MU-NLPC/Calc-aqua_rat huggingface dataset:
A grocer has a sale of Rs. 1500, Rs. 1500, Rs. 2000, Rs. 2600 for 4 consecutive months. How much sale must he have in the fifth month so that he gets an average sale of Rs. 2000?
Choose the correct choice from the following answers
A) Rs. 4980  B) Rs. 3400  C) Rs. 4000  D) Rs. 2400  E) Rs. 5000

Solution: Total sale for 4 months = Rs. (1500+1500+2000+2600) = Rs. 7600   Required sale = Rs. [ (2000 x 5) - 7600]   = Rs. (10000 - 7600)   = Rs.2400.   Rs. 2400
Answer: D
A man is 18 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is
Choose the correct choice:
A) 21 years  B) 22 years  C) 23 years  D) 12 years  E) 16 years

Solution: Explanation:   Let's Son age is x, then Father age is x+18.   => 2(x+2) = (x+18+2)   => 2x+4 = x+20   => x = 16 years   Option 16 years
Answer: E
A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely ?	Select.
A) 7 min to empty	B) 5 min to full	C) 4 min to full	D) 2 min to empty	E) 6 min to empty

Solution: 1/6-1/10 == 1/15   1/15:2/5::1 : x    2/5*15= 
 2/5*15 = 6
6 min   ANSW6 min to emptyR 6 min to empty
Answer: E
The distance between two cities A and B is 870 Km. A train starts from A at 8 a.m. and travel towards B at 60 km/hr. Another train starts from B at 9 a.m and travels towards A at 75 Km/hr. At what time do they meet?	Select the correct option
A) 09 PM  B) 07 PM  C) 03 PM  D) 05 AM  E) 03 AM

Solution: Explanation:   Suppose they meet x hrs after 8 a.m   then,   [Distance moved by first in x hrs] + [Distance moved by second in (x-1) hrs] = 870.   Therefore, 60x + 75(x-1) = 870.   => x=7.   So,they meet at (8+7) i.e, 15 =>3PM   Answer: 03 PM)
Answer: C
If the average marks of three batches of 45, 50 and 35 students respectively is 40, 50,55, what is the average marks of all the students?	Choose the correct choice:
A) 46 B) 47 C) 48 D) 49 E) 50

Solution: Average marks of batch1 = 40   Students in batch1 = 45   Total marks of batch1 = 45 × 40=1800   Average marks of batch2 = 50   Students in batch2 = 50   Total marks of batch2 = 50 × 50=2500   Average marks of batch3 = 55   Students in batch3 = 35   Total marks of batch3 = 35 × 55=1925   Total students = 45+50+35= 
45+50+35 = 130
130   Average marks of all the students=1800+2500+1925 /130 =47.88   ANSWER:48
Answer: C
What would happen in the previous question if both A and B had started at point P.	Choose the most appropriate option.
A) 800 Km	B) 600 Km	C) 1000 Km	D) 350 Km	E) 250 Km

Solution: DETAILED SOLUTION   For 22nd meeting, total distance travelled = 22 x 2 x 1400 Km   Distance travelled by A = 5/7∗44∗1400=44000Km (1400 x 31 + 600).Therefore, A would be 600 Km from Q.   CORRECT ANSWER 600 Km
Answer: B
The number 311311311311311311311 is: Options.
A) divisible by 3 but not by 11
B) divisible by 11 but not by 3
C) divisible by both 3 and 11
D) neither divisible by 3 nor by 11.
E) None of thses

Solution: Sum of digits= 35 and so it is not divisible by 3.   (Sum of digits at odd places)- (Sum of digits at even places)= 19-16= 
19-16 = 3
3, not divisible by 11.   So, the given number is neither divided by 3 nor by 11.   Answer: neither divisible by 3 nor by 11.
Answer: D
What is the sum of the first 15 terms of an A.P whose 11 th and 7 th terms are 5.25 and 3.25 respectively Choose the most appropriate option: A) 56.25 B) 60 C) 52.5 D) 5.25 E) None of these

Solution: a +10d = 5.25, a+6d = 3.25, 4d = 2, d = ½   a +5 = 5.25, a = 0.25 = ¼, s 15 = 15/2 ( 2 * ¼ + 14 * ½ )   = 15/2 (1/2 +14/2 ) = 15/2 *15/2 =225/ 4= 
225/ 4 = 225/4 = around 56.25
56.25   56.25NSWER:56.25
Answer: A
Rs.4500 amounts to Rs.5544 in two years at compound interest, compounded annually. If the rate of the interest for the first year is 12%, find the rate of interest for the second year?	Choose the correct choice from the following:
A) 10%
B) 16%
C) 70%
D) 80%
E) 20%

