessel has 500 litres of milk. 50 litres of milk is replaced with 50 litres of water in this vessel. If this operation is repeated another 2 more times, what is the percentage of milk in the vessel at the end?
a.
70.0
b.
72.9
Correct Answer
c.
80.0
d.
81.0
Step-by-Step AI Explanation
Verified Method
The operation is performed a total of $1 + 2 = 3$ times.
The fraction of milk remaining after each replacement of $\frac{50}{500} = \frac{1}{10}$ is:
$1 - \frac{1}{10} = \frac{9}{10} = 0.9$.
After 3 operations, the fraction of milk remaining is:
$(0.9)^3 = 0.729 = 72.9\%$.
Q9mcq4 marks
A shopkeeper claims to sell rice at cost price. He uses a false weight with the intention of selling rice at 25% profit. After selling Rice to a customer, he realizes that the customer has paid 10 % less than what he should have paid. What is the actual profit percentage made by the shopkeeper?
a.
6.25%
b.
10%
c.
12.5%
Correct Answer
d.
15%
Step-by-Step AI Explanation
Verified Method
Let the cost price of 1 kg of rice be Rs. 100.
To make a 25% profit while claiming to sell at cost price, the cost of the quantity of rice actually given must be:
$\text{Cost} = \frac{100}{1 + 0.25} = \text{Rs. } 80$.
The customer should have paid Rs. 100, but pays 10% less, which is:
$\text{Selling Price} = 100 \times (1 - 0.10) = \text{Rs. } 90$.
The actual profit percentage is:
$\frac{90 - 80}{80} \times 100\% = \frac{10}{80} \times 100\% = 12.5\%$.
Q10mcq4 marks
How many ten-digit numbers can be formed using all the digits of 2435753228 such that odd digits appear only in even places?
a.
2! 3! 5!
b.
$(5!)^2$
c.
$\frac{(5!)^2}{3!}$
d.
$\frac{(5!)^2}{3! (2!)^2}$
Correct Answer
Step-by-Step AI Explanation
Verified Method
The digits in 2435753228 are:
- Odd digits: 3, 5, 7, 5, 3 (5 digits: two 3s, two 5s, one 7)
- Even digits: 2, 4, 2, 2, 8 (5 digits: three 2s, one 4, one 8)
A 10-digit number has 5 even positions (2nd, 4th, 6th, 8th, 10th) and 5 odd positions (1st, 3rd, 5th, 7th, 9th).
Since the 5 odd digits must appear only in the 5 even places, the 5 even digits must occupy the 5 odd places.
Ways to arrange the odd digits in the even positions:
$\frac{5!}{2! 2!}$
Ways to arrange the even digits in the odd positions:
$\frac{5!}{3!}$
Total number of ten-digit numbers:
$\frac{5!}{2! 2!} \times \frac{5!}{3!} = \frac{(5!)^2}{3! (2!)^2}$.
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The price of an apple is twice that of an orange. The price of an orange is thrice that of a banana. If the price of an apple increases by 10%, price of an orange increases by 30% and the price of a banana increases by 20%. Find the percentage increase in the price of 20 apples, 20 oranges and 20 bananas.
a.
19%
b.
17%
c.
15%
d.
13%
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Meera and Sarika attempted to solve a quadratic equation in x. Sarika made a mistake in reading the coefficient of x and obtained the roots as 12 and 16. Meera made a mistake in reading the constant term of the equation. She obtained the roots as 22 and 6. The corrects root(s) is (are) :
(A) -16
(B) -12
(C) 12
(D) 16
Choose the correct answer from the options given below :
a.
(A) and (B) only
b.
(A) and (C) only
c.
(C) and (D) only
d.
(B) and (D) only
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A roller is 4 m long and has a diameter of 0.7 m. It takes exactly 2000 rotations of the roller to level a road. If the cost of using the roller is Rs. 4 per square metres, then the total cost of levelling the road is :
Assume, $\pi=22/7$
a.
Rs. 17600
b.
Rs. 35200
c.
Rs. 70400
d.
Rs. 140800
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In a company, the average salary of the boy is Rs. 50000. The average salary of all the employees is Rs. 48000. There are 80 boys in the company and the average salary of the girl is Rs. 40000. What is the number of girls working in the company?
a.
12
b.
15
c.
20
d.
24
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Given: Anuj takes 1 day to complete a job. Bharat takes twice the time as Anuj to complete the same job. Chetan takes twice the time as Bharat to complete that job. Dhiraj takes twice the time as Chetan to complete that job.
(A) Chetan and Dhiraj will take 8/3 days to complete the work
(B) The second fastest pair to complete the work is Anuj and Dhiraj
(C) The second slowest pair to complete the work is Bharat and Dhiraj
(D) Bharat and Dhiraj will take 4/3 days to complete the work
Choose the correct answer from the options given below:
a.
(A), (B) and (C) only
b.
(A) and (D) only
c.
(A) and (C) only
d.
