MU-NLPC/Calc-aqua_rat huggingface dataset:
One year ago the ratio of Yamini’s and Gamini’s ages was 6 : 7 respectively. Four years hence this ratio would become 7 : 8. How old is Gamini?  Choose the correct answer.
A) 35 years  B) 30 years  C) 31 years  D) Cannot be determined  E) None of these

Solution: Y : G = 6 : 7; One year before   Y : G = 7 : 8; After 4 years   Now, 1 → 5   ∴ 7 → 35   Therefore, the age of Gamini now is   35 + 1= 
  35 + 1 = 36
36 years   Answer None of these
Answer: E
A man buys 20 lts of liquid which contains 30% of the liquid and the rest is water. He then mixes it with 20 lts of another mixture with 20% of liquid. What is the % of water in the new mixture?  Choose the correct choice from the following:
A) 59  B) 95  C) 80  D) 75  E) 65

Solution: 30% in 20 lts is 6. So water = 20-6= 
20-6 = 14
14lts.20% of 20 lts= 4. So water in 2nd mixture = 20-4= 
20-4 = 16
16 lts. Now total quantity= 20 + 20= 
20 + 20 = 40
40 lts. Total water in it will be 14 + 16= 
14 + 16 = 30
30 lts. % of water= (100*30)/40= 
(100*30)/40 = 75
75.   ANSWER:75
Answer: D
The base of a right triangle is 8 and hypotenuse is 10. Its area is? Choose the correct choice from the following:  A) 12  B) 80  C) 59  D) 24  E) 25

Solution: Explanation:   h2=(10)2-(8)2-(6)2->h=6   1/2*8*6= 
1/2*8*6 = 24
24   ANSWER IS 24
Answer: D
At what price must an article costing Rs.75 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?	Pick one.
A) 62.5	B) 62.0	C) 62.6	D) 62.1	E) 98.68

Solution: CP = 75   SP = 75*(125/100)= 
75*(125/100) = 375/4 = around 93.75
93.75   MP*(95/100)= 93.75   MP = 98.68   Answer:98.68
Answer: E
Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Choose the correct choice.
A) 20.8 sec  B) 10.7 sec  C) 10.3 sec  D) 10.8 sec  E) 10.2 sec

Solution: Relative speed = 60 + 40= 
60 + 40 = 100
100 km/hr.= 100 * 5/18 = 250/9 m/sec.   Distance covered in crossing each other   = 140 + 160= 
140 + 160 = 300
300 m.   Required time= 300 * 9/250   = 54/5= 
54/5 = 54/5 = around 10.8
10.8 sec.   Answer:10.8 sec
Answer: D
A train speeds past a pole in 20 seconds and passes through a tunnel 500 m long in 40 seconds. Its length is :  Answers:
A) 200 m  B) 400 m  C) 500 m  D) 700 m  E) None of the above

Solution: Sol.Let the length of the train be x metres and its speed be y m/sec. Then, x / y = 20 ⇒ y = x / 20∴ (x + 500) / 40 = x / 20 ⇔ x = 500 m. Answer 500 m
Answer: C
In how many ways can 16 different gifts be divided among four children such that each child receives exactly three gifts?
Choose the correct choice from the following choices: A) 16^4 B) (4!)^4 C) 16!/(3!)^4 D) 16!/4! E) 4^16

Solution: Total 16 different Gifts, and 4 children.   Thus any one child gets 16C3 gifts,   then the other child gets 13C3 gifts(16 total - 3 already given),   then the third one gets 10C3 gifts,   and the last child gets 7C3 gifts.   Since order in which each child gets the gift is not imp, thus, ans :   1616!/(3!)^43 * 1316!/(3!)^43 * 1016!/(3!)^43 * 716!/(3!)^43 = 16! / (3!)^4   Ans : 16!/(3!)^4.
Answer: C
The following sets each have a mean of 50 and the standard deviations are given in variable form.
Set I = {20, 20, 20, 80, 80, 80}, standard deviation = A
Set II = {20, 30, 40, 60, 70, 80}, standard deviation = B
Set III = {50, 50, 50, 50, 50, 50}, standard deviation = C
Rank these three standard deviations from least to greatest.	Options:
A) A, B, C	B) B, C, A	C) C, A, B	D) B, A, C	E) C, B, A