Solution: Let the rate of interest during the second year be R%. Given,   4500 * {(100 + 12)/100} * {(100 + R)/100} = 5544   R = 10%   10%nswer:10%
Answer: A
A number is increased by 20% and then decreased by 20%, the final value of the number is ?	Choices.
A) does not change B) decreases by 2% C) increases by 4% D) decreases by 4% E) None of these

Solution: Here, x = 20 and y = - 20   Therefore, the net % change in value   = ( x + y + xy/100)%   = [20 - 20 + (20x - 20)/100]% or - 4%   Since the sign is negative, there is a decrease in value by 4%.   ANSWER:decreases by 4%
Answer: D
The sum of prime numbers that are greater than 60 but less than 70 is	Options
A) 67 B) 128 C) 191 D) 197 E) 260

Solution: A prime number is a number that has only two factors: 1 and itself. Therefore, a prime number is divisible by two numbers only.   Let's list the numbers from 61 to 69.   61, 62, 63, 64, 65, 66, 67, 68, 69   Immediately we can eliminate the EVEN NUMBERS because they are divisible by 2 and thus are not prime.   We are now left with: 61, 63, 65, 67, 69   We can next eliminate 65 because 65 is a multiple of 5.   We are now left with 61, 63, 67, 69.   To eliminate any remaining values, we would look at those that are multiples of 3. If you don’t know an easy way to do this, just start with a number that is an obvious multiple of 3, such as 60, and then keep adding 3.   We see that 60, 63, 66, 69 are all multiples of 3 and therefore are not prime.   Thus, we can eliminate 63 and 69 from the list because they are not prime.   Finally, we are left with 61 and 67, and we must determine whether they are divisible by 7. They are not, and therefore they must be both prime. Thus, the sum of 61 and 67 is 128.   Answer 128.
Answer: B
An empty fuel tank is filled with brand Z gasoline. When the tank is half empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand Y gasoline. At this time, what percent K of the gasoline in the tank is brand Z? Choose the most appropriate option
A) 50%  B) 40%  C) 37.5%  D) 331⁄3%  E) 25%

Solution: Work with fraction of brand Z in the tank.   1st step: brand Z is 1   2nd step: brand Z is 1/2   3rd step: brand Z is (1/2)*(1/2) + 1/2 = 3/4   4th step: brand Z is (1/2)*(3/4) K= 3/8 = 37.5%   Answer (37.5%)
Answer: C
A seller bought tea powder packet at 6 for each, how many for a rupee must he sell to gain 20%? Select the correct option
A) 5	B) 6	C) 7	D) 9	E) 10

Solution: C.P. of 6 toffees = Re. 1   S.P. of 6 toffees = 120% of Re. 1 = Rs.	6   5   For Rs.	6	, toffees sold = 6.   5   For Re. 1, toffees sold = 6 x	5 = 5   6   5
Answer: A
A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good?  Select.
A) 125/167 B) 125/118 C) 125/126 D) 125/128 E) 125/129

Solution: Required probability   = 1 - 1/126 = 125/126   Answer: 125/126
Answer: C
The number of boys in a class is 4/5 times the number of girls. Which one of the following numbers cannot represent the total number of children in the class ?  Choose the correct choice:  A) A)48  B) B)44  C) C)42  D) D)40  E) E)36

Solution: Explanation:   Let number of girls = x and number of boys = 0.8x.   Then, 0.8x + x = 1.8x = total number of students.   Thus, to find exact value of x, the total number of students must be divisible by 1.8.   Answer: 36
Answer: E
The average marks scored by Ganesh in English, Science, Mathematics and History is less than 16 from that scored by him in English, History, Geography and Mathematics. What is the difference of marks in Science and Geography scored by him?  Select the correct option:  A) 40  B) 50  C) 64  D) Data inadequate  E) None of these

Solution: E+H+G+M/4âˆ’E+S+M+H/4=16   â‡’ G - S = 64   Answer 64
Answer: C
A house wife saved $2.50 in buying an item on sale. If she spent $25 for the item, approximately how much percent she saved in the transaction?
Select the correct option.
A) 8%
B) 9%
C) 10%
D) 11%
E) 12%

