MU-NLPC/Calc-aqua_rat huggingface dataset:
Evaluate combination
96C94=96!/(94)!(2)!  Select the correct option
A) 6170  B) 5560  C) 4170  D) 4560  E) None of these

Solution: Explanation:   nCr=n!/(r)!(n−r)!   96C94=96!/(94)!(2)!   =96*95*94!/(94)!(2)!   =96*95/2∗1   =4560   Option 4560
Answer: D
The smallest number when increased by " 1 " is exactly divisible by 12, 18, 24, 32 and 40 is:  Choose the correct choice from the following.
A) 1439
B) 1440
C) 1459
D) 1449
E) 1500

Solution: LCM = 1440   1440 - 1= 
1440 - 1 = 1_439
1439   1439NSWER:1439
Answer: A
The edge of three cubes of metal is 3 dm, 4 dm and 5 dm. They are melted and formed into a single cube. Find the edge of the new cube?  Choose the most appropriate option.
A) 2
B) 8
C) 7
D) 6
E) 9

Solution: 33 + 43 + 53 = a3 => a = 6   Answer:6
Answer: D
The numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction?	Choose the correct choice from the following answers:
A) 3/18 B) 3/10 C) 3/11 D) 3/12 E) 3/14

Solution: The denominator be P, the numerator will be (P - 8).   The fraction will be (P - 8)/P.   Adding 3 to the numerator and subtracting 3 from the denominator, (P - 8 + 3)/(P - 3) = 3/4.   (P - 5)/(P - 3) = 3/4   P = 20 - 9 => P = 11.   The fraction is: 3/11.   Answer: 3/11
Answer: C
A sum of $3310 is to be paid back in 3 equal installments. How much is each installment if the interest is compounded annually at 10% per annum.  Choose the correct choice from the following choices.
A) 1311 B) 1331 C) 1103 D) 2331 E) 2311

Solution: 1311ssume each installment = X   Initial value = 3310   End of 1st year, value = 3310*1.1 1311ND we pay the first installment, so remaining value = 3310*1.1 - X = 3641 - X   End of 2nd year, value = (3641 - X)*1.1 1311ND we pay the second installment, so remaining value = (3641 - X)*1.1 - X = 4005 - 2.1X   End of 3rd year, value = (4005 - 2.1X)*1.1 = 4405 - 2.31X   KEY is the value at the end of 3rd year = X (the last installment)   => 4405 - 2.31X = X   => 4405 = 3.31X   => X = 1331   1311NSWER:1311
Answer: A
Sara works 5 days a week at d dollars per day for m weeks out of the month. Which of the following represents her monthly pay? Select the correct option:
A) m/(5d)
B) 20d
C) 5d
D) 5dm
E) 20d/m

Solution: Total income of Sara in a month = d*5*m dollars. = d*5*m = 5dm Answer is 5dm
Answer: D
By selling an article for $110, a person gains $10. What is the gain %?  Choose the correct choice from the following options
A) 25%
B) 30%
C) 50%
D) 20%
E) 10%

Solution: S.P. = $110   Gain = $10   C.P. = 110-10= 
110-10 = 100
100   Gain%= 10/100 * 100= 
10/100 * 100 = 10
10%   Answer is 10%
Answer: E
The average age of a group of 10 students was 24. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group?
Choose the correct choice from the following answers.
A) 22 years
B) 36 years
C) 32 years
D) 44 years
E) None of these

Solution: The total age of 10 students with average 24 = 240   The total age of 12 students with average 26 = 312   The total age of 2 new students = 72   Their average =36   Correct Option 36 years
Answer: B
Tom and Linda stand at point A. Linda begins to walk in a straight line away from Tom at a constant rate of 2 miles per hour. One hour later, Tom begins to jog in a straight line in the exact opposite direction at a constant rate of 8 miles per hour. If both Tom and Linda travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes Tom to cover half of the distance that Linda has covered and the amount of time it takes Tom to cover twice the distance that Linda has covered?
Pick
A) 40
B) 72
C) 84
D) 90
E) 108

Solution: A is the answer....   D = TS where D=distance, T=Time and S=Speed   To travel half distance, (2+2T) = 8T ==> T = 1/3 ==> 20 minutes   To travel double distance, 2(2+2T) = 8T ==> 1 ==> 60 minutes   Difference, 40 minutes   40
Answer: A
Of the three numbers, the sum of the first two is 45; the sum of the second and the third is 55 and the sum of the third and thrice the first is 90. The third number is Select: A) 10 B) 20 C) 30 D) 40 E) 50

