MU-NLPC/Calc-aqua_rat huggingface dataset:
A 5-letter code word consists of letters A, B, and C. If the code includes all the three letters, how many such codes are possible?  Select the correct option:	A) 90	B) 48	C) 36	D) 24	E) 18

Solution: Note that the correct answer to this question is 36, not 72.   AB-ABC can be arranged in 5!/2!2!=30 ways;   BC-ABC can be arranged in 5!/2!2!=30 ways;   AC-ABC can be arranged in 5!/2!2!=30 ways;   Total:  30+30+30= 
 30+30+30 = 90
90.   90nswer: 90.
Answer: A
If f, g, and h are positive numbers such that (f/(f+g))(10) + (g/(f+g))(20)=h and if f<g which of the following could be the value of h? Choose the correct choice from the following answers: A) 10 B) 12 C) 15 D) 18 E) 30

Solution: The answer is D. For any positive f and g, h is a number between 10 and 20. Since f < g, weight of 10 is inferior of weight of 20 -> h is > 15 -> 18 is the answer.
Answer: D
A football team lost 5 yards and then gained 10. What is the team's progress?	Answers:	A) 2	B) 4	C) 5	D) 6	E) 8

Solution: For lost, use negative. For gain, use positive.   Progress = -5 + 10= 
-5 + 10 = 5
5 yards   5
Answer: C
A man can row downstream at the rate of 45 Kmph and upstream at 23 Kmph. Find the man’s rate in still water and rate of current? Choose the correct choice from the following answers:
A) 8.5 B) 10.0 C) 12.5 D) 11.0 E) 8.25

Solution: Rate of still water = 1/2 (down stream + upstream)   = 1/2 (45 + 23) = 34 Kmph   rate of current = 1/2 (down stream - upstream)   = 1/2 (45 - 23)   = 1/2 (22)   = 11 kmph   Answer is 11.0.
Answer: D
How is 5% expressed as a decimal fraction?
Choose the most appropriate option
A) 0.5 B) 0.05 C) 0.005 D) 0.0005 E) 5

Solution: 5/100= 
5/100 = 1/20 = around 0.05
0.05   ANSWER:0.05
Answer: B
A five-digit number divisible by 3 is to be formed using numerical 0, 1, 2, 3, 4 and 5 without repetition. The total number T of ways this can be done is:	Pick:
A) 122  B) 210  C) 216  D) 217  E) 225

Solution: We should determine which 5 digits from given 6, would form the 5 digit number divisible by 3.   We have six digits: 0, 1, 2, 3, 4, 5. Their sum=15.   For a number to be divisible by 3 the sum of the digits must be divisible by 3. As the sum of the six given numbers is 15 (divisible by 3) only 5 digits good to form our 5 digit number would be 15-0={1, 2, 3, 4, 5} and 15-3={0, 1, 2, 4, 5}. Meaning that no other 5 from given six will total the number divisible by 3.   Second step:   We have two set of numbers:   1, 2, 3, 4, 5 and 0, 1, 2, 4, 5. How many 5 digit numbers can be formed using these two sets:   1, 2, 3, 4, 5 --> 5! as any combination of these digits would give us 5 digit number divisible by 3. 5!=120.   0, 1, 2, 4, 5 --> here we can not use 0 as the first digit, otherwise number won't be any more 5 digit and become 4 digit. So, desired # would be total combinations 5!, minus combinations with 0 as the first digit (combination of 4) 4! --> 5!-4!=4!(5-1)=4!*4=96   120+96= 
120+96 = 216
216=Y   Answer: 216.
Answer: C
A factory producing tennis balls stores them in either big boxes, 25 balls per box, or small boxes, 20 balls per box. If 104 freshly manufactured balls are to be stored, what is the least number of balls that can be left unboxed?  Select the correct option:
A) 1 B) 2 C) 3 D) 4 E) 5