Solution: The answer should be C, B, A as the mean is least deviated in Set III followed by Set II and then Set I.
Answer: E
A can give B 100 meters start and C 170 meters start in a kilometer race. How much start can B give C in a kilometer race?
Answers.
A) 11.77 meters	B) 55.77 meters	C) 77.77 meters	D) 113.77 meters	E) None of these

Solution: Explanation:   A runs 1000 meters while B runs 900 meters and C runs 830 meters.   Therefore, B runs 900 meters while C runs 830 meters.   So, the number of meters that 77.77 meters runs when B runs 1000 meters = (1000 x 830)/900 = 922.22 meters   Thus, B can give 77.77 meters (1000 - 922.22) = 77.77 meters start   Answer: 77.77 meters
Answer: C
A Card marked 1 and 2 on its two faces. Two colors, white and black are used to paint the two faces of the card. If the card is painted with the different colors, in how many ways can the card be painted?
Choose the correct option:
A) 3	B) 6	C) 2	D) 12	E) 27

Solution: If the base of the card is white, then in order the card to be painted with the different colors, the top must be white.Another side can be painted in Black.   But we can have the base painted in either of the two colors, thus the total number of ways to paint the card is  2*1= 
 2*1 = 2
2.   Answer: 2.
Answer: C
If the sample interest on a sum of money 20% per annum for 2 years is $400, find the compound interest on the same sum for the same period at the same rate?
Pick.
A) $460 B) $510 C) $440 D) $500 E) $550

Solution: Rate = 20%   Time = 2years   S.I. = $400   Principal = 100*400/20*2 = $1000   Amount = 1000(1+20/100)^2 = $1440   C.I. = 1440-1000= 
1440-1000 = 440
$440   Answer is $440
Answer: C
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 3 employees to 2 different offices? Select:
A) 5 B) 6 C) 7 D) 8 E) 9

Solution: for each employee there are two possibilities: first office and second office.   Therefore,   N=2^3=8   ANS:8
Answer: D
A train covers a distance of 12 km in 10 min. If it takes 7 sec to pass a telegraph post, then the length of the train is?  Choose one:  A) 298  B) 288  C) 140  D) 776  E) 991

Solution: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.   Length of the train = 20 * 7= 
20 * 7 = 140
140 m.   Answer:140
Answer: C
Let y = 2m + x^2 and m = 5x + 2. If m^2 =49, then which of the following can be a value of 2y + 3m?
Choose one:
A) 48	B) 56	C) 61	D) 51	E) 71

Solution: m^2 = 49 => m=7   7= 5x+2 => x=1   y= 2*7+1^2 = 15   2y+3m = 2*15+3*7= 
2*15+3*7 = 51
51   Answer : 51
Answer: D
There were two candidates in an election. Winner candidate received 62% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate?  Options:
A) 748	B) 744	C) 725	D) 727	E) 272

Solution: W = 62% L = 38%   62% - 38% = 24%   24% -------- 288   62% -------- ?  62  - 38= 
 62  - 38 = 24
24%   24% -------- 288   62% -------- ?=> 744   Answer:744
Answer: B
The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?	Pick one
A) 17 B) 16 C) 17 D) 19 E) 62

Solution: Average of 20 numbers = 0   Sum of 20 numbers = (0 * 20)= 
(0 * 20) = 0
0   It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (-a).   Answer: 19
Answer: D
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 5x km. Choose the correct choice from the following answers: A) 20kmph B) 25kmph C) 30kmph D) 35kmph E) 40kmph

Solution: Total time taken = x/40 + 2x/20 hours   = 5x/40 = x/8 hours   Average speed = 5x/(x/8)   = 40 kmph   Answer:40kmph
Answer: E
A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?	Choose the correct choice
A) 288 B) 127 C) 2999 D) 277 E) 299

Solution: Along one edge, the number of small cubes that can be cut   = 100/10= 
100/10 = 10
10   Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut= 10 * 10 * 10= 
10 * 10 * 10 = 1_000
1000.Answer: 2999
Answer: C
An "integrated" team consists of 2 members from the engineering team and 2 members from the design team. If the engineering team has 6 members and the design team has 4 members, how many "integrated" team formations are possible? Choose the correct option:
A) 36
B) 54
C) 76
D) 90
E) 112

Solution: Possible Integrated teams=6!/2!∗4!*4!/2!∗2=15*6= 
15*6 = 90
90   So,Correct Answer 90
Answer: D
A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey? Choose the correct choice from the following:
A) 5 B) 4 C) 6 D) 8 E) 32