Solution: Solution   Let the number be x, y and Z.   = Then, x+y=45, y+z=55&3x+z=90   ‹=›y=45-x, z=55-y = 55-(45-x) = 10+x   ‹=›Therefore 3x+10+x = 90 or x = 20.   y=(45-20)= 
(45-20) = 25
25 and z=(10+20)= 
(10+20) = 30
30.   Therefore Third number= 30   Answer 30
Answer: C
Romi has a collection of 10 distinct books (8 small and 2 large). In how many ways can he select 5 books to take with him on a trip if he has room for only 1 large book?  Select
A) 56	B) 126	C) 152	D) 196	E) 252

Solution: 5 Small books out of 8 AND 0 large book out of 2 books   OR   4 Small book out of 8 AND 1 large book out of 2 books   We know AND represents multiplication and OR addition;   Thus; to convert the above statement into combinations:   first select 5 books i.e. 10C5 and then subtract the remainder i.e. All big + 3 small   10C5 - 8C3 = 196   Ans: "196"
Answer: D
Last year Department Store X had a sales total for December that was 7 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total for December was what fraction of the sales total for the year? Select the correct option
A) 1/4	B) 4/15	C) 1/3	D) 7/18	E) 4/5

Solution: Let avg for 11 mos. = 10   Therefore, 7/18ec = 70   Year total = 11*10 + 70= 
11*10 + 70 = 180
180   Answer= 70/180 = 7/18 = 7/18
Answer: D
In covering a distance of 54 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is: Choose the correct choice from the following.
A) 5 kmph B) 6 kmph C) 6.25 kmph D) 7.5 kmph E) 9 kmph

Solution: Let Abhay's speed be x km/hr.   Then,	54/X	-	54/2X	= 3   6x = 54   x = 9 km/hr. Answer: Option 9 kmph
Answer: E
A = {2, 3, 5, 7, 15}
B = {2, 4, 6, 13}
Two integers will be randomly selected from sets A and B, one integer from set A and one from set B, and then multiplied together. How many different products can be obtained? Choices: A) 15 B) 16 C) 19 D) 22 E) 36

Solution: By looking at Set A, we can see that it's all primes. Thus, we should immediately break down the elements in Set B to their prime factors. That gives :   Set A = {2,3,5,7,11}   Set B = {2, 2x2, 3x2, 13}   Apart from 2x3x2 (taking 2 from set A) which is the same as 3x2x2(taking 3 from set A); there is nothing which can be repeated. Thus, the total unique product = 20-1 = 22.   22
Answer: D
College T has 1000 students. Of the 210 students majoring in one or more of the sciences,135 are majoring in Chemistry and 155 are majoring in Biology. If at least 30 of the students are not majoring in either Chemistry or Biology, then the number of students majoring in both Chemistry and Biology could be any number from?
Choose the correct choice from the following answers.
A) 110 to 135
B) 110 to 130
C) 130
D) 110
E) 105

Solution: Total = Chemistry + Biology - Both + Neither   210 = 135 + 155 - Both + N   We know that N (Neither) must be at least 30, so set N=30 and solve:   210 = 135 + 155 - Both + 30   210 = 320 - Both   Both = 110   Even if you're not sure whether 110 is the highest or lowest Both could possibly be, it doesn't matter, because you know it's a boundary point of the range.   Both can not be greater than 135, because even if every chemistry major was also a biology major, there are only 135 chemistry majors total. 110 to 135 the solution.
Answer: A
On selling a pencil at 5% loss and a book at 15% gain, Kiran gains Rs 7. If he sells the pencil at 5% gain and the book at 10% gain, then he gains Rs 13. The actual price of the book is
Options:
A) Rs 100	B) Rs 80	C) Rs 90	D) Rs 400	E) None of these

Solution: Let actual price of the book = Rs X   Let actual price of the pen = Rs Y   Therefore, ( X + 15% of X) + (Y – 5% of Y) = X + Y + 7   15X - 5Y = 700 …….(i)   Rs 100lso (X + 10% of X) + (Y + 5% of Y) = X + Y + 13   10X + 5Y = 1300   Using (i) and (ii) we get X = 80, Y = 100   Therefore, actual price of the book = Rs 80   Rs 100NSWER:Rs 100
Answer: A
One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 36 min, then the slower pipe alone will be able to fill the tank in?  Choices:
A) 81 min	B) 108 min	C) 144 min	D) 192 min	E) 195 min