Solution: We have to work with multiples of 20 and 25.   First, we must know the limits of this multiples, so:   105/25= 4....so the max is 4   105/20=5...so the max is 5   105-100= 
105-100 = 5
5   Answer : 5
Answer: E
A train 100 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?  Choose the correct choice from the following:	A) 28	B) 50	C) 88	D) 41	E) 12

Solution: Speed of the train relative to man = (100/10) m/sec = (10) m/sec. [(10) * (18/5)] km/hr = 36 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 36 ==> x   = 41 km/hr.Answer:41
Answer: D
A boat covers a certain distance downstream in 4 hours but takes 6 hours to return upstream to the starting point. If the speed of the stream be 3 km/hr, find the speed of the boat in still water
Choose the correct choice from the following answers:
A) 15 km/hr
B) 12 km/hr
C) 13 km/hr
D) 14 km/hr
E) None of these

Solution: Explanation :   Let the speed of the water in still water = x   Given that speed of the stream = 3 kmph   Speed downstream = (x+3) kmph   Speed upstream = (x-3) kmph   He travels a certain distance downstream in 4 hour and come back in 6 hour.   ie, distance travelled downstream in 4 hour = distance travelled upstream in 6 hour   since distance = speed × time, we have   (x+3)4=(x−3)6   => (x + 3)2 = (x - 3)3   => 2x + 6 = 3x - 9   => x = 6+9= 
6+9 = 15
15 kmph. 15 km/hrnswer : Option 15 km/hr
Answer: A
Carmen made a sculpture from small pieces of wood. The sculpture is 2 feet 10 inches tall.Carmen places her sculpture on a base that is 4 inches tall. How tall are the sculpture andbase together?  Choose the correct option.
A) 3.17 feet B) 3.2 feet C) 3.3 feet D) 3.4 feet E) 3.5 feet

Solution: we know 1 feet =12 inch then   2 feet =24 inch     24+10= 
  24+10 = 34
34 then     34+4= 
  34+4 = 38
38   38/12=3.17 feet   3.17 feetNSWER:3.17 feet
Answer: A
By investing in 1623% stock at 64, one earns Rs. 1800. The investment made is
Choose the correct choice from the following answers
A) s. 6500	B) s. 7500	C) s. 5640	D) s. 5760	E) s. 6912

Solution: s. 6912xplanation :   Market Value = Rs.64   Face Value is not given and hence take it as Rs.100   16 2/3% of the face value = 50/3   ie, to earn 50/3, investment = Rs.64   Hence, to earn Rs.1800, investment needed = 64×3×1800/50 = 6912   Answer : Option s. 6912
Answer: E
Two stations A and B are 200 km apart on a straight track. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet? Options
A) 02 p.m.	B) 06 p.m.	C) 10 p.m.	D) 12 p.m.	E) 11 p.m.

Solution: Explanation:   Assume both trains meet after 'p' hours after 7 a.m.   Distance covered by train starting from A in 'p' hours = 20p km   Distance covered by train starting from B in (p-1) hours = 25(p-1)   Total distance = 200   => 20x + 25(x-1) = 200   => 45x = 225   => p= 5   Means, they meet after 5 hours after 7 am, ie, they meet at 12 p.m.   Answer: 12 p.m.
Answer: D
Find the number of solutions for 3x+4y=60, if x and y are positive integers	Choose the correct choice from the following:  A) 1  B) 2  C) 3  D) 4  E) 5

Solution: 3x+4y=60   =>x=(60-4y)/3   as x and y are positive integers, put y=1,2,3,... & find x   y=3,x=16   y=6,x=12   y=9,x=8   y=12,x=4   (x,y)=(4,12),(8,9),(12,6),(16,3)   only 4 solution   ANSWER:4
Answer: D
A can contains a mixture of liquids A and B is the ratio 7:5. When 3 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many liter of liquid A was contained by the can initially? Choose the correct choice from the following answers
A) 7  B) 10  C) 12  D) 14  E) 16