Solution: M = 45   S = 1.5   DS = 6   US = 3   AS = (2 * 6 * 3) /9= 
(2 * 6 * 3) /9 = 4
4   Answer: 4
Answer: B
In one year, the population, of a village increased by 30% and in the next year, it decreased by 30%. If at the end of 2nd year, the population was 13650, what was it in the beginning?  Pick
A) 7787	B) 8000	C) 15000	D) 1277	E) 2081

Solution: x*130/100 * 70/100 = 13650   X*0.91=13650   X=13650/0.91= 
13650/0.91 = 15_000
> 15000   Answer:15000
Answer: C
The equation x = 2y^2 + 5y - 19, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at x = -5, the equation for l is Choose the most appropriate option
A) 3x + y + 15 = 0	B) y - 3x - 11 = 0	C) -3x + y - 19 = 0	D) -2x - y - 7 = 0	E) -3x + y + 13.5 = 0

Solution: The question is made to look difficult though it is pretty simple if you focus on just the line and use process of elimination. (Remember that GMAT does not focus on parabolas so basically, the question should be quite do-able even if someone doesn't know how to handle parabolas.)   We need equation of l. Its slope must be 3.   Slope in option A and D is not 3 so we are left with B, C and E   The line has a point (-5, y) on it where y is positive (since the point lies in upper left quadrant).   In options B and E, if you put x = -5, you get -ve value for y co-ordinate. So ignore them.   Answer must be (-3x + y - 19 = 0)
Answer: C
A man buys 50 pens at marked price of 46 pens from a whole seller. If he sells these pens giving a discount of 1% , what is the profit percent?	Choose the correct choice from the following answers
A) 7.6 % B) 7.7 % C) 7.32 % D) 3.6 % E) 7.8 %

Solution: Explanation:   Let Marked price be Re. 1 each   C.P. of 50 pens = Rs. 46   S.P. of 50 pens = 99% of Rs. 50 = Rs. 49.50   Profit % = (Profit /C.P.) x 100   Profit% = (3.50/46) x 100 = 7.6 %   7.6 %NSWER: 7.6 %
Answer: A
If a and b are each greater than x and y, which of the following must be true?
I.|a| + |b| > |x| + |y|
II. ab > xy
III. a + b > x + y	Options:
A) I only  B) II only  C) I and II  D) III only  E) I, II and III

Solution: I. a + b > x + y. Since a and b are each greater than x and y, then the sum of a and b will also be greater than the sum of x and y.   II. ab > xy. Not necessarily true, consider a = b = 0 and x = y = -1 --> ab = 0 < 1 = xy.   III. |a| + |b| > |x| + |y|. Not necessarily true, consider a = b = 0 and x = y = -1 --> |a| + |b| = 0 < 2 = |x| + |y|.   Answer: III only.
Answer: D
If a tap could fill entire tank in 20 hrs due to leakage, then in how much time
tank can be emptied by leakage if tap can fill entire tank in 12 hrs without leakage
Choose the correct option
A) 30hrs  B) 24hrs  C) 36hrs  D) 48hrs  E) 52hrs

Solution: time take to fill[withleakage] =20hrs so workdone in 1hr=1/20   time tkae to fill[without leakage]=12hrs so workdone in 1hr=1/12   if u subtract both u'll get time taken by leakage to empty...   1/20-1/12=2/60 = 1/30 so 30hrs   30hrsNSWER:30hrs
Answer: A
What is the tenth digit of (5!*5! - 5!*3!)/5?	Choose one: A) 1 B) 2 C) 0 D) 6 E) 7

Solution: (5!*5! + 5!*3!)/5   =5!(5! + 3!)/5   =120 (120+6)/5   =3024   Units digit of the above product will be equal to 2   Answer 2
Answer: B
A man can row at 5 kmph in still water. If the velocity of the current is 1 kmph and it takes him 1 hour to row to a place and come back. how far is that place.  Answers:
A) 4 km
B) 1.4 km
C) 2.4 km
D) 3.4 km
E) 4.4 km

Solution: Explanation:   Let the distance is x km   Rate downstream = 5 + 1= 
5 + 1 = 6
6 kmph   Rate upstream= 5 - 1= 
5 - 1 = 4
4 kmph   then   x/6 + x/4= 1 [because distance/speed = time]   => 2x + 3x = 12   => x = 12/5= 
12/5 = 12/5 = around 2.4
2.4 km   ANSWER IS 2.4 km
Answer: C
A man bought 10 crates of apples for $120 total. If he lost 2 of the crates, at what price would he have to sell each of the remaining crates in order to earn a total profit of 50 percent of the total cost?	Choose the correct choice from the following options:
A) $22.50	B) $25	C) $28	D) $30	E) $35