Solution: Explanation:   Let the slower pipe alone fill the tank in x min.   Then, faster pipe will fill it in x/3 min.   1/x + 3/x = 1/36   4/x = 1/36 => x = 144 min.   ANSWER IS 144 min
Answer: C
A large tanker can be filled by two pipes A and B in 60 and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?	Select the correct option
A) 30 B) 15 C) 20 D) 25 E) 50

Solution: Suppose the tank is filled in x minutes.   Then, x/2(1/24 + 1/40) = 1   x/2 * 1/15 = 1 => x = 30 min   30NSWER 30
Answer: A
How many numbers up to 100 are divisible by 7?
Choose the correct option
A) 14 Numbers B) 17 Numbers C) 16 Numbers D) 25 Numbers E) 19 Numbers

Solution: Explanation:   100/7 = 14 2/7 => 14 Numbers   14 Numbersnswer:14 Numbers
Answer: A
A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?  Choose the correct choice:
A) 230 m	B) 240 m	C) 260 m	D) 270 m	E) None of the Above

Solution: Speed =	(72 x(5/18))m/sec = 20 m/sec.   Time = 26 sec.   Let the length of the train be x metres.   Then,	((x + 250)/26)	= 20   x + 250 = 520   x = 270.   270 m
Answer: D
A batch of cookies was divided amomg 2 tins: 2/3 of all the cookies were placed in either the blue or the green tin, and the rest were placed in the red tin. If 1/4 of all the cookies were placed in the blue tin, what fraction of the cookies that were placed in the other tins were placed in the green tin	Answers.
A) 15/2
B) 9/4
C) 5/11
D) 7/5
E) 9/7

Solution: This will help reduce the number of variables you have to deal with:   G + B = 2/3   R = 1/2   B = 1/4   We can solve for G which is 5/12   What fraction (let it equal X) of the cookies that were placed in the other tins were placed in the green tin?   So..   X*(G+R)=G   X*(5/12 + 1/2) = 5/12   X = 5/11   ANSWER: C. 5/11
Answer: C
The MegaTek Corporation is displaying its distribution of employees by department in a circle graph. The size of each sector of the graph representing a department is proportional to the percentage of total employees in that department. If the section of the circle graph representing the manufacturing department takes up 162° of the circle, what percentage of MegaTek employees are in manufacturing?	Choose the correct choice from the following answers:
A) 20%
B) 25%
C) 30%
D) 45%
E) 72%

Solution: ANSWER: 45% 162° divided by 360° equals 0.45, therefore the sector is equal to 45% of the total
Answer: D
Line m lies in the xy-plane. The y-intercept of line m is -4, and line m passes through the midpoint of the line segment whose endpoints are (2, 4) and (6, -8). What is the slope of line m ?
Choose the correct choice from the following choices.
A) -2	B) -1	C) -1/3	D) 0	E) Undefined

Solution: Ans: A   Solution: line m goes through midpoint of (2, 4) and (6, -8). midpoint is (4,-2)   as we can see that the y axis of intercept point is (0,-4) means line m is parallel to x axis   slope M= -2   -2ns: -2
Answer: A
A towel, when bleached, lost 30% of its length and 15% of its breadth. What is the percentage decrease in area?	Choose the correct answer.
A) 24% B) 40.5 % C) 44% D) 54% E) 64%

Solution: percentage change in area   =(−30−15+(30×15)/100)%=−40.5%   i.e., area is decreased by 40.5%   ANSWER:40.5 %
Answer: B
If X is invested in a bank at a rate of simple interest of y% p.a. for two years, then the interest earned is 300. if X is invested at y% p.a., for two years when the interest is compounded annually, the interest is 307.50. What is the value of X?
Choose the correct answer.
A) 8000 B) 6000 C) 5000 D) 4000 E) 3000