Solution: Ci*Vi = Cf*Vf   (7/12)*(V1 - 3) = (7/16)*V1   (V1 - 3)/V1 = 3/4   3 accounts for the difference of 1 on ratio scale so Initial volume = V1 = 4*3= 
4*3 = 12
12 litres.   7/12 of the initial mixture was liquid A so liquid A was   (7/12)*12= 
  (7/12)*12 = 7
7 litres.   7nswer : 7
Answer: A
How many 3 digit numbers are divisible by 6 in all ?	Pick:
A) 150
B) 111
C) 120
D) 243
E) 345

Solution: A   150   Required numbers are 102, 108, 114, ... , 996   This is an A.P. in which a = 102, d = 6 and l = 996   Let the number of terms be n.   Then, a + (n - 1)d = 996   102 + (n - 1) x 6 = 996   6 x (n - 1) = 894   (n - 1) = 149   n = 150.
Answer: A
One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)?  Options.
A) 3/13
B) 1/13
C) 2/11
D) 3
E) 2

Solution: Clearly, there are 52 cards, out of which there are 12 face cards.   P (getting a face card) = 12/52	= 3/13   Hence 3/13nswer is 3/13
Answer: A
During a Pizza buffet where A eats more times 4 than B, and B eats 8 times less than C.find the least number of times all the three has to eat
Choose the correct choice from the following answers:
A) 7
B) 5
C) 9
D) 2
E) 4

Solution: A eats more than B if B eats 1 times than the ratio of A and B is A:B is 4:1 and as B eat 8 times less the C the the ratio of B : C is 1:8 the the least number of times all three has eat is the LCM of A,B,C that is 8 ..   ANSW4R:4
Answer: E
The ratio between the present ages of P and Q is 5:7 respectively. If the difference between Q's present age and P's age after 6 years is 2. What is the total of P's and Q's present ages?  Choose the correct choice from the following options:  A) 48 years  B) 65 years  C) 87 years  D) 20 years  E) 26 years

Solution: Let the present ages of P and Q be 5x and 7x years respectively.   Then, 7x - (5x + 6) = 2   2x = 8 => x = 4   Required sum = 5x + 7x = 12x 5  + 7= 
5  + 7 = 12
12x= 48 years.   48 yearsnswer:48 years
Answer: A
A pipe can fill a cistern in 12 minutes whereas the cistern when fill can be emptied by a leak in 18 minutes. When both pipes are opened, find when the cistern will be full? Choose the correct answer:
A) 17
B) 16
C) 70
D) 36
E) 12

Solution: 1/12 - 1/18 = 1/36   36 minutes   Answer: 36
Answer: D
Tommo spent six lucky days in Las Vegas. On his first day he won a net amount of only $20, but on each of the following days, the daily net amount he won grew by d dollars. If Tommo won a total net amount of $1620 during his stay in Las Vegas, how much did he win on the last day?	Choose the correct choice from the following:
A) 330 B) 500 C) 520 D) 540 E) 620

Solution: I drew a diagram:   1 - $20   2 -   3 -   4 - $320   5 -   6 -   Total: $1,620   Between 1 and 6 are 5 days where he won $1,600. This means he averaged $320 per day (1600/5). You can put $320 by 4 because it's the middle number. Now you just find the two points betwenn $20 and $320 (320-20 = 300 / 3= 
300 / 3 = 100
100). So each day, he earned $100 more. This means on day 6, tommo earned$520. Answer choice 520.
Answer: C
Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 4w widgets?
Choose the correct choice:
A) 4	B) 6	C) 8	D) 24	E) 12

