MU-NLPC/Calc-aqua_rat huggingface dataset:
Seven consecutive traffic signals each show either red or green. How many different arrangements of the seven signals are possible?
Select the correct option.
A) 40
B) 69
C) 88
D) 128
E) 156

Solution: Since the answer choices to the question are so small (relatively speaking), you can get to the correct answer without having to do any fancy calculations. With a drawing and a bit of 'brute force', you can answer this question relatively quickly.   We're told that 7 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 7 signals are possible.   Total Options: 128   Final Answer:   128
Answer: D
In how many different number of ways 3 boys and 3 girls can sit on a bench such that girls always sit together.
Choose the correct choice from the following answers.
A) A)720  B) B)730  C) C)740  D) D)154  E) E)144

Solution: 144   Option '144'
Answer: E
If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is?
Choose the correct choice from the following choices: A) 50 km B) 76 km C) 18 km D) 16 km E) 97 km

Solution: Let the actual distance traveled be x km. Then,   x/10 = (x + 20)/14   4x - 200 =>x = 50 km.   50 kmnswer: 50 km
Answer: A
A straight line in the xy- plane has y-intercept of 20 . On this line the x-coordinate of the point is 150 and y-coordinate is 600 then what is the slope of the line?	Choose the correct answer.
A) 3.9  B) 4.6  C) 5.2  D) 6  E) 8.1

Solution: Eq of line = Y = MX +C   C= 20   X=150   Y=150M + 20,   Substitute Y by 600 as given in question.   600=150M+20 , M =3.9   correct option is 3.9
Answer: A
The population of a town increased from 1,75,000 to 2,27,500 in a decade. The average percent increase of population per year is  Choose the correct option:
A) 4.37%
B) 5%
C) 3%
D) 8.75%
E) None

Solution: Solution   Increase in 10 years	= (227500 - 175000)= 
(227500 - 175000) = 52_500
52500.   Increase%= (52500/175000Ã—100)%   = 30%.   Required average	= (30/10)= 
(30/10) = 3
3%.   Answer 3%
Answer: C
Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 51 years. What will be the age of the B ten years hence?  Choose one
A) 39  B) 23  C) 28  D) 102  E) 26

Solution: Let the present ages of A, B and C be a, b and c respectively.   Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)   (b + c)/2 = 51 => b + c = 102 --- (2)   Answer: 102
Answer: D
If 170!/10^n is an integer, what is the largest possible value of n?  Choose the correct answer:
A) 47
B) 46
C) 41
D) 48
E) 45

Solution: The question actually asks the highest power of 10 which divides 300! ( For a number to be an integer - Without any remainder all the trailing zeroe's must be divided by the denominator)   10 = 2 x 5   170 factorial will have 41 as -   170/5= 
170/5 = 34
34   34/5= 6   6/5 =1   So answer will be (41) 41
Answer: C
By the how much is two-fifth of 300 greater than three -fifths of 125?	Choose the most appropriate option:
A) 15
B) 3
C) 5
D) 45
E) None of these

Solution: Reqd no. = 2â„5 Ã— 300 - 3â„5 Ã— 125   = 120 - 75= 
120 - 75 = 45
45   Answer 45
Answer: D
Den Bosch and Eastbourne are 2 famous cities 300 kilometer apart. Mary starts from Den Bosch at 8:24 am . An hour later pele starts from Den Bosch. After travelling for 1 hour , Pele reaches Nottingham that Mary had passed 40 minutes earlier. Nottingham falls on the way from Den Bosch to Eastbourne. If pele and Mary just reaches Eastbourne at the same time, what are the speeds of the Mary and Pele Respectively?	Choose one.
A) 120 km/hr  B) 158 km/hr  C) 98 km/hr  D) 102 km/hr  E) 100 km/hr

Solution: Let Pele x km in 1 hour. so Maradona takes (2h-40min)=1 h 20 min to cover x km. Let speed of Maradona and Pele be M and P respectively than   x = \inline M\times \frac{4}{3} and x= P x 1   \inline \Rightarrow \inline \frac{M}{P}=\frac{3}{4}   Again \inline \frac{300}{M}=\frac{300}{P}=1   \inline \Rightarrow \: \: \frac{300}{3k}-\frac{300}{4k}=1   \inline \Rightarrow k= 25   \inline \Rightarrow M= 3k = 75 km/h   and P= 4k = 100 km/h   100 km/hr
Answer: E
An 80-liter solution of cool-drink is made from 10% jasmine water. If 5 liters of jasmine and 15 liters of water were added to the solution, what percent of the solution is jasmine?
Choose the correct choice from the following answers:
A) 11%
B) 13%
C) 15%
D) 17%
E) 19%