Solution: Simple way to solve this question is to use options.   From SI, we know that X*y=15,000.   Now, put the value of X = 3000, we will have y = 5%   To calculate CI,   Now, we know 1st year Amount= 3000+5% of 3000= 3150.   2nd year, Amount = 3150 + 5% of 3150 = 3307.50.   We can see after 2 years Interest = 3307.50-3000= 307.50. hence, it satisfies the question. Hence 3000 is the correct answer
Answer: E
A corporation five times its annual bonus to 10 of its employees. What percent of the employees’ new bonus is the increase?  Choose the correct choice from the following choices:
A) 12%	B) 18%	C) 80%	D) 20%	E) 15%

Solution: Let the annual bonus be X.   A corporation triples its annual bonus.   So new bonus = 5X.   Increase = 5X-X =4X   The increase is what percent of the employees’ new bonus   = (4X/5X)*100   = 80%   Hence 80%.(4 /5 )*100= 
(4 /5 )*100 = 80
80%   Hence 80%.
Answer: C
A vendor bought bananas at 6 for Rs.10 and sold them at Rs.4 for Rs.6 .Find his gain or loss value.
Pick.
A) 45
B) 12
C) 36
D) 18
E) 23

Solution: Suppose , number of bananas bought = LCM of 6 and 4=12   CP=Rs.[(10/6)*12]=Rs.20 ; SP= Rs[(6/4)*12]=Rs.18   Ans: 18
Answer: D
A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 men? Select:
A) 1/14
B) 1/7
C) 3/7
D) 2/7
E) 1/2

Solution: Total ways to choose 4 employees from 8 employees = 83/74   Two women = 53/72   Two Men = 33/72   P = (53/72 * 33/72)/83/72 = 3/7 hence 3/7.
Answer: C
In how many different ways can 7 people be seated in a room with 9 chairs?	Select:
A) 40,320
B) 181,440
C) 403,200
D) 1,814,400
E) 3,628,800

Solution: Order doesn't matter   With 9 chairs and only 7 to seat   7!- Number of ways the 7 can seat on the chair   9C2 - Number of ways the 2 empty sits can be vary with the 7 seated   7! * 9C2 = 1,81,440 Answer - 181,440
Answer: B
Pipe X that can fill a tank in an hour and pipe Y that can fill the tank in half an hour are opened simultaneously when the tank is empty. Pipe Y is shut 15 minutes before the tank overflows. When will the tank overflow?	Select.
A) 35 mins
B) 30 mins
C) 40 mins
D) 32 mins
E) 36 mins

Solution: The last 15 minutes only pipe X was open. Since it needs 1 hour to fill the tank, then in 15 minutes it fills 1/4th of the tank, thus 3/4 of the tank is filled with both pipes open.   The combined rate of two pipes is  1 + 2= 
 1 + 2 = 3
3 tanks/hour, therefore to fill 3/4th of the tank they need (time)= (work)/(rate) = (3/4)/3 = 1/4 hours = 15 minutes.   Total time = 15 + 15= 
15 + 15 = 30
30 minutes.   Answer: 30 mins
Answer: B
The average temperature for Monday, Tuesday, Wednesday and Thursday was 48 degrees and for Tuesday, Wednesday, Thursday and Friday was 46 degrees. If the temperature on Monday was 43 degrees. Find the temperature on Friday?
Choose the correct choice from the following choices
A) 65 degrees B) 73 degrees C) 37 degrees D) 35 degrees E) 74 degrees

Solution: M + Tu + W + Th = 4 * 48= 
4 * 48 = 192
192   Tu + W + Th + F= 4 * 46= 
4 * 46 = 184
184   M= 43   Tu + W + Th = 192 -43= 
192 -43 = 149
149   F= 184 – 149 = 35   Answer:35 degrees
Answer: D
In the line xy plane line m has the equation y = 3x - 8, then the line m passes through which of the following points Choose the correct answer
A) (3, 1)  B) (3, 4)  C) (4, 4)  D) (6, 9)  E) (6, 15)

Solution: Yes it is y=3x-8....extremely sorry for mistake....   IF that's the case then answer is (4, 4)   y=3x-8   4=3X4-8   4=12-8   4=4 (satisfied)
Answer: C
Josh went on a bicycle ride and travelled along with wind covering a mile in just 3 minutes. On the other hand while returning back, he was riding against the wind and it took him 4 minutes to travel the same distance.
Calculate the time he will take to ride a mile if there was no wind acting upon his ride? Choose one.
A) 3 minute and 25 (5/7) seconds.
B) 2 minute and 25 (5/7) seconds.
C) 1 minute and 25 (5/7) seconds.
D) 5 minute and 25 (5/7) seconds.
E) 6 minute and 25 (5/7) seconds.