Solution: Let Y produce w widgets in y Days   Hence, in 1 day Y will produce w/y widgets.   Also, X will produce w widgets in y+2 days (given, X takes two more days)   Hence, in 1 day X will produce w/y+2 widgets.   Hence together X and Y in 1 day will produce {w/y + w/y+2} widgets.   Together X and Y in 3 days will produce = 3 * [{w/y + w/y+2}] widgets.   It is given that in 3 days together they produce (5/4)w widgets.   Equating, 3 * [{w/y + w/y+2}] = (5/4)w   Take out w common and move 3 to denominator of RHS   w{1/y + 1/(y+2)} = (5/12)w   Canceling w from both sides   {1/y + 1/(y+2)} = 5/12   2y+2/y(y+2) = 5/12   24y+24=5y^2 + 10y   5y^2-14y-24=0   5y^2-20y+6y-24=0   5y(y-4)+6(y-4)=0   (5y+6)+(y-4)=0   y=-6/5 or y=4   Discarding y=-6/5 as no of days cannot be negative   y=4   hence it takes Y, 4 days to produce w widgets.   Therefore, it will take X  (4+2)= 
 (4+2) = 6
6 days to produce w widgets.   Hence it will take X 4*6= 
4*6 = 24
24 days to produce 4w widgets.   Answer : 24
Answer: D
A bus moving at a speed of 45 km/hr. overtakes a truck 150 metres ahead going in the same directions in 30 seconds. The speed of the truck is  Choose the correct option.
A) 27km/hr B) 24km/hr C) 25km/hr D) 28km/hr E) None of these

Solution: Explanation:   The lag of 150 m has been covered by the bus in 30 seconds.   Therefore, the relative speed of the bus and truck is =(5X18)/5=18km/h   The speed of truck is   45-18= 
  45-18 = 27
27 Km/hr   27km/hrnswer 27km/hr
Answer: A
In triangle PQR, the angle Q = 90 degree, PQ =3 cm, QR = 8 cm. X is a variable point on PQ. The line through X parallel to QR, intersects PR at Y and the line through Y, parallel to PQ, intersects QR at Z. Find the least possible length of XZ  Select the correct option:
A) 3.6 cm
B) 2.4 cm
C) 4.8 cm
D) 2.16 cm
E) 3.2 cm

Solution: Look at the diagram below:   Now, in case when QY is perpendicular to PR, two right triangles PQR and PQY are similar: QY:QP=QR:PR --> QY:3=8:10 --> QY=2.4.   Answer: 2.4 cm.
Answer: B
The original price of a suit is $200. The price increased 25%, and after this increase, the store published a 25% off coupon for a one-day sale. Given that the consumers who used the coupon on sale day were getting 25% off the increased price, how much did these consumers pay for the suit?	Answers.
A) $178.50
B) $182.50
C) $185.50
D) $187.50
E) $200

Solution: 0.75*(1.25*200)= 
0.75*(1.25*200) = 187.5
$187.50   The answer is $187.50.
Answer: D
In Town X, 64 percent of the population are employed, and 55 percent of the population are employed males. What percent of the employed people in Town X are females?
Select: A) 14% B) 25% C) 32% D) 40% E) 52%

Solution: We are asked to find the percentage of females in employed people.   Total employed people 64%, out of which 55 are employed males, hence 9% are employed females.   (employed females)/(total employed people)=9/64=14%   14%nswer: 14%.
Answer: A
If the integer N = 139,k50 where k is the hundreds digit, N can NEVER be divisible by which of the following?  Pick one
A) 2  B) 3  C) 4  D) 6  E) 9

Solution: It is divisible by 2 irrespective of k value as unit digit's value is even(0).   It can be divisible by 3 for k values 2,5,8 as sum will be divisible by 3   It can be divisible by 6 if divisible by 2 and 3.   It can be divisible by 9 for k value 2 as sum will be divisible by 9.   Therefore answer is 4 as number is divisible if last two digits are divisible.In this case 50(No)   Hence answer 4
Answer: C
A bike owner buys petrol at Rs 75, Rs. 80 and Rs. 85 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 40000 each year?  Choose the most appropriate option:
A) Rs 79.8 B) Rs 80.4 C) Rs 85.5 D) Rs 90 E) Rs 60

