MU-NLPC/Calc-aqua_rat huggingface dataset:
A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?  Choose the correct choice from the following answers
A) 230  B) 288  C) 267  D) 256  E) 298

Solution: Relative speed = 120 + 80= 
120 + 80 = 200
200 km/hr.= 200 * 5/18 = 500/9 m/sec.   Let the length of the other train be x m.   Then, (x + 270)/9 = 500/9 => x = 230.   230nswer: 230
Answer: A
A boat travels 40 km downstream in 8 hours and 24 km upstream in 12 hours. Find the speed of the boat in still water and the speed of the water current.	Choose the correct choice:
A) 8 km/hr, 1 km/hr
B) 3.5 km/hr, 1.5 km/hr
C) 1 km/hr, 6 km/hr
D) 2 km/hr, 1 km/hr
E) 4 km/hr, 1 km/hr

Solution: Downstream speed=40km/8hrs   =5 kmph   upstream speed40  /8= 
40  /8 = 5
5 kmph   upstream speed=24km/12hrs   =2 kmph   speed of boat24  /12= 
24  /12 = 2
2 kmph   speed of boat=avg of downstream and upstream speeds   speed of boat=(5+2)/2= 
(5+2)/2 = 7/2 = around 3.5
3.5kmph.   current speed=half of the difference of downstream and upstream speeds   currend speed=(5-2)/2= 
(5-2)/2 = 3/2 = around 1.5
1.5kmph   ans is 3.5km/hr,1.5km/hr   ANSWER:3.5 km/hr, 1.5 km/hr
Answer: B
In the xy-plane, the point (2, 1) is the center of a circle. The point (-2, 1) lies inside the circle and the point (2, -5) lies outside the circle. If the radius r of the circle is an integer, then r =
Choose the correct choice from the following answers.
A) 6
B) 5
C) 4
D) 3
E) 2

Solution: An easy way to solve this question will be just to mark the points on the coordinate plane.   You'll see that the distance between the center (2, 1) and the point inside the circle (-2, 1) is 4 units   (both points are on y=1 line so the distance will simply be  2-(-2)= 
 2-(-2) = 4
4)   So the radius must be more than 4 units.   The distance between the center (2,1) and the point outside the circle (2,-5) is 6 units   (both points are on x=2 line so the distance will simply be  1-(-5)= 
 1-(-5) = 6
6)   So the radius must be less than 6 units, which implies 4 < r < 6, thus as r is an integer then r=5.   Answer: 5.
Answer: B
If there are 30 red and blue marbles in a jar, and the ratio of red to blue marbles is 3:2, what is the probability that, drawing twice, you will select two red marbles if you return the marbles after each draw?  Choose the correct option:
A) 1/25
B) 2/25
C) 6/25
D) 9/25
E) 21/25

Solution: 30 red and blue marbles in a jar, and the ratio of red to blue marbles is 3:2   So, 5x=30 ---> x=6   Red marbles = 3*x = 3*6= 
3*6 = 18
18   Blue marbles= 2*x = 2*6= 
2*6 = 12
12   Prob to select a red marble= 18/30 = 3/5   Prob to select 2 red marbles with replacement = 3/5*2*5= 
3/5*2*5 = 6
6/25   Hence, answer will be 6/25.
Answer: C
What number has a 5:1 ratio to the number 10?	Choose the correct choice from the following.
A) 22 B) 50 C) 88 D) 52 E) 12

Solution: 5:1 = x: 10   x = 50   Answer: 50
Answer: B
There are 6 letters for 3 envelopes. In how many different ways can the envelopes be filled? Choose the correct choice from the following answers
A) 120 B) 130 C) 100 D) 110 E) 140