Solution: Actual price = 25+2.50= 
25+2.50 = 27.5
$27.50   Saving= 2.50/27.50 * 100 = 100/11 = 9% approximately   Answer is 9%
Answer: B
Find the amount on Rs.4000 in 2 years, the rate of interest being 4% per first year and 5% for the second year?
Choose the correct choice from the following answers:  A) 4368  B) 6369  C) 5460  D) 5635  E) 6734

Solution: 4000 * 104/100 * 105/100= 
4000 * 104/100 * 105/100 = 4_368
> 4368   4368nswer:4368
Answer: A
There are 1500 jelly beans divided between two jars, Jar X and Jar Y. If there are 200 fewer jelly beans in jar X than three times the number of beans in jar Y, how many beans are in jar X?
Choose the correct choice.
A) 1050 B) 1075 C) 1100 D) 1125 E) 1150

Solution: X+Y=1500 so Y=1500-X   X=3Y-200   X=3(1500-X)-200   4X=4300   X=1075   The answer is 1075.
Answer: B
If the simple interest on a certain amount in at 4% rate 5 years amounted to Rs.2000 less than the principal. What was the principal? Choose the most appropriate option.
A) 1500
B) 2500
C) 2507
D) 3200
E) 11500

Solution: P - 2000 = (P*5*4)/100   P = 2500   Answer: 2500
Answer: B
A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 130 m long? Pick one:
A) 39.2 sec
B) 35 sec
C) 44 sec
D) 40 sec
E) none of these

Solution: Speed = 45 km/hr = 45 Ã— (5/18) m/s   = 150/12 = 50/4 = 25/2 m/s   Total distance = length of the train + length of the platform   = 360 + 130= 
360 + 130 = 490
490 meter   Time taken to cross the platform= 490/(25/2) = 490 Ã— 2/25 = 39.2 seconds   39.2 secNSWER:39.2 sec
Answer: A
The length and breadth of a room are 8 m and 6 m respectively. A cat runs along all the four walls and finally along a diagonal order to catch a rat. How much total distance is covered by the cat?
Options:
A) 10
B) 14
C) 38
D) 48
E) 47

Solution: diagonal=10   2(l+b)+d=38   ANSWER:38
Answer: C
In a certain game, you perform three tasks. You flip a coin, and success would be heads. You roll a single die, and success would be a six. You pick a card from a full playing-card deck, and success would be picking a spades card. If exactly one of these three tasks is successful, then you win the game. What is the probability of winning?  Choose the correct choice from the following answers:  A) 23/48  B) 11/16  C) 15/32  D) 14/36  E) 17/56

Solution: The answer is 23/48   Probability of just one enent will be happining   So, Probability heads=1/2   Probability number 6 =1/6   Probability picking a spades card =1/4   so, Probability win by getting heads= 1/2*5/6*3/4 = 15/48   Probability win by getting number 6 = 1/2*1/6*3/4 = 3/48   Probability win by picking a spades card =1/2*5/6*1/4=5/48   Probability wining= 15/48+3/48+5/48 =23/48
Answer: A
If y is an integer, which of the following must be an even integer?	Options:
A) y^2-y-1 B) y^2-4y+6 C) y^2-5y+5 D) y^2+3y+8 E) y^2+2y+10

Solution: Check the options by plugging in some values ( Preferably smaller integers like 1 and 2 )   A: y^2-y-1 = -1 { If y = 1 }   B: y^2-4y+6 = 3 { If y = 1 }   C: y^2-5y+5 = 1 { If y = 1 }   y^2+3y+8: y^2+3y+8 = 12 { If y = 1 }y^2+3y+8 = 18 { If y = 2 }   E: y^2+2y+10 = 13 { If y = 1 }   Thus the only possible answer is (y^2+3y+8)
Answer: D
At a meeting of 5 Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the Chiefs of Staff be seated around a circular table?	Choose the correct choice.
A) 9	B) 12	C) 15	D) 18	E) 21

Solution: 5 people can be arranged around a table in 4! ways.   Consider the two chiefs who will not sit together as a single unit.   The number of ways to arrange 4 units around a table is 3!   We need to multiply this by 2 as the two people can be switched in each arrangement.   The total number of ways to arrange the chiefs is 4! - 2*3! = 2*3! = 12   The answer is 12.
Answer: B
If 11.25 m of a uniform iron rod weight 42.75 kg, what will be the weight of 6 m of the same rod ?  Choose the correct choice from the following choices.
A) 22.8 kg  B) 25.6 kg  C) 28 kg  D) 26.5 kg  E) None of these