(A) only
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Given below are two statements
Statement I : $(543)_6$ is equivalent to $(317)_8$
Statement II : The last 4 bits in the binary representation of a multiple of 16 is 1000.
In light of the above statements, choose the correct answer from the options given below
a.
Both Statement I and Statement II are true
b.
Both Statement I and Statement II are false
c.
Statement I is true but Statement II is false
d.
Statement I is false but Statement II is true
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Study the pie chart and answer the questions that follow:
TOTAL GLOBAL EXPORTS: $144, 000 BILLION
Others: 50.4°
USA: 54°
Japan: 45°
Germany: 41.4°
France: 27°
China: 19.8°
India: 16.2°
Russia: 37.8°
Australia: 18°
Hong Kong: 19.8°
Note : The value of exports represents the angle corresponding to each country in the pie chart.
By how much does the value of the exports of Japan exceed that of Australia?
a.
$ 10800 billion
b.
$ 21600 billion
c.
$ 38880 billion
d.
$ 49680 billion
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Study the pie chart and answer the questions that follow:
TOTAL GLOBAL EXPORTS: $144, 000 BILLION
Others: 50.4°
USA: 54°
Japan: 45°
Germany: 41.4°
France: 27°
China: 19.8°
India: 16.2°
Russia: 37.8°
Australia: 18°
Hong Kong: 19.8°
Note : The value of exports represents the angle corresponding to each country in the pie chart.
What is number of countries whose exports are more than the average exports per country?
(Assume ‘Others’ as a single country)
a.
4
b.
5
c.
6
d.
7
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Below two pairs of numbers are given. But one number in the second pair is missing. Identify the relationship between the two numbers in first pair and find the second number of the second pair such that it follows the same relationship as that of first pair.
7: 77 :: 14 : ...
a.
196
b.
252
c.
98
d.
232
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The question below consists of a main statement followed by four options. Select the one that logically follows the main statement
If I drive a car, then it is a BMW or a Skoda.
a.
I am driving a car, means that it is a BMW or a Skoda
b.
The car is neither BMW nor a Skoda, hence I do not drive a car.
c.
I drive a car but it is not a Skoda, means it is a BMW
d.
All the above
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The question below consists of a main statement followed by four options. Select the one that logically follows the main statement
The slip fielder can catch a ball, only if the batsman is brought to the front foot and he tries to hit the ball
a.
The batsman is brought to the front foot, hence the slip fielder cannot catch the ball
b.
The batsman did not try to hit the ball, hence the slip fielder cannot catch the ball
c.
The fielder caught the ball, means that the batsman was brought to the front foot and he did not try to hit the ball
d.
All the above
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The question below consists of a main statement followed by four options. Select the one that logically follows the main statement.
'Whenever I go shopping, I end up spending more'
a.
I went for shopping means I end up spending less
b.
I did not go for shopping; implies I did not spend more
c.
I did not spend more, means I did not go for shopping
d.
Both (1) and (2)
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A number -arrangement machine, when given an input string of numbers, arranges them following a particular pattern. The following is the illustration of an input and its arrangement.
$$\begin{array}{|l|c|c|c|c|c|c|} \hline \text{Input :} & 3 & 4 & 9 & 7 & 6 & 11 \\ \hline \text{Step I} & 9 & 16 & 81 & 49 & 36 & 121 \\ \hline \text{Step II} & 12 & 20 & 90 & 56 & 42 & 132 \\ \hline \text{Step III} & 17 & 25 & 95 & 61 & 47 & 137 \\ \hline \text{Step IV} & 15 & 23 & 93 & 59 & 45 & 135 \\ \hline \end{array}$$
As per the rules followed in the above steps, find the appropriate answer
Which is the fifth number from the left end in step III of the following input?
6, 2, 14, 17, 8, 13
a.
64
b.
72
c.
75
d.
7
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A number -arrangement machine, when given an input string of numbers, arranges them following a particular pattern. The following is the illustration of an input and its arrangement.
| Input : | 3 | 4 | 9 | 7 | 6 | 11 |
| Step I | 9 | 16 | 81 | 49 | 36 | 121 |
| Step II | 12 | 20 | 90 | 56 | 42 | 132 |
| Step III | 17 | 25 | 95 | 61 | 47 | 137 |
| Step IV | 15 | 23 | 93 | 59 | 45 | 135 |
As per the rules followed in the above steps, find the appropriate answer
Which is the fifth number from the left end in step III of the following input?
6, 2, 14, 17, 8, 13
a.
64
b.
72
c.
75
d.
7
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P, Q, R, S, T, U, V, W are sitting in a row facing north
(A) P is fourth to right of T
(B) W is fourth to the left of S
(C) R and U , which are both at the ends are neighbours of Q and T respectively
(D) W is immediate left of P and P is neighbour of Q
Who are the immediate neighbours of W?
a.
Q and V
b.
V and R
c.
V and P
d.