Solution: The 1st envelope can be filled up in 6 ways.   The 2nd envelope can be filled up in 5 ways and the 3rd envelope can be filled up in 4 ways.   Therefore, by the principle of association, the three envelopes can be filled up in 6 x 5 x 4 = 120 ways   120NSWER:120
Answer: A
In a certain year, the population of a certain town was 9000. If in the next year the population of males increases by 5% and that of the females by 8% and the total population increases to 9600, then what was the ratio of population of males and females in that given year? Choose one
A) 4 : 5	B) 5 : 4	C) 2 : 3	D) Data inadequate	E) None of these

Solution: Let the population of males = x; then the population of females = 9000 – x   Now, 5% of x + 8% of (9000 – x)   = (9600 – 9000 ) = 600   or 0.05x + 720 – 0.08x = 600   or 720 – 600 = 0.08x – 0.05x   or, 120 = 0.03x   x = 4000   Reqd ratio of population of males and females   4000/9000−4000=4000/5000=4:5   4 : 5nswer 4 : 5
Answer: A
In how many ways can 8 Indians and, 4 American and 4 Englishmen can be seated in a row so that all person of the same nationality sit together?  Options:
A) 3! 4! 8! 4!  B) 3! 8!  C) 4! 4!  D) 8! 4! 4!  E) None

Solution: Solution: Taking all person of same nationality as one person, then we will have only three people.   These three person can be arranged themselves in 3! Ways.   8 Indians can be arranged themselves in 8! Way.   4 American can be arranged themselves in 4! Ways.   4 Englishman can be arranged themselves in 4! Ways.   Hence, required number of ways = 3!*8!*4!*4! Ways.   3! 4! 8! 4!nswer: Option 3! 4! 8! 4!
Answer: A
In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 82 more candidates got selected than A. What was the number of candidates appeared from each State?	Choose the correct choice from the following:
A) 8400	B) 8200	C) 6000	D) 5000	E) 4000

Solution: State A and State B had an equal number of candidates appeared.   In state A, 6% candidates got selected from the total appeared candidates   In state 8200, 7% candidates got selected from the total appeared candidates   8200ut in State 8200, 82 more candidates got selected than State A   From these, it is clear that 1% of the total appeared candidates in State 8200 = 82   => total appeared candidates in State 8200 = 82 x 100 = 8200   => total appeared candidates in State A = total appeared candidates in State 8200 = 8200
Answer: B
The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is? Choose the correct choice from the following:
A) 3%
B) 4%
C) 5%
D) 6%
E) 7%

Solution: 65*(90/100)*((100-x)/100) = 56.16   x = 4%   ANSWER:4%
Answer: B
A container holding 12 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 4 ounces of a solution that is 1 part alcohol to 3 parts water. What is the ratio of alcohol to water in the resulting solution?  Select the correct option.
A) 2:5 B) 3:7 C) 3: 5 D) 5:11 E) 7:3

Solution: Container 1 has 12 ounces in the ratio 1:2   or,   x+2x=12 gives x(alcohol)=4 and remaining water =8   container 2 has 4 ounces in the ratio 1:3   or,   x+3x=4 gives x(alcohol)=1 and remaining water =3   mixing both we have alcohol=4+1 and water =8+3   ratio thus alcohol/water =5/11   Answer 5:11
Answer: D
By using the numbers 1, 2, 3, 5 and 9 only once, how many five digit numbers can be made that are divisible by 25?	Options.
A) 0
B) 1
C) 4
D) 8
E) 6

Solution: A number to be divisible by 25 must end with 00, 25, 50, or 75.   So, there are the following cases possible:   139-25 --> the first three digits can be arranged in 3=6 ways.   Total = 6.   Answer: 6.
Answer: E
A man can do a piece of work in 5 days, but with the help of his son he can do it in 2 days. In what time can the son do it alone ?  Choose the correct option:
A) 7 1/2 days
B) 6 1/2 days
C) 5 1/3 days
D) 3 1/3 days
E) None of these