Solution: Solution   Let the required weight be x kg. Then, Less length, Less weight   ∴ 11.25 : 6 :: 42.75 : x ⇔ 11.25 × x = 6 × 42.75 ⇔ x = ⇔ x = (6x42.75)/11.25=22.8. 22.8 kgnswer 22.8 kg
Answer: A
If a and b are positive integers of Y such that a/b=2.86, which of the following must be a divisor of a? Options.
A) 10
B) B.13
C) 18
D) 26
E) 50

Solution: The prompt gives us a couple of facts to work with:   1) A and B are positive INTEGERS   2) A/B = 2.86   We can use these facts to figure out POSSIBLE values of A and B. The prompt asks us for what MUST be a divisor of A. Since we're dealing with a fraction, A and B could be an infinite number of different integers, so we have to make both as SMALL as possible; in doing so, we'll be able to find the divisors that ALWAYS divide in (and eliminate the divisors that only SOMETIMES divide in).   The simplest place to start is with...   A = 286   B = 100   286/100= 
286/100 = 143/50 = around 2.86
2.86   These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)...   A= 143   B = 50   143/50= 
143/50 = 143/50 = around 2.86
2.86   There is no other way to reduce this fraction, so A must be a multiple of 143 and B must be an equivalent multiple of 50. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A....   Since A is a multiple of 143, we have to 'factor-down' 143. This gives us (11)(13). So BOTH of those integers MUST be factors of A. You'll find the match in the answer choices.   Final Answer:   B.13
Answer: B
The cost of 2 chairs and 3 tables is Rs.1300. The cost of 3 chairs and 2 tables is Rs.1200. The cost of each table is more than that of each chair by?
Pick one:
A) 377  B) 268  C) 297  D) 272  E) 100

Solution: 2C + 3T = 1300 --- (1)   3C + 3T = 1200 --- (2)   Subtracting 2nd from 1st, we get   -C + T = 100 => T - C = 100   Answer: 100
Answer: E
Robert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15 kmph. At what speed musthe travel to reach A at 1 PM? Choose the correct option:
A) 10 kmph  B) 11 kmph  C) 12 kmph  D) 13 kmph  E) 13 kmph

Solution: Let the distance travelled by x km.   Then, x - x = 2   10 15   3x - 2x = 60   x = 60 km.   Time taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs.   10   So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.   Required speed = 60 kmph. = 12 kmph.   5   12 kmph
Answer: C
select which is different..342,511,126,215. Choose the correct choice from the following choices:
A) 342
B) 511
C) 126
D) 215
E) can't be calculated

Solution: 7*7*7= 
7*7*7 = 343
343,343-1=342   8*8*8= 
8*8*8 = 512
512,512-1=511   5*5*5= 
5*5*5 = 125
125,125+1=126   6*6*6= 
6*6*6 = 216
216,216-1=215   answer 126
Answer: C
A man invests Rs. 7,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum?	Choose the correct choice from the following answers
A) Rs. 1200
B) Rs. 1300
C) Rs. 3500
D) Rs. 2000
E) None of these

Solution: Explanation :   Interest on Rs.7000 at 5% per annum = ( 7000 × 5 × 1) / 100 = Rs. 350   Let his additional investment at 8% = x   Interest on Rs.x at 8% per annum = ( x × 8 × 1 ) / 100 = 2x/25.   To earn 6% per annum for the total, interest = (7000 + x) × 6 × 1/100.   => 350 + 2x/25 = (7000 + x) × 6 × 1/100.   => 35000 + 8x = (7000 + x) × 6.   => 35000 + 8x = 42000 + 6x.   => 2x=7000.   => x=3500.   Answer : Rs. 3500
Answer: C
If xy > 0, which of the following must be negative? Select the correct option: A) -x/y B) x/y C) x+y D) x^2 E) y^2

Solution: Given xy> 0 So both will be the positive integers. If both are positive, then B,C,D,E also positive.   -x/ynswer : -x/y
Answer: A
One tap, working alone at its maximum constant rate, can fill a certain sink in 287 seconds. A second tap, working alone at its maximum constant rate, can fill the same sink in 283 seconds. If both taps work together at their respective maximum constant rates, the time it will take to fill the sink is closest to  Choose the correct choice from the following choices.
A) 142 seconds	B) 150 seconds	C) 177 seconds	D) 200 seconds	E) 270 seconds