Solution: The percent of jasmine in the resulting solution is: (amount of jasmine) / (total volume)   (0.1(80) + 5) / 100 = 13/100 = 13%   The answer is 13%.
Answer: B
If -11 and -8 are negative integers, then -11*-8 + 5 is  Choose the most appropriate option: A) -14 B) 14 C) 33 D) 83 E) 93

Solution: Answer : 93
Answer: E
Set X consists of all two-digit primes and set Y consists of all positive multiples of 6 less than 100. If the two sets are combined into one, what will be the range of the new set?
Choose the correct choice:
A) 84	B) 89	C) 90	D) 92	E) 91

Solution: Set X = {11, 13, 17,............., 83, 89, 97}   Set Y = {6, 12, 18,..............., 84, 90, 96}   Combining two sets, say Set Z   Set Z = {6, 11, 12, 13, 17, 18,..................., 83, 84, 89, 90, 96,97}   Range = Max Value - Min Value   Range (Z) = 97 - 6= 
97 - 6 = 91
91   OA 91 is the answer.
Answer: E
If you have 8 New Year greeting cards and you want to send them to 6 of your friends, in how many ways can this be done?  Choose the most appropriate option:
A) 20160
B) 22100
C) 23000
D) 24500
E) None

Solution: Solution   We have to find number of permutations of 6 objects out of 8 objects. This number is 8P6=8(8-1)(8-2)(8-3)(8-4)(8-5)=8*7*6*5*4*3= 
8*7*6*5*4*3 = 20_160
20160   20160nswer 20160
Answer: A
The diameter of a cylindrical tin is 6cm and height is 5 cm. Find the volume of the cylinder?	Options:
A) 33 B) 45 C) 66 D) 77 E) 21

Solution: r = 3 h = 5   π * 3 * 3 * 5 = 45 π cc   Answer:45
Answer: B
How many words can be formed by taking 4 letters at a time out of the letters of the word MATHEMATICS.
Choices
A) 2154 B) 2454. C) 2254 D) 2354 E) 1245

Solution: There are 8 distinct letters: M-A-T-H-E-I-C-S. 3 letters M, A, and T are represented twice (double letter).   Selected 4 letters can have following 3 patterns:   1. abcd - all 4 letters are different:   8P4=16808 (choosing 4 distinct letters out of 8, when order matters) or 8C4∗4!=16808 (choosing 4 distinct letters out of 8 when order does not matter and multiplying by 4! to get different arrangement of these 4 distinct letters);   2. aabb - from 4 letters 2 are the same and other 2 are also the same:   3C2∗4!/2!2!=18 choosing which two double letter will provide two letters (out of 3 double letter - MAT), multiplying by 4!/2!2! to get different arrangements (for example MMAA can be arranged in 4!/2!2! # of ways);   3. aabc - from 4 letters 2 are the same and other 2 are different:   3C1∗7C2∗4!/2!=756 choosing which letter will proved with 2 letters (out of 3 double letter - MAT), 7C2 choosing third and fourth letters out of 7 distinct letters left and multiplying by 4!/2!to get different arrangements (for example MMIC can be arranged in 4!/2!# of ways).   1680+18+756= 
1680+18+756 = 2_454
2454   Answer: 2454.
Answer: B
If the weight of 13 meters long rod is 13.4 kg. What is the weight of 6 meters long rod ?
Choose the correct choice from the following choices:
A) 7.2 kg. B) 10.8 kg. C) 12.4 kg. D) 6.18 kg E) None

Solution: Answer   ∵Weight of 13 m long rod = 13.4 kg   ∴ Weight of 1 m long rod = 13.4 / 13 kg   ∴ Weight of 6 m long rod = 13.4 x 6 / 13   = 6.18 kg   Option: 6.18 kg
Answer: D
A salt manufacturing company produced a total of 4000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its ave66rage daily production for that year?
Choose the correct choice from the following choices.
A) 140	B) 149	C) 156	D) 195	E) 100