Solution: Explanation:   In this type of question, where we have one person work and together work done. Then we can easily   get the other person work just by subtracting them. As   Son's one day work =   (1/2−1/5)=(5−2)/10=3/10   So son will do whole work in 10/3 = 3 1/3 days   Answer: 3 1/3 days
Answer: D
If p and q are positive integers and q ≠ 1, then pq(q −1) is  Choose the correct choice from the following answers
A) p+q  B) p-q  C) pq^2-pq  D) pq^2  E) pq

Solution: pq(q-1) = pq^2-pq   Answer : pq^2-pq
Answer: C
During the first week of performances of a certain play, 5,400 tickets were sold, all at reduced price. During the remaining weeks of performances, 5 times as many tickets were sold at full price as were sold at reduced price. If the total number of tickets sold T was 25,200, how many of them were sold at full price?
Choose the correct choice from the following
A) 21,000	B) 19,800	C) 16,500	D) 15,800	E) 8,700

Solution: Given:   The question tells us about the number of tickets sold in the first week at reduced price = 5,400. It also tells us that during the remaining weeks, the number of tickets sold at full price was 5 times the no. of tickets sold at reduced price. The total tickets sold was 25,200, and we are asked to find the number of tickets that where sold at full price.   Approach:   The question asks us to find the number of ticket sold at full price. We know that the number of tickets sold at full price was 5 times the no. of tickets sold at reduced price in remaining weeks. Hence, assuming tickets sold at reduced price in remaining weeks to be x would give us the no. of tickets sold at full price to be 5x.   Tickets sold in first week + Tickets sold in remaining weeks = Total no. of tickets soldi.e.   Tickets sold in first week + Tickets sold at full price in remaining weeks + Tickets sold at reduced price in remaining weeks = Total no. of tickets sold   We know the no. of tickets sold during first week and the total no. of tickets sold. We will use this relation to get to our answer.   Working Out:   Tickets sold in first week + Tickets sold at full price in remaining weeks + Tickets sold at reduced price in remaining weeks = Total no. of tickets sold   Substituting values in the equation, we get   5,400 + 5x + x = 25,200   x= 3,300   Tickets sold at full price = 5x = 16,500   Answer: Option 16,500
Answer: C
If 55 percent of congress are Democrats and the rest are Republicans. In a vote on a new law , if 40 percent of the members who are Democrats and 20 percent of the members who are Republicans are expected to vote for the new law , what percent of the members are expected to vote for the new law ? Choose the correct choice from the following options.
A) 30%
B) 31%
C) 33%
D) 35%
E) 39%

Solution: Say there are total of 100 members in the congress . Thus 55 are Democrats and 45 are Republicans.   55*0.4= 
55*0.4 = 22
22 Democrats are expected to vote for the new law ;    45*0.20= 
 45*0.20 = 9
9 Republicans are expected to vote for the new law.   Thus total of   22+9= 
  22+9 = 31
31 members are expected to vote for the new law, which is 31% of the total number of congress members .   Answer: 31%.
Answer: B
In a competitive examination in a state A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each state?
Choose the correct choice from the following answers:  A) 8000  B) 7540  C) 6500  D) 9100  E) 6000

Solution: Let the number of candidates appeared be x   then, 7% of x - 6% of x = 80   1% of x = 80   x = 80*100= 
80*100 = 8_000
8000   8000nswer is 8000
Answer: A
If one person completes a journey in 10 hrs. He travels 1st half of the journey at the rate of 21 km/hr and 2nd half at therate of 24 km/hr. Find the total journey in km.
Choose the correct option:
A) 200 km
B) 220 km
C) 224 km
D) 230 km
E) 254 km

Solution: distance = speed x time   Let time taken to travel the first half = x hr   then time taken to travel the second half = (10 - x) hr   Distance covered in the the first half = 21x   Distance covered in the the second half = 24(10 - x)   But distance covered in the the first half = Distance covered in the the second half   => 21x = 24(10 - x)   => 21x = 240 - 24x   => 45x = 240   => 9x = 48   => 3x = 16   ⇒x=163Hence Distance covered in the the first half = 21x=21×163=7×16=112 kmTotal distance = 2×112=224 km   224 km
Answer: C
A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?	Select:
A) 40 ft	B) 34 ft	C) 68 ft	D) 78 ft	E) 88 ft

