MU-NLPC/Calc-aqua_rat huggingface dataset:
a survey of n people in the town of badaville found that 50% of them prefer brand A.another survey of 100 people in the town of Chotaville found that 60% prefer brand A.In total 55% of all the people surveyed prefer brand A.What is the total number of people surveyed?	Choose the correct answer:  A) 100  B) 200  C) 300  D) 400  E) 500

Solution: .5*n+.6*100=.55*(n+100)   n=100   total people surveyed=n+100= 
+100 = 100
100+100= 
100+100 = 200
200   ANSWER:200
Answer: B
The average age of 36 students in a group is 14 years. When teacher’s age is included to it, the average increases by one. What is the teacher’s age in years?  Choose the correct option: A) 31 B) 36 C) 41 D) 51 E) None

Solution: Sol.   Age of the teacher = ( 37 × 15 – 36 × 14 ) years = 51 years.   Answer 51
Answer: D
The average age 18 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?  Choose the correct choice from the following answers
A) 18  B) 99  C) 77  D) 26  E) 36

Solution: 18 * 2= 
18 * 2 = 36
36 years   Answer: 36
Answer: E
Of the three-digit integers greater than 600, how many have two digits that are equal to each other and the remaining digit different from the other two?
Choose the correct choice from the following answers: A) 90 B) 82 C) 80 D) 107 E) 36

Solution: Three digit number can have only following 3 patterns:   A. all digits are distinct;   B. two digits are alike and third is different;   C. all three digits are alike.   We need to calculate B. B=Total - A - C   Total numbers from 600 to 999 = 399 (3-digit numbers greater than 600);   A. all digits are distinct = *4*9*8=288 (first digit can have only three values 7, 8, or 9   C. all three are alike =4 (666,777, 888, 999).   So, 399-288-4=107   Answer: 107
Answer: D
A group of n students can be divided into equal groups of 4 with 3 student left over or equal groups of 5 with 3 students left over. What is the sum of the two smallest possible values of n?	Select.
A) 66
B) 46
C) 49
D) 53
E) 86

Solution: 4x+3 = 5y+3...........ie: 4x-5y = 0   x,y must be >1 and y is even ie ( 2,4,6,..etc)   if y = 2 thus x = fraction (not possible)   if y = 4 thus x =5 n =23   if y = 6 thus x = not possible fraction   if y =8 thus x = 10 n =43   23+43 = 66.....   66
Answer: A
A and B start a business with Rs.1500 and Rs.3000 respectively. Hoe should they share their profits at the end of one year?  Select the correct option: A) 3:5 B) 3:4 C) 3:1 D) 1:2 E) 3:9

Solution: They should share the profits in the ratio of their investments.   The ratio of the investments made by A and B =   1500 : 3000 => 1:2   Answer:1:2
Answer: D
A trader sells goods to a customer at a profit of k% over the cost price, besides it he cheats his customer by giving 880 g only instead of 1 kg. Thus his overall profit percentage is 255. Find the value of k? Select
A) 8.33%	B) 8.25%	C) 10%	D) 12.5%	E) None

Solution: Solution: % Profit = 25 /100 = (120 +k)/ 880   → k = 100   Thus,   Net % profit = (100 *100) /1000= 
(100 *100) /1000 = 10
10%.   Answer: Option 10%
Answer: C
Three numbers are in the ratio 3:5:7. The largest number value is 42. Find difference between Smallest & largest number is?
Pick one:
A) 20  B) 24  C) 26  D) 28  E) 30

Solution: == 3:5:7   Total parts = 15   = The largest number value is 42   = The largest number is = 7   = Then 7 parts -----> 42 ( 7 * 6 = 42 )   = smallest number = 3 & Largest number = 7   = Difference between smallest number & largest number is = 7 - 3= 
7 - 3 = 4
4= Then 4 parts -----> 24 (4 * 6 = 24)   24
Answer: B
A train running at the speed of 56 km/hr crosses a pole in 9 seconds. Find the length of the train?  Answers.
A) 140 B) 272 C) 278 D) 277 E) 112

Solution: Speed = 56*(5/18) m/sec = 140/9 m/sec   Length of Train (Distance) = Speed * Time     (140/9) * 9= 
  (140/9) * 9 = 140
140 meter   140nswer: 140
Answer: A
A train which is 150m. long passes a platform of 200 m in 15 sec. What is the speed of the train?
Select
A) 36 km/hr
B) 64 km/hr
C) 84 km/hr
D) 91 km/hr
E) 95 km/hr