U and P
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If A # B is the mother of A
A $ B means A is the father of B
A % B means A is sister of B
A * B means A is the son of B
A @ B means A is brother of B and
A ! B means A is the daughter of B
In the expression P $ Q # R @ S, how is R related to P?
a.
Grandson
b.
Great Grandson
c.
Son
d.
Daughter
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The question below consists of a main statement followed by four options. Select the one that logically follows the main statement
Unless I score well, I will not get selected
a.
I was not selected, means I did not score well
b.
I am selected, implies I scored well
c.
I did not score well, means I will not be selected
d.
Both (2) and (3)
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P, Q, R, S, T, U, V and W are sitting round the circle and are facing the centre:
P is second to the right of T who is the neighbour of R and V. S is not the neighbour of P.
V is the neighbour of U. Q is not between S and W. W is not between U and S.
U is the right of S.
Who is sitting adjacent to V?
a.
U and T
b.
U and R
c.
T and P
d.
W and P
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The question below consists of a main statement followed by two statements. Select the one that logically follows the main statement
"Private property, trespassers will be prosecuted" - A notice on a plot of land. Given below are two statements
Statement I: The passer-by may read the notice and may not trespass.
Statement II: The people are scared of prosecution
In light of the above statements, choose the most appropriate answer from the options given below
a.
Only Statement I is implicit
b.
Only Statement II is implicit
c.
Both Statements I and II are implicit
d.
Neither I nor II are implicit
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How many pages of the book Ram read on Monday. The book was read completely by Tuesday.
Statement I: Ram read last 30 pages of the book on Tuesday
Statement II: The book has 600 pages out of which half were read by Ram before Monday
In light of the above statements, choose the most appropriate answer from the options given below
a.
Data in Statement I alone is sufficient to find the answer
b.
Data in Statement II is sufficient enough to find answer
c.
Data in Statements I and II together is not sufficient to find the answer
d.
Data in both the Statements is sufficient to find the answer
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Among the six persons P, Q, R, S, T, U, each is having different weights
P is heavier than 3 persons. R is lighter than T
S is lighter than only Q
R is not the lightest
Who is lighter and heavier than P respectively?
a.
T and S
b.
R and S
c.
S and R
d.
T and Q
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Read the passage below and answer the question that follows:
Human beings are connected at the level of feeling and emotion; in such a degree that there is practically a subterranean network of the psyche in which some encounters are damaging, some nourishing. This emotional exchange is typically at a subtle, almost imperceptible level. The way a colleague says 'thank you' can leave one feeling ignored, resented or genuinely welcomed and appreciated. We catch feelings from one another as though they were some kind of social virus. Every space is full of emotional signals and every time people connect, they transmit and receive those signals. These emotional encounters have an effect on all the people in that particular circle. Those who are socially skillful can control these emotional messages. A civil and polite society is able to regulate and control these emotional relationships in less damaging ways. The Emotional Quotient of a society is the sum total of the emotional intelligence of its citizens. When we compliment others for being considerate, we are actually acknowledging their emotional intelligence. The company of such people is a relaxing experience and they are a valuable and enriching presence in any society. Whether we like it or not, we are all interdependent in terms of our feelings and emotions and our emotional intelligence form the framework of society.
The company of what kind of people is relaxing?
a.
Emotional people
b.
Considerate people
c.
Emotionally intelligent people
d.
Emotionally calm people
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There was a ________________ possibility that war would be declared soon.
Select the word that best fits the above incomplete sentence and completes it:
a.
Probable
b.
Distinct
c.
Dubious
d.
Distinctive
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Indonesia has released special commemorative stamp on theme of Ramayana to mark 70th anniversary of establishment of its diplomatic ties with India. Which scene of Ramayana has been depicted on the stamp?
a.
Ram, Sita and Laxman return to Ayodhya after 14 years
b.
Sita's Swayamwar
c.
Jatayu fights to save Sita
d.
Hanuman carries the mountain with Sanjeevani booti
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Consider the following statements about a classical dance form
(A) Tribhanga is a special feature of this dance.
(B) The torso movement is very important and is a unique feature of this dance.
(C) Many of today's Gurus of this style belong to the Gotipua tradition.
Identify the classical dance form using the above clues.
a.
Kuchipudi
b.
Odissi
c.
Sattriya
d.
Kathakali
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India has begun discussions with which of the following countries on launching a trilateral Supply Chain Resilience Initiative (SCRI) to reduce dependency on China, necessitated by Beijing's aggressive political and military behaviour?
a.
Sri Lanka and Japan
b.
Japan and South Korea
c.
Japan and Australia
d.
New Zealand and Australia
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Which of the following indicators are parts of the Inclusive Development Index?
(A) Living Standards
(B) Environmental Sustainability
(C) Protection of Future Generations from Further Indebtedness
(D) Financial Inclusion
a.
(A), (B) and (C)
b.
(A), (C) and (D)
c.
(B), (C) and (D)
d.
(A), (B) and (D)
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