Solution: We have: l = 20 ft and lb = 680 sq. ft.   So, b = 34 ft.   Length of fencing = (l + 2b) = (20 + 68)= 
(20 + 68) = 88
88 ft.   ANSW88 ftR:88 ft
Answer: E
Train X crosses a stationary train Y in 60 seconds and a pole in 25 seconds with the same speed. The length of the train X is 300 m. What is the length of the stationary train Y? Choose one:
A) 228
B) 420
C) 882
D) 661
E) 222

Solution: Let the length of the stationary train Y be LY   Given that length of train X, LX = 300 m   Let the speed of Train X be V.   Since the train X crosses train Y and a pole in 60 seconds and 25 seconds respectively.   => 300/V = 25 ---> ( 1 )   (300 + LY) / V = 60 ---> ( 2 )   From (1) V = 300/25= 
300/25 = 12
12 m/sec.   From (2) (300 + LY)/12= 60   => 300 + LY = 60 (12) = 720   => LY = 720 - 300= 
720 - 300 = 420
420 m   Length of the stationary train= 420 m   Answer:420
Answer: B
Two persons start at the same point, walk in opposite directions with 6 km/hr and 4 km/hr respectively.
What is the distance separated after 4 and half hrs?  Choices:
A) 45 km  B) 48 km  C) 50 km  D) 29.250 km  E) 25.250 km

Solution: As the two persons are moving in the opposite direction, so they will be separateed in 1 hour = 6 + 4= 
6 + 4 = 10
10 km.   They will be separated in 4.5 hours= 10 * 4.5= 
10 * 4.5 = 45
45 km   45 kmNSWER:45 km
Answer: A
Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same period is? Answers.
A) 81.6	B) 88.6	C) 81.1	D) 81.5	E) 81.2

Solution: SI = 40 + 40   CI = 40 + 40 + 1.6= 
40 + 40 + 1.6 = 81.6
81.6   81.6nswer: 81.6
Answer: A
In a BCCI meeting there are 11 people. All shake hands with each other once. How many handshakes will be there altogether? Choose the correct choice from the following
A) 28  B) 10  C) 11  D) 19  E) 18

Solution: There will be n-1 handshakes as A person will shake hands with all the other members.   =11-1= 
11-1 = 10
10   Answer:10
Answer: B
Simplify:(4x2 - 2x) - (-5x2 - 8x)  Choose the correct option.
A) 2x(3x + 2)  B) 4x(3x + 2)  C) 2-(3x + 2)  D) 3x(3x - 2)  E) 3x(3x + 2)

Solution: (4x2 - 2x) - (-5x2 - 8x)   = 4x2 - 2x + 5x2 + 8x.   = 4x2 + 5x2 - 2x + 8x.   = 9x2 + 6x.   = 3x(3x + 2).   Answer: (3x(3x + 2)) 3x(3x + 2)
Answer: E
A train moves fast a telegraph post and a bridge 260 m long in 8 sec and 20 sec respectively. What is the speed of the train? Choose the correct option
A) 79.5 B) 39.5 C) 79.9 D) 78.0 E) 79.0

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 8 => x = 8y   (x + 260)/20 = y   y = 21.67   Speed = 21.67m/sec = 21.67 * 18/5 = 78 km/hr.   Answer:78.0
Answer: D
20 is subtracted from 60% of a number, the result is 88. Find the number? Choose the correct choice from the following answers:	A) 120	B) 300	C) 180	D) 170	E) 148

Solution: (60/100) * X â€“ 20 = 88   6X = 1080   X = 180   Answer:180
Answer: C
The sum of the ages of a father and son is 45 years. Five years ago, the product of their ages was four times the father’s age at that time. The present age of father and son, repectively are Choose the correct choice from the following choices:
A) 25 years , 10 years	B) 36 years, 9 years	C) 39 years, 6 years	D) 40 years, 6 years	E) None of these

