MU-NLPC/Calc-aqua_rat huggingface dataset:
2 dice are thrown simultaneously. Find the probability of getting a multiple of 2 on 1 dice and multiple of 3 on the second dice? Select the correct option:	A) 9/13	B) 11/36	C) 12/32	D) 13/45	E) 13/41

Solution: 11/36   11/36
Answer: B
John makes $60 a week from his job. He earns a raise and now makes $120 a week. What is the % increase?  Choose one
A) 16% B) 100% C) 17% D) 17.61% E) 17.56%

Solution: Increase = (60/60)*100 = (6/6)*100= 
(6/6)*100 = 100
100%.   100%
Answer: B
A professional gambler has won 40% of his 25 poker games for the week so far. If, all of a sudden, his luck changes and he begins winning 80% of the time, how many more games must he play to end up winning 60% of all his games for the week?
Pick
A) 20  B) 25  C) 30  D) 35  E) 40

Solution: Initially the person has played 25 games with probablity of winning as 40%   Thus, number of games won = 10   Later when the probability of winning changes to 80% and assuming x games were played by him:   Total number of win, 60% of all games =0.6(x+25)=10+0.8x=0.6(x+25)=10+0.8x   0.2x=50.2x=5   x=25 x=25   so, he has to play 25 games.   Alternatively, this could be solved by allegation method.   25 = 25games ;ANSWER:25
Answer: B
If two-third of a bucket is filled in four minutes then the time taken to fill the bucket completely will be . Pick:	A) 90 seconds	B) 70 seconds	C) 60 seconds	D) 100 seconds	E) 6 minutes

Solution: 2/3 filled in 4 mint   1/3 filled in 2 mint   then 2/3+1/3=4 + 2= 
4 + 2 = 6
6 minutes   ANSW6 minutesR: 6 minutes
Answer: E
Can you tell Which of the following fractions is the largest?	Select the correct option
A) 5/6
B) 11/14
C) 12/15
D) 17/21
E) 29/35

Solution: another way is by taking LCM of denominators(2*3*5*7)   (a) 175 (as lcm is 2*3*5*7 where 2*3 part is already in denominator just multiply 5*7 to numerator) ,similarly   (b) 165   (c)168   (d)170   (e)174   clearly (a) is largest..   5/6ns 5/6
Answer: A
The product of two positive integers is 323 and their difference is 2. What is the smaller number?
Select:
A) 17
B) 18
C) 16
D) 19
E) 14

Solution: Let's use trial and error to find the two numbers.   20*18= 
20*18 = 360
360 (too high)   19*17= 
19*17 = 323
323   The answer is 17.
Answer: A
A merchant marks his goods up by 20% and then offers a discount of 5% on the marked price. What % profit does the merchant make after the discount?  Choose the correct choice from the following options
A) 8%  B) 6 %  C) 21%  D) 14%  E) 17%

Solution: Let the price be 100.   The price becomes 120 after a 20% markup.   Now a discount of 5% on 120.   Profit=114-100   14%   answer 14%
Answer: D
The monthly incomes of A and B are in the ratio 5 : 2. B's monthly income is 12% more than C's monthly income. If C's monthly income is Rs. 15000, then find the annual income of A? Choose the correct choice
A) 187888	B) 276889	C) 267777	D) 504000	E) 297112

Solution: B's monthly income = 15000 * 112/100 = Rs. 16800   B's monthly income = 2 parts ----> Rs. 16800   A's monthly income = 5 parts = 5/2 * 16800 = Rs. 42000   A's annual income = Rs. 42000 * 12 = Rs.504000   Answer:504000
Answer: D
Vinod climbs 60 steps in 40 seconds. At that rate, how many steps could he climb in 150 seconds?	Choose the correct option:
A) 223
B) 221
C) 222
D) 224
E) 225

Solution: Solution:   Let's calculate the steps he climbs per second: 60:40 = 1.5   So he climbs 1.5 steps per second.   For 150 seconds Vinod climb: 1.5 × 150 = 225   Answer 225
Answer: E
Bookman purchased 60 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for $10 each. If 14 copies were sold and the total value of the remaining books was 660, how many paperback copies were sold?
Choose the correct choice from the following choices
A) 22
B) 24
C) 26
D) 28
E) 30