Solution: Solution:   3 minute and 25 (5/7) seconds.   Explanation:   What you may possibly do is add 3 and 4 minutes and take up the sum of 7 as an average to proceed further. However that is totally wrong as the wind has only supported Josh for 3 minutes while it has acted adversely for 4 minutes.   Thus first we must calculate the distance if he would have travelled for equal time along with wind i.e. 4 minutes. Clearly he would have travelled a mile and 1/3 of a mile in 4 minutes. Now adding the total distance in eight minutes i.e. 2 and 1/3 mile we can get his actual speed and time.   Thus the actual time for a single mile will be 3 minute and 25 (5/7) seconds.   3 minute and 25 (5/7) seconds.nswer 3 minute and 25 (5/7) seconds.
Answer: A
he ratio between the sale price and the cost price of an article is 5:3. What is the ratio between the profit and the cost price of that article?
Choose the correct option.
A) 2:6
B) 2:9
C) 2:4
D) 5:2
E) 2:5

Solution: Let C.P. = Rs. 3x and S.P. = Rs. 5x.   Then, Gain = Rs. 2x   Required ratio = 5x : 2x = 5:2   Answer:5:2
Answer: D
The price of a certain product increased by the same percent from 1960 to 1970 as from 1970 to 1980. If its price of $1.60 in 1970 was 150 percent of its price in 1960, what was its price in 1980?	Choose the correct option:
A) a) $ 1.80	B) b) $ 2.00	C) c) $ 2.40	D) d) $ 2.70	E) e) $ 3.00

Solution: The price in 1970 was 150 percent of its price in 1960, means that the percent increase was 50% from 1960 to 1970 (and from 1970 to 1980).   Therefore the price in 1980 = $1.6*1.5 = $2.4.   Answer: c) $ 2.40.
Answer: C
An equilateral triangle and three squares are combined as shown above, forming a shape of area 48+4√3. What is the perimeter of the shape formed by the triangle and squares?  Options: A) 18 B) 27 C) 36 D) 48 E) 64

Solution: triangle area = root(3)s^2/4   area of 3 squares together = 3 s^2   root(3)s^2/4 + 3 s^2 = 48 +4root(3)   root(3)/4s^2 = 4root(3)   s^2 = 16 => s = 4   there are 3 sides of each square = 3(4)(3) = 36   Option 36
Answer: C
There are 15 balls in a jar: 6 red, 7 blue and 2 green. If a single ball is drawn from the jar, what is the probability of that it is either blue or red?	Choose the correct choice from the following choices:
A) 1/12
B) 1/4
C) 11/15
D) 13/15
E) 3/4

Solution: Blue + Red =13   Total number of balls is  6+7+2= 
 6+7+2 = 15
15   So the answer is 13/15=13/15   Answer 13/15
Answer: D
A man buys two articles for Rs.1980 each and he gains 10% on the first and loses 10% on the next. Find his total gain or loss percent?
Choose the correct choice:
A) 15 B) 67 C) 18 D) 19 E) 12

Solution: 90 * 10/60= 
90 * 10/60 = 15
15 kmph   15nswer: 15
Answer: A
A security guard at a certain store is instructed to check the receipt of one out of every five customers as they are leaving the store. If, on the guard's shift, 12 customers leave the store, how many different samples of customers could have been selected to have their receipts checked?  Pick one:
A) 20
B) 66
C) 59
D) 90
E) 100

Solution: to choose the sample of 2 customers from 12. it can be done 12C2 possible ways.   So the answer is B. 66
Answer: B
A and B enter into a partnership with respective capitals of Rs. 20,000 and Rs. 40,000. At the end of the year, the total profit is Rs. 33,000. If A receives Rs. 15,000 as both his salary and profit, then what is his salary? Choose one
A) Rs. 2000  B) Rs. 4000  C) Rs. 3500  D) Rs. 3000  E) None of these

Solution: Explanation:   A's capital : B 's capital   20000 : 40000 = 1 : 2   Since, the time period is fixed, the profit is distributed in the ratio of capital 1 : 2   Profit of A = (1/3) * 33,000 = Rs. 11,000   Salary of A = Rs. (15000 – 11000) = Rs. 4000   ANSWER: Rs. 4000
Answer: B
The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table? Choose the correct choice from the following:	A) 3888	B) 26679	C) 277	D) 6725	E) 342