Solution: total distance cover by train in 15sec=150+200m   speed=distance/time   speed=350/15(m/s)   speed in km/hr=350/15*18/5= 
350/15*18/5 = 84
84km/hr   ANSWER:84 km/hr
Answer: C
A certain lab experiments with white and brown mice only. In one experiment, 2/3 of the mice are white. If there are 15 brown mice in the experiment, how many mice in total are in the experiment?
Select the correct option
A) 45 B) 33 C) 26 D) 21 E) 10

Solution: Let total number of mice = M   Number of white mice = 2/3 M   Number of brown mice = 1/3 M = 15   => M = 45   45nswer 45
Answer: A
If you divide 7^777 by 5, which remainder do you get?  Choose the correct choice from the following answers:
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: The units digit of 7^1 is 7.   The units digit of 7^2 is 9.   The units digit of 7^3 is 3.   The units digit of 7^4 is 1.   The units digit of 7^5 is 7.   etc...   The units digit of 7^n repeats in blocks of 4: {7, 9, 3, 1}   The remainder of 777/4 is 1.   So the units digit of 7^777 is 7.   The remainder of 7^777 / 5 is 2.   The answer is 2.
Answer: C
If y exceeds x by 10%, then x is less than y by?  Choose the correct choice from the following options:	A) 16 2/9%	B) 16 3/3%	C) 16 2/3%	D) 12 2/3%	E) 9 1/11%

Solution: X=100	y=110   110------10   100-------? => 9 1/11%   Answer:9 1/11%
Answer: E
A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A?
Pick
A) 2399 B) 2889 C) 2830 D) 2878 E) 3000

Solution: 3000xplanation:   60*5:36*6:75*3   100: 72: 75   100/247 * 7410= 
100/247 * 7410 = 3_000
3000   Answer: 3000
Answer: E
A gardener increased the length of a rectangle-shaped garden by 20 percent and decreased its width by 5 percent. The area of the new garden	Choose one
A) has increased by 18 percent  B) has increased by 14 percent  C) has increased by 7 percent  D) is exactly the same as the old area  E) cannot be expressed in percentage terms without actual numbers

Solution: Let L be the original length and let W be the original width.   The original area was L*W.   The new area is 0.95W*1.2L = (0.95)(1.2)L*W = 1.14*L*W   The answer is has increased by 14 percent.
Answer: B
Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 52% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?	Choices.
A) 60%	B) 50%	C) 25%	D) 17%	E) 10%

Solution: {Total} = {finance} + {marketing} - {both} + {neither}   100 = 25 + 52 - {both} + 40   {both} = 17%.   Answer: 17%.
Answer: D
In a business, A and C invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by A and B was 3 : 2 . If Rs 157300 was their profit, how much amount did B receive? Choose the correct choice from the following answers:
A) 48000
B) 48200
C) 48400
D) 48600
E) None of these

Solution: Explanation :   Assume that investment of C = x   Then, investment of A =2x   Investment of B = 4x/3   A:B:C = 2x : 4x/3 : x = 2 : 4/3 : 1 =6 : 4 : 3   B's share = 157300 * 4/(6+4+3) = 157300*4/13   = 12100*4= 
12100*4 = 48_400
48400. Answer : Option 48400
Answer: C
At what time between 2 and 3 o'clock will the hands of a clock be together? Select the correct option.
A) 120/28 B) 120/22 C) 120/19 D) 120/11 E) 120/112

Solution: The hands of a clock would be together when the angle between The hour hand and minute hand is Zero. Now apply the formula: θ=∣∣∣30h−112m∣∣∣θ=|30h−112m|   Here θθ = 0   ⇒11/2m – 30h = 0   ⇒11/2m – 30×2 = 0   ⇒ m = 120/11   Answer : 120/11
Answer: D
The purchase price of an article is $48. In order to include 15% of cost for overhead and to provide $12 of net profit, the markup should be Choices.
A) 15%  B) 25%  C) 35%  D) 40%  E) 45%

Solution: Cost price of article = 48$   % of overhead cost = 15   Net profit = 12 $   We need to calculate % markup   Net profit as % of cost price = (12/48)*100= 
(12/48)*100 = 25
25%   Total markup should be= 25 + 15= 
25 + 15 = 40
40%   Answer 40%
Answer: D
Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm.  Pick one
A) 200	B) 234	C) 285	D) 345	E) 244