Solution: $22.50s given, after lost, the remaining 8 crates total cost = $120   So, 1 crate cost = 120/8= 
120/8 = 15
15   To get 50% profit, 1 crate cost should be=15+15*50/100= 
15+15*50/100 = 45/2 = around 22.5
$22.5   $22.50nswer : $22.50
Answer: A
If the quantity 3^4+ 3^6 + 3^8 is written as (a + b)(a – b), in which both a and b are integers, which of the following could be the value of b?
Choose the most appropriate option.
A) 57 B) 26 C) 52 D) 81 E) 25

Solution: (a+b)(a-b) = a^2 - b^2   3^4+ 3^6 + 3^8 = 3^4 (1+3^2+3^4)   if the above expression is solved even then every term of the expression will remain a multiple of 3^4 which is out of parenthesis   hence, b must be a multiple of 3^4 i.e. 81   Answer: option 81
Answer: D
Balls of equal size are arranged in rows to form an equilateral triangle. the top most row consists of one ball, the 2nd row of two balls and so on. If 19 balls are added, then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did. How many balls made up the triangle?
Choose the correct option.
A) 465
B) 2209
C) 2878
D) 1210
E) 1560

Solution: As expected, this question boils down to 2 equation,   Consider total number of Balls in Triangle = T and number of balls in last row = x.   1+2+3+...+x = T   x(x+1)/2 = T ----(a)   As mentioned in the question, side of a square will be (x-8) and total number of Balls in square will be (T+19)   (x-8)^2 = T+19 -----(b)   Now the hardest part of the question will be to solve these 2 equations and this looks like time consuming BUT the easy way will be plug and play. Also, we've to find a value of T (from 5 optiosn given below) which can make a square of a a number. One we know this, it will be a cake walk.   We can see that option A fits this criteria in eq (b). 465dd - 465+19 = 484 = 22^2 = (x-8)^2 Hence, x = 30   Cross check by putting in eq (a) = x(x+1)/2 = T = > 30*31/2= 
30*31/2 = 465
465   Hence, answer is 465.
Answer: A
The average of a couple was 28Yrs when they were married 5Yrs ago.The avg age of
the couple and a child, who was born during the interval, is 23Yrs now. How old is the
child now ?  Choose the correct choice from the following answers.
A) 2 Yrs B) 4 Yrs C) 3 Yrs D) 1 Yrs E) None of these

Solution: (a+b-5-5)/2=28;   a+b=66;   a+b+c/3=23;   solving both c=3   ANSWER:3 Yrs
Answer: C
If 8 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days?	Choose the correct choice.
A) 127
B) 237
C) 287
D) 450
E) 281

Solution: Explanation:   Let the required no of hectares be x. Then   More men, More hectares (450irect proportion)   More days, More hectares (450irect proportion)   Men\: 8:36\\ 450ays\: 24:30 \end{matrix}\right\} :80:x   \inline \fn_jvn \therefore \inline \fn_jvn 8\times 24\times x=36\times 30\times 80 \inline \fn_jvn \Leftrightarrow \inline \fn_jvn x=\frac{36\times 30\times 80}{8\times 24} \inline \fn_jvn \Leftrightarrow x= 450   Answer: 450
Answer: D
What proximate value should come in place of the question mark (?) in the following question?
6.695 Ã— 1084 + 2568.34 â€“ 1708.34 = ?  Choose the correct option
A) 6,000 B) 12,000 C) 10,000 D) 8,096 E) 9,000

Solution: ? â‰ˆ 6.7 Ã— 1080 + 2560 â€“ 1700 â‰ˆ 7236 + 860 â‰ˆ 8096   Answer 8,096
Answer: D
Twenty four men can do a work in 48 days. How many men are required to complete the work in 12 days? Choose the correct choice from the following options.
A) 85 B) 46 C) 50 D) 96 E) 60

Solution: 96   96   We have M1 961 = M2 962   So, 24 * 48 = M2 * 12 => M2 = 96.
Answer: D
A train 360 m long is running at a speed of 45 kmph.In what time will it pass a bridge 140 m long?	Choices
A) 40 sec	B) 42 sec	C) 45 sec	D) 48 sec	E) 49 sec