Solution: Total production of salt by the company in that year = 4000 + 4100 + 4200 + .... + 5100 = 54600.   Average monthly production of salt for that year = 54600/365 â‰ˆ 149   ANSWER:149
Answer: B
Arun's Ice Cream Shop sells ice cream at x cents a scoop. For an additional y cents, a customer can add 4 toppings to his or her sundae. How much would a sundae with 4 scoops and 4 toppings cost, in terms of x and y? Choose the most appropriate option:
A) 3x+y
B) 5x+y
C) 6x+y
D) 4x+y
E) 7x+y

Solution: 3x+ynswer 3x+y 4x+y
Answer: A
A certain university will select 1 of 5 candidates eligible to fill a position in the mathematics department and 2 of 8 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?  Options:
A) 138
B) 140
C) 142
D) 145
E) 148

Solution: 1C5*2C8 = 5*28= 
5*28 = 140
140   the answer is (140)
Answer: B
If cost of sugar increases by 15%. How much percent consumption of sugar should be decreased in order to keep expenditure fixed?	Answers:
A) 13%
B) 50%
C) 20%
D) 80%
E) 30%

Solution: 100   115   -----   115 ----- 15   100 ------ ? => 13%   13%nswer: 13%
Answer: A
A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 66 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ?	Choose the correct option:
A) 16%  B) 32%  C) 83%  D) 84%  E) 92%

Solution: This is easiest to solve with a bell-curve histogram. m here is equal to µ in the Gaussian normal distribution and thus m = 50% of the total population.   So, if 66% is one st.Dev, then on either side of m we have  66/2= 
 66/2 = 33
33%. So, 33% are to the right and left of m (= 50%). In other words, our value m + d = 50 + 33= 
50 + 33 = 83
83% goingfrom the mean m, to the right of the distributionin the bell shaped histogram.. This means that 83% of the values are below m + d.   Like I said, doing it on a bell-curve histogram is much easier to fullygethow this works, or you could apply GMAT percentile jargon/theory to it   83%
Answer: C
In an examination, questions were asked in five sections. Out of the total students, 5% candidates cleared the cut-off in all the sections and 5% cleared none. Of the rest, 25% cleared only one section and 20% cleared four sections. If 24.5% of the entire candidates cleared two sections and 300 candidates cleared three sections. Find out how many candidates appeared at the examination?  Choose the correct choice from the following answers:
A) 1000
B) 1200
C) 1500
D) 2000
E) 1800

Solution: Solution: Passed in none = 5%   Passed in all = 5%   Passed in four = 20% 0f 90% = 18%   Passed in three = 24.5%   Passed in three =(100-5-5-22.5-24.5-18)= 
(100-5-5-22.5-24.5-18) = 25
25%.   But given 300 students passed in three.   Hence, 25%= 300.   So, 100% = 1200.   1200 students must have appeared.   Answer: Option 1200
Answer: B
A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?	Pick one:
A) 3	B) 6	C) 7	D) 4	E) 5

Solution: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.   Given x + y = 18 --- (1)   and x - y = 10 --- (2)   From (1) & (2) 2x = 28 => x = 14, y = 4.   Answer:4
Answer: D
In a certain candy store, 22% of the customers are caught sampling the candy and are charged a small fine, but 15% of the customers who sample the candy are not caught. What is the total percent of all customers who sample candy?	Answers.
A) 22%
B) 23%
C) 24%
D) 26%
E) 34%

Solution: Since 15% of the customers who sample the candyare notcaught, then 88% of the customers who sample the candyarecaught:   {% of customers who sample candy}*0.85 = 0.22;   {% of customers who sample candy} = 0.259   Answer: 26%.
Answer: D
The ratio of the ages of Anil and his son at present is 7:3. Six years hence, the ratio of the ages of the Anil's wife and the son will be 2:1. Find the ratio of the present ages of Anil and his wife?  Choose the correct choice from the following answers:
A) 5:4
B) 6:5
C) 4:3
D) Cannot be determined
E) None of these

Solution: Let the present ages of Anil and his son be 7x and 3x years respectively.   Let the present age of the son's mother be m years.   (m + 6)/(3x + 6) = 2/1   m = 6x + 6   Ratio of the present ages of Anil and his son's mother = 7x/(6x + 6).   This cannot be found uniquely.   Answer: Cannot be determined
Answer: D
A water tank is one-third full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
Select
A) 5 min. to empty	B) 6 min. to full	C) 9 min. to empty	D) 9 min. to full	E) 8 min. to full