Solution: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (15) = 285 cm2   Answer: Option 285
Answer: C
If a and b are the roots of the equation x2 - 9x + 20 = 0, find the value of a2 + b2 + ab?  Select the correct option.
A) 57	B) 59	C) 61	D) 63	E) 65

Solution: a2 + b2 + ab = a2 + b2 + 2ab - ab   i.e., (a + b)2 - ab   from x2 - 9x + 20 = 0, we have   a + b = 9 and ab = 20. Hence the value of required expression (9)2 - 20 = 61.   Option 61
Answer: C
there are 10 girls and 20 boys in a classroom. what is the ratio of girls to boys?
Pick:
A) 1/2
B) 1/3
C) 1/5
D) 10/30
E) 2/5

Solution: If girls is 10 and boys is 20, then 10/20.   so ratio of girls to boys is = 10/20 = 1/2   1/2NSWER:1/2
Answer: A
Rahul is 30 years older than his daughter Mary. In 20 years Rahul will be twice as old as Mary. What is Mary current age.  Choose the correct choice from the following choices:	A) 12	B) 14	C) 10	D) 16	E) 18

Solution: Now: Mary = x, Rahul =x+30   In 20 years Mary = x+20, Rahul= x+30+20 or 2(x+20)   x+30+20= 2(x+20)   x+50=2x+40   50-40=2x-x   x= 10   Mary is 10 years old   Answer : 10
Answer: C
In how many T ways can 4 white and 3 black chess pieces be arranged in a row such that they occupy alternate places? Assume that the pieces are distinct. Answers
A) T=288	B) T=144	C) T=12	D) 48	E) 96

Solution: 4 white chess pieces can be arranged in 4! ways and 4 black pieces can be arranged in 3 ! ways.   W_W_W_W   Number of ways = 4!*3! = 24 * 6= 
24 * 6 = 144
144   Answer T=144
Answer: B
The first term in a sequence is 1 and the second term is 21. From the third term on each term is the average (arithmetic mean) of all preceding terms. What is the 38th term in the sequence?	Pick one.
A) 8
B) 11
C) 21
D) 38
E) 49

Solution: The third term is 11 since this is the average of 1 and 21.   Then the next terms will all be 11 since the average stays at 11.   The answer is 11.
Answer: B
A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?	Pick one
A) 3.7	B) 2.8	C) 2.5	D) 4.7	E) 2.7

Solution: 2.5   100*(20/100)= 
100*(20/100) = 20
20 --- 10   ? --- 1=> Rs.2   100 --- 80   ? --- 2 => Rs.2.5
Answer: C
During 2001, a stock lost 40 percent of its value. During the following year, the stock's value increased by 200 percent. Which of the following is the percent change in the stock's value during those two years?
Select:
A) 60 percent decrease  B) 40 percent decrease  C) 20 percent increase  D) 80 percent increase  E) 140 percent increase

Solution: Let the value of the stock in 2000 be 100, then in 2001 its value would be 100*(1-40/100)=100*0.6= 
100*0.6 = 60
60 and in 2002 its value would be   60*(1+200/100)= 
  60*(1+200/100) = 180
180. Hence during those two years the value of the stock increased from 100 to 180, so by 80%.   Answer: 80 percent increase.
Answer: D
2, 6, 14, 26, 42, ?  Select.
A) 62
B) 56
C) 74
D) 57
E) 32

Solution: The pattern is + 4, + 8, + 12, + 16, +20   62nswer : 62.
Answer: A
The average of five integers is 63, and none of these integers is greater than 100. If the average of three of the integers is 65, what is the least possible value of one of the other two integers? Choose the correct choice from the following answers:
A) 5	B) 15	C) 20	D) 21	E) 30

Solution: The sum of two other integers = 63*5-65*3= 
63*5-65*3 = 120
120   the least possible value of one integer when the other integer has the highest value of 100=120 - 100= 
120 - 100 = 20
20   ANSWER:20
Answer: C
According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 6 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice? Choose the correct choice.
A) 25
B) 34
C) 50
D) 67
E) 50

Solution: Orange juice concentrate: water::1:3   total quantity of orange juice = 200*6= 
200*6 = 1_200
1200 oz   so Orange juice concentrate: water :: 300 oz:900 oz   no. of 6 oz can= 300 oz/6 oz = 50   Answer 50, 50 cans
Answer: E
There are n members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 36 possible combinations in which Michael is not selected, what is the value of n?	Choose the correct choice from the following
A) 8  B) 9  C) 10  D) 11  E) 12