Solution: The bookman had 10 hardback ad  60-10= 
 60-10 = 50
50 paperback copies;   14 copies were sold, hence  60-14= 
 60-14 = 46
46 copies were left. Let # of paperback copies left be p then 10p+20(46-p)=660 --> 10 p=260 --> p=26   # of paperback copies sold is 50-26= 
50-26 = 24
24   Answer: 24
Answer: B
If a fair 6-sided die is rolled three times, what is the probability that exactly one 6 is rolled? Choose the correct option
A) 25/216 B) 50/216 C) 25/72 D) 25/36 E) 5/6

Solution: Total ways in which a 6-sided die can be rolled three times = 6*6*6= 
6*6*6 = 216
216   To get exactly one 6, there are three ways:   A 6 on the first roll and non 6 on other two rolls. This can be done in 1*5*5= 
1*5*5 = 25
25 ways.   The 6 could be on the second or third roll too. So total favorable cases= 25*3= 
25*3 = 75
75   Required Probability= 75/216 = 25/72   Answer (25/72)
Answer: C
Company A imported 10,000 widgets made of either brass or aluminum. The widgets are painted blue, red or green. If 20 percent of the widgets are made of brass and of those 20 percent are painted green and 40 percent are painted red how many brass widgets painted blue were imported?  Select: A) 420 B) 840 C) 800 D) 1680 E) 2100

Solution: Answer A.   We are told that 10% of all imported widgets are made of brass and of those, 20% are green and 40% are red. Since we know that there are only three colors, the remaining 40% must be blue. 40% blue of 20% brass widgets leads to 8% blue brass widgets out of the total 10,550 widgets.   10,000 /100 * 8 = 800.   Answer 800.
Answer: C
What is the probability that a leap year has 53 Sundays and 52 Mondays? Options.
A) 1/9 B) 1/7 C) 1/5 D) 1/1 E) 1/2

Solution: A leap year has 52 weeks and two days   Total number of cases = 7   Number of favourable cases = 1   i.e., {Saturday, Sunday}   Required Probability = 1/7   Answer:1/7
Answer: B
Some of the people in Town A are left-handed, some are tall, some are both, and some are neither. In Town Y, three times as many people are left-handed > as are left-handed in Town A, three times as many people are tall as are tall in Town A, three times as many people are both as are both in Town A, but no one is neither. If the total number of people in Town A is four times greater than the total number of people in Town Y, which of the following could be the number of people in Town A who are neither left-handed nor tall?	Choose the correct option:  A) 23  B) 39  C) 72  D) 143  E) 199

Solution: Yes, correct answer is indeed D.   {A}={Left} + {Tall} - {Both} + {Neither};   {Y} = 3*{Left} + 3*{Tall} - 3*{Both};   Since the total number of people in Town A is four times greater than the total number of people in Town Y, then:   {Left} + {Tall} - {Both} + {Neither}=4*(3*{Left} + 3*{Tall} - 3*{Both});   {Neither}=11*({Left} + {Tall} - {Both}), which means that # of people in Town A who are neither left-handed nor tall must be a multiple of 11.   Only answer choice D, is a multiple of 11: 143=11*13.   Answer: 143.
Answer: D
What is the difference between the local value of 6 and 6 in the number 2664?
Select the correct option
A) 540
B) 377
C) 288
D) 277
E) 112

Solution: Explanation:   600 â€“ 60 = 540   540nswer: 540
Answer: A
Company X sells a selection of products at various price points. Listed below are unit sales made for one particular day. How many unit sales on that day were greater than the mean sale price but less than the median sale price?
$50, $50, $97, $97, $97, $120, $155, $155, $155, $199, $199 Choose the correct choice from the following answers.
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: Taking the prices of products in ascending order(already arranged)   $50, $50, $97, $97, $97, $120, $155, $155, $155, $199, $199   we see that median value is the 6th value as there in total 11 values given   0rithmetic mean = total/number of entries = 1374/11 =124.9090   We are asked to find how many unit sales on that day were greater than the mean sale price but less than the median sale price   as we can clearly see that there is no value between $120 and $124.90, answer is 0 unit   Correct 0nswer - 0   0nswer is 0.
Answer: A
Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is not an even ?  Choose the correct choice from the following options.
A) 1/2 B) 1/4 C) 2/3 D) 2/5 E) 3/7