Solution: Clearly, pipe B is faster than pipe A and so, the tank will be emptied.   Part to be emptied = 1/3   Part emptied by (A + B) in 1 minute = (1/6 - 1/10) = 1/15   1/15 : 1/3 :: 1 : x   x = (1/3 * 1 * 15)= 
(1/3 * 1 * 15) = 5
5 min.   So, the tank will be emptied in 5 min.   5 min. to emptyNSWER:5 min. to empty
Answer: A
Last year, a certain public transportation system sold an average (arithmetic mean) of 40,000 tickets per day on weekdays (Monday through Friday) and an average of 18,000 tickets per day on Saturday and Sunday. Which of the following is closest to the total number of tickets sold last year?
Select:
A) 1 million B) 1.25 million C) 10 million D) 12.2 million E) 125 million

Solution: If you type that into the calculator, it results in 12.3 mil   [D], 12.2 mil, is the correct answer... see 2 posts above for quick approx method
Answer: D
If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time? Choices.
A) Rs.51.25	B) Rs.51.27	C) Rs.51.79	D) Rs.51.8	E) Rs.51.93

Solution: Sum = (50 * 100) / (2 * 5) = Rs. 500   Amount = [500 * (1 + 5/100)2] = Rs. 551.25   C.I. = (551.25 - 500)   = Rs.51.25.   Rs.51.25nswer: Rs.51.25
Answer: A
If A is to be chosen at random from the set {14, 7, 25, 6} and B is to be chosen at random from the set {2, 5, 8}, what is the probability that AB will be even?	Choose the correct choice from the following options:
A) 2/3
B) 8/3
C) 5/6
D) 1/3
E) 4/3

Solution: Method-1   A8/3 will be even when   1) A is even and 8/3 is odd, Probability of A even is (2/4) and Probability of 8/3 odd is (1/3), so Probability of Case(1) = (2/4)*(1/3) = (2/12)   2) A is Odd and 8/3 is Even, Probability of A Odd is (2/4) and Probability of 8/3 Even is (2/3), so Probability of Case(2) = (2/4)*(2/3) = (4/12)   3) A is even and 8/3 is Even, Probability of A even is (2/4) and Probability of 8/3 Even is (2/3), so Probability of Case(1) = (2/4)*(2/3) = (4/12)   Total Favorable Probability = (2/12)+(4/12)+(4/12) = (32/12) = 8/3   Answer: option 8/3
Answer: B
A pack of 52 playing cards, 2cards are drawn together at random. Find the probability of both the cards being king? Choose one:
A) 1/113  B) 2/213  C) 1/221  D) 3/341  E) 3/215

Solution: Two cards can be drawn from a pack of 52 playing cards in 52C2 ways. i,e., 52 x 51 / 2 = 1326 ways. The event that two kings appear in a single drawn of cards is 4C2 ways, i.e 6 ways.   ∴ The probability that the two cards drawn from a pack of 52 cards are kings = 6/1326 = 1/221   1/221
Answer: C
It takes 6 beavers 10 hours to build a certain dam, working at a uniform rate. If two beavers start to build the same dam at 7:00 AM, and one beaver per hour is added beginning at 4:00 PM, at what time will the dam be complete?  Choose one
A) 7:30 PM B) 8:00 PM C) 9:00 PM D) 10:00 PM E) 11:00 PM

Solution: The rate of 1 beaver is 1/60.   The amount of work done by 2 beavers in 9 hours is 2/60 *9 = 18/60   In the next hour, 3 beavers do 3/60 for a total of 21/60.   In the next hour, 4 beavers do 4/60 for a total of 25/60.   In the next hour, 5 beavers do 5/60 for a total of 30/60.   In the next hour, 6 beavers do 6/60 for a total of 36/60.   In the next hour, 7 beavers do 7/60 for a total of 43/60.   In the next hour, 8 beavers do 8/60 for a total of 51/60.   In the next hour, 9 beavers do 9/60 for a total of 60/60.   The dam will be completed at 11:00 pm.   The answer is 11:00 PM.
Answer: E
A man sells an article at 15% loss. Had he sold it for Rs. 210/- more he could have gained 20%. What is the cost price of the article?  Pick one
A) Rs.420/-
B) Rs.400/-
C) Rs.600/-
D) Rs.680/-
E) None of these