Solution: The combinations of two people, in which Michael was not selected = 36   The number of ways two people can be selected from m people = m*(m-1)/2   Let m be the number of people excluding Michael.   Then m*(m-1) = 72 = 9*8   Thus, n = m + 1(Michael) = 10   The answer is 10.
Answer: C
A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
Choose the correct choice from the following answers:  A) Rs.3600  B) Rs.3700  C) Rs.3800  D) Rs.3900  E) Rs.4000

Solution: Area = (l + b – d) d   (80 + 60 – 10)10 => 1300 m2   1300 * 3 = Rs.3900   ANSWER:Rs.3900
Answer: D
A thief steels a car at 6a.m. and drives it at 50kmph. The theft is discovered at 7a.m. and the owner sets off in another car at 70 kmph. When will he overtake the thief?	Options.
A) 9a.m. B) 9.30a.m. C) 10a.m. D) 11.45a.m. E) 10.15a.m.

Solution: Suppose the thief overtakes x hours after 6a.m.   Distance covered by the thief in x hrs = distance covered by the owner in (x-1 hours)   50x = 70(x-1)   20x = 70   x = 7/2 hrs   Thief is overtaken at 9.30a.m.   Answer is 9.30a.m.
Answer: B
Six persons A,B,C,D,E &F went to soldier cinema. There are six consecutive seats. A sits in the first seat followed by B, followed by C and so on. If A taken on of the six seats, then B should sit adjacent to A. C should sit adjacent to A or B. D should sit adjacent to A, B or C and so on. How many possibilities are there ?	Answers: A) 30 B) 32 C) 34 D) 36 E) 38

Solution: First we have to arrange A, there is 1 method for it, for second person 32, there are 2 methods one left and one right, for third 2 methods are there same as for 32 similarly for others, so total number of methods = 1*2*2*2*2*2= 
1*2*2*2*2*2 = 32
32   ANSWER:32
Answer: B
a man owns 2/3 of market reserch beauro buzness,and sells 3/4 of his shares for 30000rs,what is the value of buzness? Select:
A) 75000	B) 160000	C) 170000	D) 60000	E) 70000

Solution: If value of business=x   Total sell (2x/3)(3/4)=30000   ->x=60000   ANSWER:60000
Answer: D
In what time will a train 100 m long cross an electric pole, it its speed be 162 km/hr?  Choose the correct choice from the following answers
A) 2.5 B) 2.9 C) 2.4 D) 2.8 E) 2.22

Solution: Speed = 162 * 5/18= 
162 * 5/18 = 45
45 m/sec   Time taken= 100/45   = 2.22 sec.   Answer:2.22
Answer: E
A basket has 5 oranges and 4 oranges. Three fruits are picked at random. The probability that at least 2 oranges are picked is  Choose the correct choice from the following
A) 23/41	B) 1/23	C) 25/42	D) 34/57	E) 3/41

Solution: Total fruits = 9   Since there must be at least two oranges,   (⁵25/42₂ * ⁴25/42₁)/⁹25/42₃ + ⁵25/42₃/⁹25/42₃ = 25/42   25/42
Answer: C
The volumes of two cones are in the ratio 1 : 40 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?  Choose the correct option:
A) 8:5	B) 8:9	C) 2:2	D) 8:2	E) 2:8

Solution: The volume of the cone = (1/3)πr2h   Only radius (r) and height (h) are varying.   Hence, (1/3)π may be ignored.   V1/V2 = r1^2 . h1/r2^2. h2 => 1/40   = (1)^2h1/(2)^2h2   => h1/h2 = 8/5   i.e. h1 : h2 = 8:5   8:5nswer: 8:5
Answer: A
1, 2, 3, 10, ?, 9802
Choose the most appropriate option:
A) 99	B) 8	C) 73	D) 28	E) 27

Solution: 99nswer: 99) 99
Answer: A
A shopkeeper sells 300 metres of cloth for Rs. 9000 at a loss of Rs.6 per metre. Find his cost price for one metre of cloth? Choose the correct answer:
A) s.59	B) s.58	C) s.36	D) s.46	E) s.13