Solution: Total number of cases = 6*6= 
6*6 = 36
36   Favourable cases= [(1,3),(1,5),(1,1),(3,1),(3,3),(3,5),(5,1),(5,3),(5,5)] = 9   So Probability = 9/36 = 1/4   Answer is 1/4
Answer: B
If x and y are positive odd integers, then which of the following must also be an odd integer? I. x^(y+2) II. x(y+3) III. (y+1)^(x-1) + 1
Choose the correct option:
A) I only  B) I,III only  C) II only  D) III only  E) II,III only

Solution: let x= 5, y= 3   I. 5^5 = > Odd   II. 5*6 = > even   III. 4^4 +1 = > Odd   Answer : I,III only
Answer: B
Bills' school is 10 miles from his home. He travels 4 miles from school to football practice, and then 2 miles to friend's house. If he is then x miles from home, what is the range of possible values for x?  Choose the correct choice from the following answers.
A) 2≤x≤10	B) 4≤x≤10	C) 4≤x≤12	D) 4≤x≤16	E) 6≤x≤16

Solution: 1.If his football ground and his friend's house lie on the way to his house.   then the distance can be minimum .   10 -(4+2)= 
10 -(4+2) = 4
4   2.If his football ground and his friends house lie in the opposite direction from the way to his house.   this will then give us the maximum distance.   10+(4+2)= 
10+(4+2) = 16
16   therefore , x will lie between 4 and 16   So, Correct answer will d) 4≤x≤164≤x≤16   ANSWER:4≤x≤16
Answer: D
A man whose speed is 4 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1 kmph, find his average speed for the total journey?
Select.
A) 5	B) 4	C) 4.5	D) 3.75	E) 3

Solution: M = 4   S = 1   3.75S = 5   US = 3   AS = (2 * 5 * 3) /8= 
(2 * 5 * 3) /8 = 15/4 = around 3.75
3.75   Answer: 3.75
Answer: D
If a shirts can be purchased for c rupees, how many shirts can be purchased for t rupees?	Choose the correct answer:
A) at/c
B) a/c
C) ac/t
D) t/(ac)
E) c/(at)

Solution: at/cns = at/c
Answer: A
A certain sum of money is invested for one year at a certain rate of simple interest. If the rate of interest is 3% higher, then the invest earned will be 25% more than the interest earned earlier. What is the earlier rate of interest?  Pick one
A) 11	B) 787	C) 17	D) 12	E) 77

Solution: If the interest earned is 25% more than the earlier interest then the rate of interest also should be 25% higher than the earlier rate.   Let the earlier rate of interest be x%.   Now it will be (x + 3)%   % increase = (x + 3) - x/x * 100 = 25   => x = 12   Answer: 12
Answer: D
How many 4 digit numbers can be formed with the digits 0, 1, 2, 3, 4, 5, 6, 7 and 6?  Select
A) a. 220	B) b. 249	C) c. 432	D) d. 216	E) e. 288

Solution: Taking Question with it's same language as given   To make number divisible by 5, the unit digit should be either 0 or 5 only   Case 1: If unit digit is fixed as zero   With two6s The choice to fill the remaining three digits = 3C2 x 5 = 15   With all remaining 3 digits different, The choice to fill the remaining three digits = 6 x 5 x 4= 120   Total Such cases = 120+15= 
120+15 = 135
135   Case 2: If unit digit is fixed as Five   With two6s and one0The choice to fill the remaining three digits= 2 [6605 or 6065]   With two6s and without0The choice to fill the remaining three digits = 3C2 x 4 = 12   With all remaining 3 digits different, and one0The choice to fill the remaining three digits = 2 (ways to place zero) x 5 x 4= 40   With all remaining 3 digits different, and without0The choice to fill the remaining three digits = 3 x 5 x 4= 60   Total Such cases = 2+12+40+60= 
2+12+40+60 = 114
114   Total numbers= 135+114 = 288   ANSWER OPTION d. 216
Answer: D
A basketball coach is making the starting lineup for his team of 10 players. There are 4 guards on the team and 6 post players. How many different groups of 5 players could he choose assuming he must pick 2 guards and 3 post players? Select
A) 100 B) 120 C) 140 D) 160 E) 180