Solution: Explanation :   Total quantity of petrol consumed in 3 years = 40000/75 + 40000/80 + 40000/85 litres   = 40000 (1/75 + 1/80 + 1/85 ) = 40000(767/20,400) = 76700/51 litres   Total amount spent = Rs. (3 x 40000) = Rs. 120000.   Average cost = Rs. 120000 x 51/76700   = Rs. 61200/767   = Rs. 79.8   Rs 79.8nswer : Rs 79.8
Answer: A
The equation a = 2y2 + 5y - 17, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at a = -5, the equation for l is	Choose the correct choice from the following:
A) + y + 15 = 0	B) - 3x - 11 = 0	C) + y - 16.5 = 0	D) - y - 7 = 0	E) + y + 13.5 = 0

Solution: Is option+ y - 16.5 = 0: -3a + y -6.5= 0=c
Answer: C
The average marks obtained by 120 cndidates in a certainexaminationis 35.if the average marks of passed candidate is 39 and that of the failedcandidates is 15,what is the number of candidates who passed the examination
Answers:	A) 15 years	B) 16 years	C) 14 years 8 month	D) 16 years 2 month	E) 19 years 8 month

Solution: (d) Let No. of passed candidates are x   So, x * 39 + (120 – x) 15= 120 * 35   x = 100   2.(a) Total increase = 8 * 2= 
8 * 2 = 16
16 years   So, total age of two women= 35 + 45 +16= 
35 + 45 +16 = 96
96   Average age of two women=96/2= 
96/2 = 48
48 years   3(d) Total decrease= 20 * 2= 
20 * 2 = 40
40 month= 3 years 4 month   So, age of new boy = 18 years – 3 years 4 month   = 14 years 8 month   14 years 8 month
Answer: C
What should come next in the following letter sequence?
A A B A B C A B C D A B C D E A B C D Choose the correct answer:  A) T  B) E  C) H  D) F  E) V

Solution: Answer: E)
Answer: B
Find the value of (55 + 113/78) × 78	Options: A) 4423 B) 4403 C) 4413 D) 2403 E) 4375

Solution: =(55 + 113/78) × 78   =(4290 + 113)/78 × 78   =4403/78× 78   =4403   Answer is 4403.
Answer: B
3 men can complete a piece of work in 6 days. Two days after they started the work, 3 more men joined them. How many days will they take to complete the remaining work? Choose the correct answer:
A) 2	B) 4	C) 5	D) 6	E) 7

Solution: Explanation:   3 man 1 day work = 1616   3 man 2 days work = 2626   Remaining work = (1 – 2626 ) = 2/3 parts.   6 man together perform the work in 1 day is = 1616 + 1616 = 2626 parts   2626 parts completed in 1 day   2323 parts will b completed in 2 days   2nswer:2
Answer: A
If n is a prime number, which of the following could be true  Options:  A) n^n=n  B) n^n/4 = 1^(n-1)  C) (n)(n^n) = is negative  D) n^2+n^3= n^5  E) n^2/4= is even

Solution: B should be the answer.   2^2/4 = 1^(2-1)
Answer: B
The vertex of a parallelogram are (1, 0), (3, 0), (1, 1) and (3, 1) respectively. If line L passes through the origin and divided the parallelogram into two identical quadrilaterals, what is the slope of line L?	Choose the most appropriate option.
A) . 1/2  B) 2  C) 1/4  D) 3  E) 3/4

Solution: Soln:-   Added the line BE (the required line that divides the given parallelogram into 2 identical quadrilaterals).   Careful observation reveals that slope of the diagonal AD = (1-0)/(3-1) = 0.5. Thus the slope of line BE should be < slope of AD   Only option 1/4 is < 0.5 and is thus the correct answer.
Answer: C
If a man can cover 14 metres in one second, how many kilometres can he cover in 3 hours 45 minutes? Select:  A) 288  B) 162  C) 189  D) 168  E) 122