Solution: speed of the train 45* 5/18 = 25/2 m/sec   time = (360+140)/25/2   = 500*2/25= 
500*2/25 = 40
40sec   40 secNSWER:40 sec
Answer: A
kumar saves 32% of his monthly salary. If he spends Rs. 27200, then find his savings?	Choose the correct option:
A) 15400
B) 14300
C) 13200
D) 12800
E) 9500

Solution: Answer: Option D   Let the monthly salary of kumar be Rs. x.   68% of x = 27200   => x = (27200 * 100)/68= 
(27200 * 100)/68 = 40_000
40000   His savings= 32/100 * 40000= 
32/100 * 40000 = 12_800
12800.
Answer: D
When a whole no. n is divided by 4,we will get 3 as remainder. What will be the remainder if 2n is divided by 4?	Choose the correct choice:
A) 1	B) 4	C) 2	D) 6	E) 7

Solution: Let n ÷ 4 = p , remainder = 3   => n = 4p + 3   2n = 2(4p + 3)   = 8p + 6   = 8p + 4 + 2   = 4(2p + 1) + 2   Hence, if 2n is divided by 4, we will get 2 as remainder.   2
Answer: C
Sn = n^2 + 5n + 94 and K = S6 – S5 + S4 – S3 - S2 + S1. What is the value of K?	Select the correct option:  A) 67  B) 20  C) 45  D) 41  E) 36

Solution: I used brute force for this question:   S6: 36+30+94=160   S5: 25+25+94=144   S4: 16+20+94=130   S3: 9+15+94=118   S2: 4+10+94=108   S1: 1+5+94=100   S6-S5+S4-S3+S2-S1= 16+12-8= 
16+12-8 = 20
20   Answer 20
Answer: B
A total of x tourists were transported by bus to a certain museum. If there were y tourists on each bus, which of the following expresses the number of buses used?  Choose the correct choice from the following:
A) xy
B) x/y
C) y/x
D) x - y
E) y^2

Solution: IMHO (x/y) x/y as well !   Number of buses used = Total number of tourists / Number of tourists per bus => x/y   PS : In case of any doubt , plug in some numbers   Total number of tourists transported by bus = 500   Number of tourists per bus = 10   No of buses required = 500/10
Answer: B
John bought a total of 16 Mangoes and Oranges. Each Mango costs 80 cents and each orange costs 60 cents. If the average price of the 16 mangoes and oranges that John originally purchased was 65 cents, then how many oranges needs to return to raise the average price of his purchase to 72 cents? Choose the most appropriate option: A) 4 B) 5 C) 6 D) 7 E) 10

Solution: Let number of mangoes be x, number of oranges be 16-x   0.80x +(16-x)0.60/16 = 0.65   solving for x, we get x = 4 --> Mangoes 4, Oranges 12   Now, number of oranges to be returned be y   0.80*4 + (12-y)*0.60/16-y = 0.72   solving for y, y = 10   Ans:10
Answer: E
To mail a package, the rate is 10 cents for the first pound and 5 cents for each additional pound. Two packages weighing 4 pounds and 6 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?
Choose the correct choice from the following choices
A) Combined, with a saving of 15 cents
B) Combined, with a saving of 10 cents
C) Combined, with a saving of 5 cents
D) Separately, with a saving of 5 cents
E) Separately, with a saving of 15 cents

Solution: 4 pounds cost = 10+3*5= 
10+3*5 = 25
25   6 pounds cost= 10+5*5= 
10+5*5 = 35
35   Total= 60   10 pounds cost = 10+ 9*5= 
10+ 9*5 = 55
55   Answer : Combined, with a saving of 5 cents
Answer: C
The probability of Sam passing the exam is 1/5. The probability of Sam passing the exam and Michael passing the driving test is 1/6. What is the probability of Michael passing his driving test? Choose the correct choice from the following options
A) 5/6.	B) 1/2.	C) 1/3.	D) 2/3.	E) 2/5

Solution: 1/5 *1/m= 1/6 , 1/m = 5/6   5/6.nswer 5/6.
Answer: A
If the compound interest on an amount of Rs. 29000 in two years is Rs. 9352.5, what is the rate of interest?	Select.
A) 11  B) 9  C) 15  D) 18  E) 25