Solution: (4c2)*(6c3)   [4!/(2!*2!)]*[6!/(3!*3!)]   6*20   120   120
Answer: B
A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?  Answers
A) 222 B) 287 C) 277 D) 400 E) 281

Solution: 2*12 : 3*12 : 4*24   1: 3: 4   1/8 * 3200= 
1/8 * 3200 = 400
400   Answer: 400
Answer: D
A white paper 2 inches wide is placed around a rectangular black paper with dimensions 8 inches by 12 inches. What is the area of the white paper, in square inches? Choose the most appropriate option.
A) 96 B) 196 C) 128 D) 144 E) 168

Solution: This question is an example of a 'punch out' question - we have to find the area of EVERYTHING, then 'punch out' the part that we don't want.   We're told that a white paper 2 inches wide is placed around a rectangular black paper with dimensions 8 inches by 12 inches. We're asked for the area of the frame, in square inches.   Area of a rectangle = (length)(width)   So the area of the black paper is... (8)(12) = 96   The white paper 'adds' 2 inches to the top, bottom, left and right 'sides' of the picture, so the area of EVERYTHING is...   (8+2+2)(12+2+2) = (12)(16) = 196   When we 'punch out' the area of the black paper, we'll be left with the area of the white paper:   192 - 96= 
192 - 96 = 96
96   Final Answer:   196
Answer: B
A number exceeds by 25 from its 3/8 part. Then the number is?	Choose the correct choice from the following options:
A) 38	B) 29	C) 27	D) 40	E) 91

Solution: Explanation:   x â€“ 3/8 x = 25   x = 40   Answer: 40
Answer: D
As x Decreases from 169 to 166, which of the following must increase?
I. 2x - 5
II. 1 - 1/x
III. 1/(x^2 - x) Select the correct option
A) I only	B) III only	C) I and II	D) I and III	E) II and III

Solution: I. 2x - 5 --> x decreases from 169 to 166 --> 2x decreases --> 2x - 5 decreases.   II. 1 - 1/x --> x decreases from 169 to 166 --> 1/x increases --> 1 -1/x decreases.   III. 1/(x^2 - x) --> x decreases from 169 to 166 --> x^2-x decreases --> 1/(x^2 - x) increases.   Answer: III only.
Answer: B
If a is the sum of p consecutive positive integers and b is the sum of q consecutive positive integers. For which of the following values of p and q is it impossible that a = b?
Choose the correct option
A) p = 2; q = 6	B) p = 3; q = 6	C) p = 10; q = 4	D) p = 7; q = 9	E) p = 10; q = 7

Solution: I approached this in a different way, although may be longer but it's certainly more intuitive   It is impossible that a = b if one of them is necessarily even while the other is necessarily odd   for two consecutive integers the sum is necessarily odd   for six consecutive integers the sum is necessarily odd (sum of 3two consecutive integerswhich are all odd)   Thus A is incorrect.   The sum of 3 consecutive integers can be even or odd (an odd integer from the first 2 + an additional integer which can be even or odd). Thus B is incorrect. You can do a similar approach for D and E (it follows that the sum of a specified odd number of consecutive integers can be odd or even).   Leaving us with C to be the only not-wrong answer. To confirm, you can easily deduce that the sum of 4 consecutive integers (sum of 2 odd integers) is necessarily even while the sum of 10 consecutive integers (sum of 5 odd integers) is necessarily odd. Thus p = 10; q = 4 is the right answer.
Answer: C
In a square box of side 16 centimeters small square boxes of side 4 centimeters are arranged. How many small square boxes fit into the large square box? Choose the correct choice from the following:
A) 12
B) 25
C) 16
D) 30
E) 20

Solution: The 4 centimeter side should be aligned to the 16 centimeter side ( 4 layer)   4 centimeter side should be aligned to the 16 centimeter side. (4 layer)   Maximum number of squares =4*4= 
4*4 = 16
16   Answer is 16
Answer: C
Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time? Pick:
A) 17 1/9 B) 17 1/0 C) 17 1/7 D) 17 1/2 E) 17 1/3

Solution: 1/20 + 1/30 - 1/40 = 7/120   120/7 = 17 1/7   Answer: 17 1/7
Answer: C
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 42 degrees. Find the temperature on Friday? Options.
A) 99  B) 277  C) 27  D) 34  E) 77