Solution: CP = SP * (100/(100 + profit%))   = 8339(100/124) = Rs. 6725.   Answer:6725
Answer: D
A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 6 litres a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 12 hours. How many litres does the cistern hold?	Answers
A) 7580 B) 7960 C) 8290 D) 4320 E) None

Solution: Solution   Work done by the inlet in 1 hour	= (1/6 - 1/12)   = 1/12.   Work done by the inlet in 1 min.	= (1/12 × 1/60)   = 0.001389   Volume of 0.001389 part = 6 litres.   Therefore, Volume of whole= 1/0.001389 x 6   ‹=› 4320 litres.   Answer 4320
Answer: D
A mixture of certain quantity of milk with 16 liters of water is worth 90 P per liter. If pure milk be worth Rs1.08 per liter, how proportion milk is there in the mixture?  Pick:  A) 5/2  B) 5/1  C) 5/7  D) 3/5  E) 1/2

Solution: The mean value is 90 P and price of water is 0 P   5/1y the alligation rule : Quantity of milk / Quantity of water   = (90 - 0) / (108 - 90)   = 90 / 18= 
90 / 18 = 5
5/1   proportion milk is 5/1 there in the mixture   5/1
Answer: B
A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man? Choose the correct answer:
A) 5.79
B) 5.28
C) 5.76
D) 32.9
E) 5.73

Solution: M = 6   S = 1.2   DS = 7.2   US = 4.8   x/7.2 + x/4.8 = 1   x = 2.88   D = 2.88 * 2= 
2.88 * 2 = 5.76
5.76   Answer:5.76
Answer: C
If the average of 5x and 8y is greater than 90, and x is twice y, what is the least integer value of x ? Choices.
A) 4	B) 5	C) 20	D) 21	E) 23

Solution: If y is greater than 110 percent of x, is y greater than 75?   (1)x>75x>75   (2) y−x=10y−x=10   Pls verify.   1) Sufficient.   y > 1.1 x and x > 75. Min(x) = 75   y > 1.1 * 75   y > 82.5   2) Insufficient. Substituting (x=y-10) in y > 1.1x   y > 1.1(y-10)   y < 110   Hence 4.
Answer: A
Sum of the squares of three numbers is 138 and the sum of their products taken two at a time is 131. Find the sum?
Choose the correct choice:	A) 20	B) 21	C) 24	D) 26	E) 28

Solution: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 138 + 2* 131   a + b + c = √400 = 20   20
Answer: A
A certain bacteria colony doubles in size every day for 11 days, a which point it reaches the limit of its habitat and can no longer grow. If two bacteria colonies start growing simultaneously, how many days will it take them to reach the habitat’s limit?
Pick:
A) 6.33  B) 7.5  C) 10  D) 15  E) 19

Solution: Case 1: Consider the bacteria num to be B. As it doubles every day, number of bacteria at the end of each day would be   Day 1 – B   Day 2 – 2B   Day 3 – 4B   Day 4 – 8B   .   .   .   Day 11 – 2^19 B   It can be implied that the capacity of the habitat is 2^19 B.   Case 2: There are 2 bacteria which keep doubling every day. So, the count would be   Day 1 – 2B   Day 2 – 4B   Day 3 – 8B   .   .   .   Day 18 – 2^18 B   Day 19 – 2^19 B --> this is the point where the habitat is filled to its capacity.   Hence, 10 is the answer   10
Answer: C
The average of five numbers is 27. If one number is excluded, the average becomes 24. The excluded number is?
Choose the correct choice from the following answers.
A) 36 B) 37 C) 38 D) 39 E) 40

Solution: Excluded number = (27 * 5) - (24 * 4)   = 135 - 96= 
135 - 96 = 39
39.   Answer: 39
Answer: D
If rupee one produces rupees nine over a period of 40 years, find the rate of simple interest?
Choose the correct choice from the following options:  A) 22 1/7%  B) 22 7/2%  C) 29 1/2%  D) 22 1/2%  E) 22 1/3%

Solution: 9 = (1*40*R)/100   R = 22 1/2 %   Answer: 22 1/2%
Answer: D