Solution: Explanation:   Short cut method:   Loss =====> 15 %   Profit ====> 20 %   ~   ----------------   35 % ---------> Rs. 210/-   100 % --------> Rs. 600/-   Answer: Option Rs.600/-
Answer: C
The banker's discount on $1600 at 15% per annum is the same as true discount on $1680 for the same time and at the same rate. The time is:  Choose the correct choice from the following answers: A) 2 months B) 1 months C) 4 months D) 8 months E) 9 months

Solution: S.I. on $1600 = T.D. on $1680.   THEREFORE $1600 is the P.W. of $1680, i.e., $80 is on $1600 at 15%.   Time =(100 x 80/ 1600 x 15) year	=	1/3	year = 4 months.   ANSWER:4 months
Answer: C
The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?
Choose the correct answer: A) 20.9 B) 28.9 C) 28.6 D) 11.5 E) 12.8

Solution: 1 to 11 = 11 * 10.9= 
11 * 10.9 = 119.9
119.9   1 to 6= 6 * 10.5= 
6 * 10.5 = 63
63   6 to 11= 6 * 11.4= 
6 * 11.4 = 68.4
68.4   63 + 68.4= 
63 + 68.4 = 131.4
131.4 – 119.9= 11.5   6th number = 11.5   Answer: 11.5
Answer: D
Find the average of all the numbers between 6 and 34 which are divisible by 5?
Pick:
A) 32  B) 20  C) 28  D) 11  E) 18

Solution: Average = (10 + 15 + 20 + 25 + 30)/5   = 100/5= 
100/5 = 20
20.   Answer: 20
Answer: B
A man purchased $510 worth savings bonds in denominations of $15 and $30, including at least 1 of each denomination. He gave away 8 of the bonds as gifts but then lost all the rest of the bonds he had purchased. If the number of $30 bonds he gave away was a multiple of the number of $15 bonds he gave away, what was maximum possible value of the bonds that he lost?	Select
A) 180
B) 225
C) 285
D) 300
E) 330

Solution: Let the number of 15$ bonds given be x, then the number of 30$ bills given = kx, where k is an integer.   Thus, x+kx = 8 --> x(1+k) = 8. Thus, we could have   x = 1, k=7 --> The value left with him = 510 - (15+210)= 
510 - (15+210) = 285
285   x= 8,k =0 --> The value left with him = 510 - (120)= 
510 - (120) = 390
390   x=4, k =1 --> The value left with him = 510 - (60+120)= 
510 - (60+120) = 330
330   x=2,k=3 --> The value left with him = 510 - (30+180)= 
510 - (30+180) = 300
300   Thus, the answer is 330.
Answer: E
6 pints of a 20 percent solution of alcohol in water are mixed with 4 pints of a 10 percent alcohol in water solution. The percentage alcohol in the new solution is
Choices.
A) 16	B) 15	C) 14	D) 13	E) 12

Solution: Percentage of alcohol in new solution   =( 6*.2 + 4 * .1) / 10   =(1.2 + .4 ) / 10   = 1.6/10= 
1.6/10 = 0.16
.16   Percentage of alcohol in new solution= 16 %   16nswer :16
Answer: A
If x is divisible by 10, 14, and 70, which of the following must be the least multiple of x?	Choose the correct choice from the following answers
A) 70
B) 140
C) 210
D) 350
E) 700

Solution: We are looking for the LCM (which is not 0) of 10 = 2*5, 70 = 2*7*5, 14 = 2*7:    2 * 5 * 7= 
 2 * 5 * 7 = 70
70   The answer is 70.
Answer: A
Five children, Anaxagoras, Beatrice, Childeric, Desdemona, and Ethelred, sit randomly in five chairs in a row. What is the probability that Childeric and Ethelred sit next to each other? Choose the correct choice from the following choices:
A) 1/30
B) 1/15
C) 1/5
D) 2/5
E) 7/20

Solution: Total no of empty space is 5 so total no of ways A B C D and E can sit is 5 !   Solution 1:   Now condition is C&E will sit together   If they sit at 1st and 2nd place . # of ways will be 1*3! but C&E can be either at 1 or at 2 so # of ways will be 1*3!*2!   Similarly they can sit together at position 2 and 3 or 3 and 4 or 4 and 5   So total # ways will be 1*3!*2! + 1*3!*2! + 1*3!*2! + 1*3!*2! = 4 *1*3! *2 !   So probability is (4! * 2! ) / 5! = 2/5   Solution 2:   Consider C*E as 1 person . So we have 4 ppl and 4 places . # of ways they can sit is 4!   C&E can sit as C&E or E&C so total # of ways is 4! * 2!   So probability will be 2/5   Answer:2/5
Answer: D
A 4 digit number is formed by repeating a 2 digit number such as 2525, 3232 etc. Any number of this form is exactly divisible by	Pick one.
A) 7	B) 11	C) 13	D) Smallest 3 digit prime number	E) None