Solution: M + Tu + W + Th = 4 * 48= 
4 * 48 = 192
192   Tu + W + Th + F= 4 * 46= 
4 * 46 = 184
184   M= 42   Tu + W + Th = 192 -42= 
192 -42 = 150
150   F= 184 – 150 = 34   Answer:34
Answer: D
A four-character password consists of one letter of the alphabet and three different digits between 2 and 9, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible? Choose the correct choice from the following
A) 5,040	B) 17,472	C) 26,000	D) 37,440	E) 52,000

Solution: 4 character password: DLDD   First digit can be chosen in 8 ways.   The letter can be chosen in 26 ways.   Next digit can be chosen in 7 ways.   Next digit can be chosen in 6 ways.   This gives us 8*26*7*6ways   Now, the letter can also be DDLD so there will be another 8*26*7*6 ways   Total = 8*26*7*6*2 = 17,472 ways 17,472
Answer: B
if remainder is 19 , quotient is 61 and dividend is 507 then what is divisor ?	Choose the correct choice
A) 8  B) 18  C) 10  D) 12  E) 14

Solution: we know   dividend = divisor * quotient + remainder===> 507 = divisor * 61 + 19 =====> 488/61 = divisor ===> divisor = 8 8ns - 8
Answer: A
Train X crosses a stationary train Y in 60 seconds and a pole in 25 seconds with the same speed. The length of the train X is 300 m. What is the length of the stationary train Y?	Choose the correct choice: A) 187 m B) 420 m C) 197 m D) 167 m E) 186 m

Solution: Let the length of the stationary train Y be LY   Given that length of train X, LX = 300 m   Let the speed of Train X be V.   Since the train X crosses train Y and a pole in 60 seconds and 25 seconds respectively.   => 300/V = 25 ---> ( 1 )   (300 + LY) / V = 60 ---> ( 2 )   From (1) V = 300/25= 
300/25 = 12
12 m/sec.   From (2) (300 + LY)/12= 60   => 300 + LY = 60 (12) = 720   => LY = 720 - 300= 
720 - 300 = 420
420 m   Length of the stationary train= 420 m   Answer: 420 m
Answer: B
What is the present worth of Rs. 176 due in 2 years at 5% simple interest per annum	Select the correct option
A) 110
B) 120
C) 150
D) 160
E) None of these

Solution: Explanation:   Let the present worth be Rs.x   Then,S.I.= Rs.(176 - x)   = (x*5*2/100) = 176 - x   = 10x = 17600 - 100x   = 110x = 17600   x= 160   Answer:160
Answer: D
if Juan takes 10 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?	Pick: A) 11x/y B) 10x/y C) x/11y D) 11/xy E) xy/11

Solution: Answer is B.   The rate of running hards: 10 minutes per y hards.   Thus the time for running x hards = x hards * 10 minutes/y hards = 10x/y
Answer: B
The weight of four dogs is determined to be 25 pounds, 31 pounds, 43 pounds and 41 pounds respectively. The weight of a fifth dog is determined to be y pounds. If the average (arithmetic mean) weight of the first four dogs is the same as that of all five dogs what is the value of y?	Choose one
A) 31  B) 33  C) 35  D) 37  E) 39

Solution: Total weight of the 4 dogs = (25+31+43+41)= 
(25+31+43+41) = 140
140   Avg= 140/4= 
140/4 = 35
35   Total weight of 5 dogs= 140+y or 4(35)+y   Average of 5 dogs as per Question = 35   Equation:   4(35) + y = 5 (35), or y = 35.   35hoose 35
Answer: C
What is the slope of a line on a standard
xy-plane that passes through the point
(1, 3) and (4, –3)?	Choose the most appropriate option:  A) -1  B) 2  C) -2  D) 1/2  E) -1/2

Solution: Plug the values for the coordinates into the formula for the slope of a line:   Slope=y2-y1/x2-x1=-3-3/4-1=-6/3=-2   correct answer -2)-2
Answer: C
A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?	Choose the correct answer.
A) 200 m
B) 700 m
C) 800 m
D) 100 metre
E) 400 m