Solution: let interest rate be x.   (2x+(x^2)/100)*(1/100)*29000 = 9352.5   x = 15   ANSWER:15
Answer: C
Rs.8000 become Rs.8487.20 in a certain interval of time at the rate of 3% per annum of C.I. Find the time?  Choose the correct choice from the following choices
A) 6 years	B) 8 years	C) 9 years	D) 3 years	E) 2 years

Solution: 8487.20 = 8000(34/30)N   (34/30)^2 = (34/30)N => N = 2   At the end of three years what will be the comp.Answer: 2 years
Answer: E
My watch gains 5 min every hour. How many degrees the second hand moves in every min?	Choices
A) 300	B) 350	C) 390	D) 400	E) 450

Solution: Gain 5 min   every 1 hr   degrees moves ==>390   ANSWER 390
Answer: C
Three candidates contested an election and received 1136, 7636 and 14000 votes respectively. What percentage of the total votes did the winning candidate get?
Choose the correct choice from the following answers
A) 46% B) 61% C) 74% D) 63% E) 68%

Solution: 61%   14000/(1136 + 7636 + 14000) = 61%.
Answer: B
At the end of year 1998, Shepard bought nine dozen goats. Henceforth, every year he added p% of the goats at the beginning of the year and sold q% of the goats at the end of the year where p > 0 and q > 0. If Shepard had nine dozen goats at the end of year 2002, after making the sales for that year, which of the following is true?	Pick:	A) p = q	B) p < q	C) p > q	D) p = q/2	E) None of these

Solution: Explanation :   The number of goats remain the same. If the percentage that is added every time is equal to the percentage that is sold, then there should be net decrease.   The same will be the case if the percentage added is less than the percentage sold.   The only way the number of goats remain the same if p>q.   Answer : p > q
Answer: C
A can do a certain job in 25 days which B alone can do in 20 days. A started the work and was joined by B after 10 days. The number of days taken in completing the wotk were ?	Answers
A) 14 2/3kmph  B) 15 2/3kmph  C) 16 2/3kmph  D) 17 2/3kmph  E) 18 2/3kmph

Solution: Explanation:   Work done by A in l0 days = (1/25) *10 = 2/5   Remaining work = 1 - (2/5) = 3/5   (A+B)s 1 days work = (1/25) + (1/20) = 9/100   9/100 work is done by them in 1 day.   hence 3/5 work will be done by them in (3/5)*(100/9)   = 20/3days.   Total time taken = (10 + 20/3) = 16*(2/3) days   Option 16 2/3kmph
Answer: C
Suppose there is an outlet which is pouring water at a constant rate and is able to fill a swimming pool in nine hours. There is another outlet that is able to fill the pool in five hours. If we open both the outlets and let them pour the water together How many hours will it take to fill the pool ? Choose the correct choice from the following answers.
A) 3.11 hours B) 2.21 hours C) 3.21 hours D) 4.21 hours E) 5.21 hours

Solution: total work=1/9+1/5=14/45 so reqired time=45/14   =3.21 hours   ANSWER:3.21 hours
Answer: C
Carol is three times Alice’s age but only twice as old as Betty. Alice is twenty-four years younger than Carol. How old is Betty?  Choose the correct choice from the following answers:
A) 26 B) 19 C) 22 D) 18 E) 24

Solution: Beyond the obvious Algebra approach to this question, it can also be solved by TESTing THE ANSWERS.   We're told 3 facts about the relative ages of 3 people:   1) Carol's age is 3 times Alice's age   2) Carol's age is 2 times Betty's age   3) Carol is 24 years older than Alice   We're asked for BETTY'S age.   From the answer choices and the information provided, Carol can't be that old (The difference of 12 years = 3 times; that relationship can only occur when the numbers are relatively small). Since Carol is TWICE Betty's age, Betty is clearly younger than Carol, so we'll TEST a smaller answer first.   IF....   Betty = 18   Then Carol = 2(18) = 36   Then Alice = 36 - 24= 
36 - 24 = 12
12 AN18 36/3= 12   All of these values mesh perfectly with the facts and with one another, so Betty MUST be 18   18
Answer: D
If the sides of a triangle are 9 cm, 16 cm and 19 cm, what is its area?	Select the correct option:  A) 69  B) 72  C) 75  D) 89  E) 93

Solution: The triangle with sides 9 cm, 16 cm and 19 cm is right angled, where the hypotenuse is 19 cm.   Area of the triangle = 1/2 * 9 * 16= 
1/2 * 9 * 16 = 72
72 cm2   Answer: Option 72
Answer: B