Solution: Sol.   Smallest 3 digit prime number is 101.   Clearly, 2525 = 25 x 101;   3232 = 32 x 101, etc.   ∴ Each such number is divisible by 101.   Answer Smallest 3 digit prime number
Answer: D
If 12 men and 16 boys can do a piece of work in 5 days and 13 men together will 24 boys can do it in 4 days. Compare the daily work done by a man with that of a boy.	Choose the correct choice from the following choices
A) 2:9  B) 2:1  C) 2:7  D) 2:5  E) 2:2

Solution: 12M + 162:1 ----- 5 days   13M + 242:1 ------- 4 days   60M + 802:1 = 52M + 962:1   8M = 162:1 => 1M = 22:1   M: 2:1 = 2:1   Answer:2:1
Answer: B
In a covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay double his speed, then he would take 1 hour less than Sammer. Abhay's speed is? Choose the correct choice
A) 5 km/hr B) 7 km/hr C) 1 km/hr D) 9 km/hr E) 4 km/hr

Solution: Let Abhay's speed be x km//hr.   Then, 30/x - 30/2x = 3   x = 5 km/hr.   5 km/hrnswer:5 km/hr
Answer: A
A woman says, "If you reverse my own age, the figures represent my husband's age. He is, of course, senior to me and the difference between our ages is one-eleventh of their sum." The woman's age is
Choose the correct choice from the following answers
A) 23 years B) 34 years C) 45 years D) 54 years E) None of these

Solution: Explanation:   Let x and y be the ten's and unit's digits respectively of the numeral denoting the woman's age.   Then, woman's age = (10X + y) years; husband's age = (10y + x) years.   Therefore (10y + x)- (10X + y) = (1/11) (10y + x + 10x + y)   (9y-9x) = (1/11)(11y + 11x) = (x + y) 10x = 8y x = (4/5)y   Clearly, y should be a single-digit multiple of 5, which is 5.   So, x = 4, y = 5.   Hence, woman's age = 10x + y = 45 years.   Answer: 45 years
Answer: C
144, 121, 100, 81, 64, ?	Choices
A) 9
B) 16
C) 25
D) 36
E) 49

Solution: Explanation :   The pattern is 12^2, 11^2, 10^2, 9^2, 8^2, ...   So next number is 7^2 = 49   Answer : Option 49
Answer: E
Indu gave Bindu Rs.1250 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?  Options:  A) 8  B) 2  C) 4  D) 6  E) 1

Solution: 1250 = D(100/4)2   D = 2   Answer: 2
Answer: B
When a boat moves at an average speed of 25 kmph it reaches its destination on time. When its average speed becomes 35 kmph, then it reaches its destination 15 minutes early. Find the length of journey rounded to two decimal places. Choose the correct choice from the following answers:
A) 18.67 km
B) 24.50 km
C) 21.88 km
D) 17.98 km
E) None

Solution: Sol.   Difference between timings = 15 min = 1/4 hr.   Let the length of journey be x km.   Then, x/25 - x/35 = 1/4   â‡” 7x - 5x = 43.75   â‡” 2x = 43.75   â‡” x = 21.88 km.   Answer 21.88 km
Answer: C
Nicole cycles at a constant rate of 10 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 20 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?  Options.
A) a) x minutes	B) b) x/2 minutes	C) c) 2x/3 minutes	D) d) 3x/2 minutes	E) e) 2x minutes

Solution: Speed of nicole = 20km/h or 20/60 km/min = 1/3 km/min.   Once jessica passed the nicole, the distance between the nicole and jessica will increase at the rate of   (30-20)= 
  (30-20) = 10
10km/h or 1/6 km/min   now jessica is cycling for x minutes after passing the nicole, so in those x minutes distance between jessica and nicole would be (1/6)*x= x/6 km.   So, the time taken by nicole to travel x/6 km = (x/6)/(1/3) = x/2. hence answer should be   b) x/2 minutes
Answer: B