Solution: 14 m/s = 14 * 18/5 kmph   3 hours 45 minutes = 3 3/4 hours = 15/4 hours   Distance = speed * time = 14 * 18/5 * 15/4= 
14 * 18/5 * 15/4 = 189
189 km.   Answer: 189
Answer: C
For positive integers n, the integer part of the nth term of sequence D equals n, while the infinite decimal part of the nth term is constructed in order out of the consecutive positive multiples of n, beginning with 2n. For instance, D_1 = 1.2345678…, while D_2 = 2.4681012… The sum of the first seven terms of sequence D is between: Choose the correct choice from the following answers.
A) 28 and 29	B) 29 and 30	C) 30 and 31	D) 31 and 32	E) 32 and 33

Solution: First, construct the first seven terms, though only out to a few decimal places, following the given pattern.   D_1 = 1.23…   D_2 = 2.46…   D_3 = 3.69…   D_4 = 4.812…   D_5 = 5.10…   D_6 = 6.12…   D_7 = 7.14…   Now, to add up the first seven terms, you should be strategic about how many decimal places to keep. You can drop the hundredths place and get a good approximation with the tenths place—and if you find the sum too close to a boundary between choices, then you can refine your answer if necessary.   1.2 + 2.4 + 3.6 + 4.8 + 5.1 + 6.1 + 7.1= 
1.2 + 2.4 + 3.6 + 4.8 + 5.1 + 6.1 + 7.1 = 30.3
30.3   Including more decimal places would only add a couple of tenths to the sum—not enough to tip the sum over 31.   The correct answer is 30 and 31.
Answer: C
An aeroplane covers a certain distance of 420 Kmph in 6 hours. to cover the same distance in 4 2/3 hours, it Must travel at a speed of Choose the correct option
A) 580 Kmph
B) 550 Kmph
C) 540 Kmph
D) 530 Kmph
E) 520 kmph

Solution: Explanation:   Speed of aeroplane = 420 Kmph   Distance travelled in 6 hours   = 420 * 6= 
420 * 6 = 2_520
2520 Km   Speed of aeroplane to acver 2520 Km in 14/3= 2520*3/14= 
2520*3/14 = 540
540 Km   Answer: Option 540 Kmph
Answer: C
price of apple mobile is double than samsung and triple than oppo.the mean off all three phone's price is 25000.what is price of samsung.  Select the correct option:
A) 21,200.20
B) 22,000
C) 20,454.54
D) 23,300.33
E) 24,000

Solution: solution   let the price of oppo is x,then price of apple 3x and price of samsung 1.5x   (x+3x+1.5x)/3=25000   5.5x=75000   x=75000/5.5=13,636.36   Samsung price=1.5x=20,454.54   answer 20,454.54
Answer: C
The area of a triangle is with base 4m and height 5m? Choose the correct choice
A) 76 m2  B) 10 m2  C) 27 m2  D) 18 m2  E) 17 m2

Solution: 1/2 * 4 * 5= 
1/2 * 4 * 5 = 10
10 m2   Answer:10 m2
Answer: B
an operation * is defined by the equation:
a*b=a-b/a+b, for all numbers a and b such that a is not equal to -b, if a is not equal to -w and a*w=0, then w=? Select.
A) a) -a  B) b) -1/a  C) c) 1/a  D) d)0  E) e)a

Solution: If a*w=0 and a=-w then a-w = o of a=w, so answer e)a
Answer: E
The ratio between the speeds of two Bullet trains is 7: 8. If the second Bullet train runs 520 kms in 4 hours, then the speed of the first train is:
Select the correct option:
A) 89.25 km/hr. B) 37.25 km/hr. C) 90.25 km/hr. D) 113.75 km/hr. E) 96.25 km/hr.