Solution: SP per metre = 9000/300   = Rs. 30 Loss per metre   = Rs. 6 s.36P per metre = 30 + 6   = Rs.36   Answer: s.36
Answer: C
Andrew travelling to 7 cities. Gasoline prices varied from city to city.
$1.75, $1.61, $1.79, $2.11, $1.96, $2.09, $1.83. What is the median gasoline price?	Answers
A) $1 B) $1.83 C) $1.92 D) $2.13 E) $2.15

Solution: Ordering the data from least to greatest, we get:   $1.61, $1.75, $1.79, $1.83, $1.96, $2.09, $2.11   The median gasoline price is $1.83. (There were 3 states with higher gasoline prices and 3 with lower prices.)   $1.83
Answer: B
Anu can do a work in 6 days and Binu alone in 9 days. Anu and Binu undertook to do it for Rs.4800. With help of Minu, they completed the work in 3 days. How much is to be paid to Minu and Anu?  Answers: A) s.750, Rs.2250 B) s.2000, Rs.750 C) s.750, Rs.2000 D) s.800, Rs.2400 E) s.900, Rs.1250

Solution: Minuâ€™s one dayâ€™s work = 1/3 - 1/6 + 1/9= 1/3 - 5/18 = 1/18   Anuâ€™s wages: Binuâ€™s wages: Minuâ€™s wages = 1/6 : 1/9 : 1/18 = 6: 4: 2   Minuâ€™s share = Rs.4800* 2/12 = Rs.800   Anuâ€™s share = Rs.4800* 6 /12= 
.4800* 6 /12 = 0.24
Rs.2400   ANSWER:s.800, Rs.2400
Answer: D
A bowl was filled with 10 ounces of water, and 0.007 ounce of the water evaporated each day during a 50-day period. What percent of the original amount of water evaporated during this period? Choose the correct choice
A) 0.004%
B) 0.04%
C) 0.40%
D) 4%
E) 3.5%

Solution: Total amount of water evaporated each day during a 50-day period = .007 * 50   =.007 * 100/2   = .7/2= 
.7/2 = 0.35
.35   percent of the original amount of water evaporated during this period= (.35/10) * 100= 
(.35/10) * 100 = 3.5
3.5 %   Answer 3.5%
Answer: E
xa=yb=zc and y2=xz. Find b.	Select the correct option:  A) 2ac/a+c  B) 7ac/a+c  C) 1ac/a+c  D) 6ac/a+c  E) 3ac/a+c

Solution: 2ac/a+cNSWER : 2ac/a+c
Answer: A
A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 6x km.	Choose the correct choice from the following options.
A) 16 B) 48 C) 24 D) 19 E) 12

Solution: Total time taken = x/40 + 2x/20 hours   = 5x/40 = x/8 hours   Average speed = 6x/(x/8) = 48 kmph   Answer: 48
Answer: B
The sum of a number and the number preceding it is 33. By how much is two less than six times the
number?  Pick.
A) 196	B) 94	C) 90	D) 100	E) 120

Solution: two numbers must be 16 and 17   16+17= 
16+17 = 33
33   required number is 17   six times of this number= 6*17= 
6*17 = 102
102   two less than 102= 102-2= 
102-2 = 100
100   ANSWER:100
Answer: D
A seller has 1000 kg of rice part of which he sells at 8% profit and the rest at 18% profit. He gains 14%. The quantity sold at 18% profit is? Select the correct option:
A) 300 kg B) 350 kg C) 550 kg D) 600 kg E) 700 kg

Solution: By rule of alligation,   Profit% by selling 1st part Profit% by selling 2nd part   8 18   Net % profit   14   18-14= 
18-14 = 4
4 14-8=6   => Quantity of part1 : Quantity of part2 = 4 : 6 = 2 : 3   Total quantity is given as 1000 kg. So quantity of part2 (quantity sold at 18% profit)   =1000×35   = 600 kg   600 kg
Answer: D
An equity analyst needs to select 3 stocks for the upcoming year and rank these securities in terms of their investment potential. If the analyst has narrowed down the list of potential stocks to 7, in how many ways can she choose and rank her top 3 picks?
Select the correct option:
A) 21 B) 35 C) 210 D) 420 E) 840

Solution: Number of ways of choosing 3 stocks = 72103   Number of ways of ranking the chosen stocks = 3!   Hence total ways of choosing and ranking = 72103 * 3! = 7!/4! = 7*6*5= 
7*6*5 = 210
210   210orrect Option: 210
Answer: C
How many positive integers less than 300 can be formed using the numbers 1, 2, 3 and 5 for the digits?	Choose the correct choice from the following
A) 48 B) 52 C) 66 D) 68 E) 84