Solution: Explanation:   A can give B (5 min - 4 1/2 min) = 30 sec start.   The distance covered by B in 5 min = 1000 m.   Distance covered in 30 sec = (1000 * 30)/300= 
(1000 * 30)/300 = 100
100 m.   A can give B 100m start.   Answer:100 metre
Answer: D
Simplify: (4 – 5) – (13 – 18 + 2).
Choices:
A) 5 B) 4 C) -3 D) 2 E) -1

Solution: (4 – 5) – (13 – 18 + 2).   = -1-(13+2-18).   = -1-(15-18).   = -1-(-3).   = -1+3.= 
-1+3. = 2
2.   correct answer 2
Answer: D
I chose a number and divide it by 5. Then I subtracted 154 from the result and got 6. What was the number I chose?	Answers:
A) 600
B) 700
C) 800
D) 900
E) None

Solution: Solution:   Let xx be the number I chose, then   x/5−154=6   x/5=160   x=800   Answer 800
Answer: C
A rower can row upstream at 7 km/hr and downstream at 13 km/hr. What is the rower's rate in still water? Choose the correct choice from the following choices:
A) 8 km/hr
B) 9 km/hr
C) 10 km/hr
D) 11 km/hr
E) 12 km/hr

Solution: The rate in still water is 1/2 * (13 + 7)= 
1/2 * (13 + 7) = 10
10 km/hr   The answer is 10 km/hr.
Answer: C
A work as fast as B. If B can complete a work in 12days independently,the number of days in which A and B can together finish the work in?	Select: A) 2days B) 3days C) 4days D) 5days E) 6days

Solution: Ratio of rates of working of A and B = 2:1   ratio of times taken = 1:2   A's 1day work = 1/6   B's 1day work = 1/12   A+B 1day work = 1/6 + 1/12  +  1= 
 +  1 = 1
1/6 + 1/12= 3/12 = 1/4   A and B can finish the work in 4days   Answer is 4days
Answer: C
The equation of line f is y = 4/3*x - 100. What is the smallest possible distance in the xy-plane from the point with coordinates (0, 0) to any point on line f? Pick one:
A) 48
B) 50
C) 60
D) 75
E) 100

Solution: This can be solve in two steps and without any complex calculation.   Given : equation of line f as y=(4/3)x -100. So the line intercept the axes at (0,-100) and (75,0).   This can be considered a right angle triangle with right angle at (0,0) . So Base=100 , Height=75 and Hypotenuse =125 (By Pythagoras triplet)   So a perpendicular from the (0,0) to hypotenuse will be the answer.   Area of triangle= 0.5*100*75=0.5*125* x   => x=60;   SO answer is 60=60
Answer: C
seven children, Arya, Betsy, Chen, Daniel, Emily, and Franco, are to be seated in a single row of six chairs. If Betsy cannot sit next to Emily, how many different arrangements of the six children are possible?
Choose the most appropriate option:
A) 240
B) 480
C) 540
D) 720
E) 840

Solution: Since it is more time consuming and error prone to find ways Betsy and E not sitting together, It is better we find ways in which they will be together and then subtract from total ways..   total ways = 6!..   ways B and E will be sitting together..   take both B and E as one, then these two together with other 4 can sit in 5! ways ...   Also B and E can sit within themselves in 2! ways..   so the answer required = 6!-2*5!=540..   ans 540
Answer: C
There are 1000 doors that are of the open-close type. When a person opens the door he closes it and then opens the other. When the first person goes he opens-closes the doors in the multiples of 1 i.e., he opens and closes all the doors. when the second goes he opens and closes the doors 2, 4 6 8 respectively. Similarly when the third one goes he does this for 3 6 9 12 15th doors respectively. Find number of doors that are open at last.  Choose the correct choice from the following answers
A) 29
B) 31
C) 32
D) 24
E) 21

Solution: 31. only the perfect squares between 1 to 1k   ANSWER:31
Answer: B
If the simple interest on a sum of money at nineteen percent per annum for two years is Rs.12000, compound interest on the same sum for the same period at the same rate of interest is
Choose the correct choice from the following answers
A) 13,041.00 B) 11,430.00 C) 13,410.00 D) 11,340.00 E) 13,140.00

Solution: S I for 2 years = 12000 ie for one year =6000   The compound interest for Rs.6000 for the second year = 6000*19/100= 
6000*19/100 = 1_140
1140   The CI for two years 12000+1140= 13,140.00   ANSW13,140.00R:13,140.00
Answer: E