Solution: Tap 1 : 283 secs   Tap 2 : 287 secs   Considering the average of these 2 taps : 285 secs.   So 1 tap can fill the tank in 285 secs, so 2 taps can fill the tank in 285/2= 
285/2 = 285/2 = around 142.5
142.5 secs.   Closest answer is 142 seconds.
Answer: A
A BAG CONTAINS 6 RED AND 4 BLUE BALLS .2 BALLS ARE DRAWN AT RANDOM. FIND THE PROBABILITY THAT THEY ARE OF SAME COLOUR.
Answers
A) 4/15 B) 5/15 C) 6/15 D) 7/15 E) 8/15

Solution: LET S BE THE SAMPLE SPACE   THEN N(S)=NO OF WAYS OF 7/15RAWING 2 BALLS OUT OF   (6+4)= 
  (6+4) = 10
10C2=(10*9)/(2*1)= 
(10*9)/(2*1) = 45
45   LET E=EVENT OF GETTING BOTH BALLS OF SAME COLOUR   THEN N(E)=NO OF WAYS(2 BALLS OUT OF SIX) OR(2 BALLS OUT OF 4)   =(6C2+4C2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6= 
15+6 = 21
21   P(E)=N(E)/N(S)=21/45=7/15   Option: 7/15
Answer: D
A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?	Answers.
A) 210 m  B) 230 m  C) 240 m  D) 260 m  E) 270 m

Solution: Speed =72x(5/18) m/sec =20m/sec   Time = 26 sec.   Let the length of the train be x metres.   (x+250)/26 =20   x + 250 = 520   x = 270.   answer :270 m
Answer: E
A man walks at a speed of 6 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?  Pick one
A) 1 4/2 hours
B) 1 5/8 hours
C) 2 1/6 hours
D) 2 1/1 hours
E) 2 1/2 hours

Solution: Required time   = (5 1/4)/6 + (5 1/4)/7   = 1 5/8 hours.   Answer:1 5/8 hours
Answer: B
A sucrose solution contains 10 grams of sucrose per 100 cubic centimeters of solution. If 60 cubic centimeters of the solution were poured into an empty container, how many grams of sucrose would be in the container?	Answers.
A) 4.00
B) 6.00
C) 5.50
D) 6.50
E) 6.75

Solution: We are given that a sucrose solution contains 10 grams of sucrose per 100 cubic centimeters of solution. Since we are dealing with a solution, we know that the grams of sucrose is proportional to the number of cubic centimeters of solution. Thus, to determine how many grams of sucrose would be in the container when we have 60 cubic centimeters of solution, we can set up a proportion.   We can say: “10 grams of sucrose is to 100 cubic centimeters of solution as x grams of sucrose is to 60 cubic centimeters of solution.” Let’s now set up the proportion and solve for x.   10/100 = x/60   When we cross multiply we obtain:   (10)(60) = 100x   600 = 100x   6.00 = x   There are 6.00 grams of sucrose in the solution in the container.   The answer is 6.00.
Answer: B
The workforce of Company X is 60% female. The company hired 20 additional male workers, and as a result, the percent of female workers dropped to 55%.How many employees did the company have after hiring the additional male workers?
Choose the correct answer:
A) 160	B) 220	C) 240	D) 360	E) 420

Solution: Let's xx be total quantity of employees   0.6x=females before adding men   0.55(x+20)=females after adding men   as quantity of women doesn't change we can make an equation:   0.6x=0.55(x+20)   0.05x=11   x=220 - this is quantity of employees before adding 2020 men   So after adding it will be 240   Answer is 240
Answer: C
The product of the squares of two positive integers is 9. How many pairs of positive integers satisfy this condition?
Choose the correct choice.
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: Ans:B - 1 pairs   (xˆ2)(yˆ2) = 9 [square root both sides]   xy = 3   3 = 1x3, 3x1   Cancel the repeats   This leaves us with exactly 1 options.   Hence, 1
Answer: B
If xy ≠ 0 and x^2y^2 − 3xy = 28, which of the following could be y in terms of x?
I. 1/(2x)
II. -4/x
III. 7/x Select
A) I only	B) II only	C) I and II	D) I and III	E) II and III only

Solution: (x^2)(y^2) – 3xy - 28 = 0   (xy – 7)(xy + 4) = 0   xy – 7 = 0 or xy + 4 = 0   xy = 7 or xy = -4   Since we need y in terms of x, we can isolate y in both of our equations.   y = 7/x or y = -4/x   Answer: II and III only
Answer: E
4, 7, 13, 25, 49, (...)
Choices:
A) 22  B) 35  C) 97  D) 32  E) 25