Solution: Let the speed of two bullet trains be 7x and 8x km/hr.   Then, 8x = (520/4)= 
(520/4) = 130
130   x= (130/8)= 
(130/8) = 65/4 = around 16.25
16.25   Hence, speed of first bullet train= (7 x 16.25) km/hr = 113.75 km/hr.   113.75 km/hr.
Answer: D
Of the 600 residents of Clermontville, 35% watch the television show Island Survival, 40% watch Lovelost Lawyers and 50% watch Medical Emergency. If all residents watch at least one of these three shows and 18% watch exactly 2 of these shows, then how many Clermontville residents Z watch all of the shows? Answers
A) 150 B) 108 C) 42 D) 21 E) -21

Solution: OA is D.   100= A+B+C-AB-AC-BC+ABC, which is the same as the following formula   100= A+B+C+(-AB-AC-BC+ABC+ABC+ABC)-2ABC.   The term between parantheses value 18% so the equation to resolve is   100=35+40+50-18-2ABC   therefore the value of ABC is Z =3.5% of 600, is 21. 21 is the correct answer
Answer: D
The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 17%, then the cost price of the article is:
Choices.
A) 500  B) 334  C) 555  D) 664  E) 526

Solution: 110% of S.P. = 616   S.P. = (616 * 100)/110 = Rs. 560   C.P = (110 * 560)/117 = Rs. 526   Answer: Option 526
Answer: E
1000 men have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now?
Choose the correct choice from the following options.
A) 12.9	B) 12.0	C) 12.5	D) 12.2	E) 12.1

Solution: 1000*15 = 1200*x   x = 12.5   Answer:12.5
Answer: C
A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is: Choose the most appropriate option:
A) 29 B) 37 C) 54 D) 42 E) 60

Solution: After 10 days : 150 men had food for 35 days.   Suppose 125 men had food for x days.   Now, Less men, More days (Indirect Proportion)   125 : 150 :: 35 : x   125 * x = 150 x 35   x =	(150 x 35)/125   x = 42.   Answer is 42.
Answer: D
The average age of students of a class is 15.7 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is?  Pick one:  A) 3:7  B) 7:3  C) 2:5  D) 2:1  E) 2:4

Solution: Let the ratio be k : 1. Then,   k * 16.4 + 1 * 15.4 = (k + 1) * 15.7   = (16.4 - 15.7)k = (15.7 - 15.4)   = k = 0.3/0.7 = 3/7   Required ratio = 3/7 : 1 = 3:7.   3:7nswer:3:7
Answer: A
When the smallest of 3 consecutive odd integers is added to four times the largest, it produces a result 731 more than 4times the middle integer. Find the numbers? Choose the correct option:  A) 650  B) 731  C) 698  D) 710  E) 729

Solution: x + 4 (x + 4) = 731 + 4 (x + 2)   Solve for x and find all three numbers   x + 4 x + 16 = 731 + 4 x + 8   x = 723   x + 2 = 725   x + 4 = 727   Check: the smallest is added to four times the largest   723 + 4 * 727= 
723 + 4 * 727 = 3_631
3631   four times the middle   4 * 725= 
4 * 725 = 2_900
2900   3631 is more than 2900 by   3631 - 2900= 
3631 - 2900 = 731
731   731
Answer: B
Three positive integers a, b, and c are such that their average is 22 and a ≤ b ≤ c. If the median is (a + 13), what is the least possible value of c? Choose the correct choice.
A) 27 B) 26 C) 25 D) 24 E) 23

Solution: Solution:   We know that the average value is 22 therefore (a+b+c)/3 = 22   so a+b+c = 66   and b = a + 13   therefore a + (a + 13) + c = 66   The least value of c is when c = b   so take c = a + 13   hence, a + (a + 13) + (a + 13) = 66   i.e., a = 40/3 a non integer therefore c is not equal to b   so take c = b+1 therefore c = a+14   a + (a + 13) + (a + 14) = 66   i.e., a= 39/3= 
39/3 = 13
13   hence, a= 13, b = 26, and c = 27   27nswer: 27
Answer: A