1. Professor nitwit obtains a hash number of a given positive integer > 3 as follows. He substracts 2 from the number (to get the new number), and multiplies the new number by 2 to get a term. He repeats this with the new number (to get newer numbers and terms) until the number becomes 2 or 1. The hash is defined as the sum of all the numbers generated in the process.
For example, with the number 5, he multiples (5-2 = 3) by 2 to get the first term 6. He multiplies (3 - 2 = 1) by 2 to get the second term 2. As the number has become 1, he stops. The hash is the sum of the two numbers (6+2) = 8.
If professor Nitwit is given 3 numbers 4, 9 and 13, what is the sum of the hash numbers he obtains for the three numbers?
a. 108
b. 120
c. 113
d. 103

Answer: A

Explanation:
As we are subtracting 2 continuously from the resulting numbers, get a progression with a common difference of 2 and we need to multiply the sum by 2 to get hash number.
For 5 we will get the hash number like this: (3 + 1) × 2 = 8
4 : (4 – 2) × 2 = 2 × 2 = 4
9 : (7 + 5 + 3 + 1) × 2 = 32
13: (11 + 9 + 7 + 5 + 3 + 1) × 2 = 72
Sum of the hash numbers = 4 + 32 + 72 = 108

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2. Out of a group of swans, 7/2 times the square root of total number are playing on the shore of the pond. The remaining 2 are inside the pond. Find the total number of swans.
a. 4
b. 25.
c. 9
d. 16

Answer: D

Explanation:
Let the number of swans = $x$
$ \Rightarrow \dfrac{7}{2}\sqrt x + 2 = x$
Check the options.
$x$ should be a perfect square.
Option D satisfies.

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3. Find the length of the longest pole that can be placed in an indoor stadium 24 m long, 18m wide and 16 m high.
a. 25 m
b. 34 m
c. 36 m
d. 30 m

4. 1/4 of the tank contains fuel when 11 litres of the fuel is poured into the tank the indicater rests at the 1/2 mark.find the capacity of the tank in litres.
a. 44
b. 8
c. 6
d. 36

Answer: D

Explanation:
Let the capacity of the tank be $v$ liters.
Given, $\dfrac{v}{4} + 11 = \dfrac{v}{2}$
$\dfrac{v}{2} - \dfrac{v}{4} = 11 \Rightarrow v = 44$

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5. In a village, every weekend, three-eigth of the men and one-third of the women participate in a social activity. If the total number of participants is 54, and out of them 18 are men then the total number of men and women in the village is:
a. 156
b. 228
c. 180
d. 204

Answer: A

Explanation:
Let the total number of men be $x$ and number of women be $y$.
Total number of participants = 54.
Given that number of men participants = 18.
So, number of women participants are = 54 – 18 = 36.
Given that $\dfrac{3}{8}$ of the men participate in a social activity.
$\dfrac{3}{8}x = 18 \Rightarrow x = 48$
Also given that $\dfrac{1}{3}$ of the women participate in social activity.
$\dfrac{1}{3}y = 36 \Rightarrow y = 108$.
Therefore, total number of men and women in the village = 108 + 48 = 156.

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6. In a certain city, 60% of the registered voters are congress supporters and the rest are BJP supporters. In an assembly election, if 75% of the registered congress supporters and 20% of the registered BJP supporters are expected to vote for candidate A, what percent of the registered voters are expected to vote for candidate A?
a. 53
b. 60
c. 75
d. 20

Answer: C

Explanation:
Let the people in the city be 100
Congress supporters = 60% of 100 = 60
40% of them are BJP = 40% of 100 = 40
out of 60,75% voted for congress = 75%(60) = 45
out of 40%,20% voted for congress = 20%(40) = 8
Total = 45 + 8 = 53
Total percent = 53%

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7. How many 6-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 and 7 so that the digits should not repeat and the second last digit is even?
a. 2160
b. 320
c. 6480
d. 720

Answer: D

Explanation:
Last two digits are even.
_ _ _ _ E E
Therefore, These two digits are filled in ${}^3{P_2} = 6$ ways.
Now remaining 4 places are to be filled with 5 digits.
This can be done in ${}^5{P_4} = 120$ ways.
Total ways = $6 \times 120 = 720$ ways.

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8. You have been given a physical balance and 7 weights of 47, 46, 43, 48, 49, 42, and 77 Kgs.. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 178 Kgs.?
a. 174
b. 175
c. 177
d. 172

Answer: A

Explanation:
Choose 77, 49 and 48 then we get 174
If you dont chose 77, then we have to choose any 4 from the remaining and the maximum sum is becoming 178. So 174 is maximum.