Solution: Explanation :   4   4 × 2 - 1= 7   7 × 2 - 1 =13   13 × 2 - 1 = 25   25 × 2 - 1 = 49   49 × 2 - 1 = 97   Answer : Option 97
Answer: C
What is the greatest possible length which can be used to measure exactly the lengths 8 m, 4 m 20 cm and 12 m 20 cm?	Choose the correct choice from the following choices.
A) 20 cm	B) 23 cm	C) 25cm	D) 10 cm	E) 28 cm

Solution: Required length = HCF of 800 cm, 420 cm, 1220 cm = 20 cm   20 cmnswer is 20 cm
Answer: A
For a finite sequence of non zero numbers, the number of variations in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 3, -3, 2, 5, -4, -6 ? Choose one
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: Given sequence: {1, -3, 2, 5, -4, -6}   The questions basically asks: how manypairs of consecutive termsare there in the sequence such that the product of these consecutive terms is negative.   1*(-3)=-3=negative;   -3*2=-6=negative;   2*5= 
2*5 = 10
10=positive;   5*(-4)=-20=negative;   (-4)*(-6)= 
(-4)*(-6) = 24
24=positive.   So there are 3 pairs of consecutive terms of the sequence for which the product is negative.   1nswer: 1.
Answer: A
It is required to seat 3 boys and 2 girls in a row so that the girls occupy the even places. How many such arrangements are possible?	Choose the correct choice from the following options:  A) 28  B) 21  C) 30  D) 22  E) 12

Solution: Total number of candidates = 3 + 2= 
3 + 2 = 5
5. In the row of 5 positions, the even places are 2nd, 4th.   Now, number of even places= 2.   Number of girls to occupy the even places = 2.   Even places can be filled = P (2, 2) ways.   Number of boys = 3.   The remaining 3 places can be filled by 3 boys = P (3, 3) ways   By the fundamental principle of counting:   The required number of seating arrangements   P(2, 2) x P(3, 3) = 2! x 3! = 2 x 6 = 12   ANSW12R:12
Answer: E
The price of a jacket is reduced by 25%. During a special sale the price of the jacket is reduced another 20%. By approximately what percent must the price of the jacket now be increased in order to restore it to its original amount?
Choose the correct choice from the following answers:
A) 66.67	B) 35	C) 48	D) 65	E) 67.5

Solution: 1) Let the price of jacket initially be $100.   2) Then it is decreased by 25% , therefore bringing down the price to $75.   3) Again it is further discounted by 20%, therefore bringing down the price to $60.   4) Now 60 has to be added byX %in order to equal the original price.   60 + ( X% ) 60 = 100.   Solving this eq for X, we get X = 66.67   66.67ns is 66.67.
Answer: A
walking at ¾ of his usual speed ,a man is late by 2 ½ hr. the usual time is Choices
A) 7 1/9
B) 7 1/2
C) 7 1/5
D) 7 1/8
E) 7 1/7

Solution: Usual speed = S Usual time = T Distance = D New Speed is ¾ S New time is 4/3 T 4/3 T – T   = 5/2 T=15/2   = 7 1/2   Aswer: 7 1/2
Answer: B
United Telephone charges a base rate of $6.00 for service, plus an additional charge of $0.25 per minute. Atlantic Call charges a base rate of $12.00 for service, plus an additional charge of $0.20 per minute. For what number of minutes would the bills for each telephone company be the same?	Select the correct option
A) 20 minutes B) 110 minutes C) 120 minutes D) 140 minutes E) 160 minutes

Solution: Lets take number of minutesx.   Given that, 6+0.25x=12+0.2x ->0.05x=2 -> x=120minutes   ANS 120 minutes
Answer: C
Eight people are on an elevator that stops at exactly 8 floors. What is the probability that exactly one person will push the button for each floor?	Answers.
A) 8!/8^8
B) 8^8/8!
C) 8/8!
D) 8/8^8
E) 1/8^8

Solution: Each person out of 8 has 8 options, hence total # of outcomes is 8^8;   Favorable outcomes will be 8!, which is # of ways to assign 8 different buttons to 8 people   So basically # of arrangements of 8 distinct objects: 8!.   P=favorable/total=8!/8^8   8!/8^8nswer: 8!/8^8.
Answer: A