Solution: Notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero:   0 1 1   1 2 2   2 3 3   2 5 5   Number of possibilities = 3*4*4= 
3*4*4 = 48
48.   Then, just add up the number of 1 digits numbers= 4, so total is  48+4= 
 48+4 = 52
52.   Answer: 52
Answer: B
70, 75, 80, 85, 90, 105, 105, 130, 130, 130
The list shown consists of the times, in seconds, that it took each of 10 schoolchildren to run a distance of 400 on of meters. If the standard devastation of the 10 running times is 25.4 seconds, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times?
Choices:	A) one	B) two	C) three	D) four	E) five

Solution: The most time consuming part in this question is to define the mean. Under exam pressure and time pressure it is very easy to make mistake.   it is easier to group numbers:  130*3= 
 130*3 = 390
390; 105*2=210; 75+85=160; 70+80=150; 90;   Next stage combine results, again using more convenient ways to calculate: 390+210= 
390+210 = 600
600; 160+150=310; 90. 600+310+90=1000. Since there are 10 numbers the mean is 100. Questions asks to find the quantity of numbers one SD BELOW the mean, which is 100-25,4=74,6. There are only two numbers below 74,6. The answer is two
Answer: B
A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 2 employees to 3 different offices? Choose the correct option
A) 5  B) 6  C) 7  D) 8  E) 9

Solution: Ans. Each employee can go into any of the two offices. Thus we have   => 3 * 3= 
3 * 3 = 9
9   Answer : 9
Answer: E
f1 (x) = x 0 ≤ x ≤ 1
= 1 x ≥ 1
= 0 otherwise
f2 (x) = f1(–x) for all x
f3 (x) = –f2(x) for all x
f4 (x) = f3(–x) for all x
How many of the following products are necessarily zero for every x:
f1(x) f2 (x), f2 (x) f3 (x), f2(x) f4 (x)
Pick one
A) 0  B) 1  C) 2  D) 3  E) 4

Solution: Explanation :   We have to consider positive and negative numbers for all the cases.   f1(x) is positive for positive numbers, and 0 for negative numbers. (0 for x = 0)   f2(x) is 0 for positive numbers, and positive for negative numbers. (0 for x = 0)   f3(x) is 0 for positive numbers, and negative for negative numbers. (0 for x = 0)   f4(x) is negative for positive numbers, and 0 for negative numbers. (0 for x = 0)   So, we see that, out of the 3 products in the question, f1(x)*f2(x) and f2(x)*f4(x) are always zero, for any x.   Answer : 2
Answer: C
If the simple interest on a certain sum of money for 6 years is one–fifth of the sum, then the rate of interest per annum is  Choose the correct choice from the following
A) 3.3%
B) 7.2%
C) 6.1%
D) 5.0%
E) 3.1%

Solution: Explanation:   Let the Principal(P) be x   Then, Simple Interest(SI) = x/5   Time(T) = 6 years   Rate of interest per annum(R) = (100×SI)/PT   = (100 × (x/5)/(x × 6) = 20/6 = 3.3%   3.3%nswer: Option 3.3%
Answer: A
The number of people at Ovations Bar in the hour from 12 p.m. to 1 p.m. was 50% greater than the number of people there from 11 a.m. to 12 p.m. The number of the people at the bar from 11 a.m. to 12 p.m. was 25% less than the number there from 10 a.m. to 11 a.m. If 75 people were at the bar from 11 a.m. to 1 p.m., which of the following is the number of people in the bar from 10 a.m. to 11 a.m.?	Choose the correct option
A) 10 B) 20 C) 30 D) 40 E) 50

Solution: No of people from 10 - 11 is x   No of people from 11 - 12 is 3x/4   No of people from 12 to 1 is (3/2)(3x/4)   Given that 3x/4 + (3/2)(3x/4) = (3x/4)(5/2) = 75   Then x = 40   40
Answer: D
The speed at which a man can row a boat in still water is 22 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 80 metres?
Choose the correct choice:
A) 12.59 B) 11.53 C) 15.69 D) 14.56 E) 18.98

Solution: Speed of the boat downstream = 22 + 3= 
22 + 3 = 25
25 kmph= 25 * 5/18 = 6.94 m/sHence time taken to cover 80 m = 80/6.94= 11.53 seconds.Answer:11.53
Answer: B