Solution: Let son’s age = x years. The father’s age = (45 - x) years   we have (x - 5)(45 - x - 5) = 4(45 - x - 5)   =>x - 5 = 4   => x = 9   Thus, ages are 36 years and 9 years.   ANSWER:36 years, 9 years
Answer: B
A tank can supply water to a village for 80 days. If a leak at the bottom of the tank drains out 10 liters per day, the supply lasts for 60 days only. For how many days will the supply last if the leak drains out 20 liters per day?
Pick
A) 42	B) 45	C) 48	D) 50	E) 55

Solution: Losing 10 liters per day results in a loss of 600 liters in 60 days. So, those 600 liters were for 20 days, making daily consumption of the village 30 liters per day. Thus the capacity of the tank is  30*80= 
 30*80 = 2_400
2400 liters.   Losing 20 liters plus 30 liters gives 50 liters per day. At this rate the supply will last   2400/50= 
  2400/50 = 48
48 days.   The answer is 48.
Answer: C
The ratio by weight, measured in pounds, of books to clothes to electronics in a suitcase initially stands at 7:4:3. Someone removes 6 pounds of clothing from the suitcase, thereby doubling the ratio of books to clothes. How many pounds do the electronics in the suitcase weigh?
Choose the correct option.
A) 1	B) 3	C) 5	D) 7	E) 9

Solution: The weights of the items in the suitcase are 7k, 4k, and 3k.   If removing 6 pounds of clothes doubles the ratio of books to clothes, then 6 pounds represents half the weight of the clothes.   2k = 6 pounds and then k = 3 pounds.   The electronics weigh 3(3) = 9 pounds.   The answer is 9.
Answer: E
The rate of spin of a certain gyroscope doubled every 10 seconds from the moment a particular stopwatch started. If after a minute and a half the gyroscope reached a speed of 1600 meters per second, what was the speed, in meters per second, when the stopwatch was started?
Choose the most appropriate option
A) 25/3	B) 25/4	C) 25/8	D) 25/16	E) 25/32

Solution: Let x be the original speed when the stopwatch was started.   In 90 seconds, the speed doubled 9 times.   2^9 * x = 1600   x = (2^6 * 25) / 2^9 = 25/8   The answer is 25/8.
Answer: C
In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 8 eggs. If the cost of each pound of rice is $0.33, then how many E cents does a liter of kerosene cost? [One dollar has 100 cents.] Choose the correct choice from the following:
A) 0.33 B) 0.44 C) 0.55 D) 44 E) 55

Solution: Main thing to remember is answer is asked in cents, however when we calculate, it comes up as 0.44 $   Just multiply by 100, Answer E= 44.44
Answer: D
If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is ? Options.
A) 1/9 B) 1/2 C) 1/6 D) 3/2 E) 1/4

Solution: The number of exhaustive outcomes is 36.   Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2   P(E) = 1 - 1/2 = 1/2.   Answer: 1/2
Answer: B
Students of three different classes appeared in common examination. Pass average of 10 students of first class was 55%, pass average of 15 students of second class was 60% and pass average of 25 students of third class was 80% then what will be the pass average of all students of three classes?
Choose the correct choice from the following answers
A) 74% B) 75% C) 69% D) 72% E) None

Solution: Solution:   Sum of pass students of first, second and third class,   = (55% of 10) + (60% of 15)+ (80% of 25)   = 5.5+9+20= 
5.5+9+20 = 34.5
34.5   Total students appeared,= 10+15+25= 
10+15+25 = 50
50   Pass average,= 34.5*100/50= 
34.5*100/50 = 69
69%.   Answer: Option 69%
Answer: C
If a farmer sells 5 of his chickens, his stock of feed will last for 4 more days than planned, but if he buys 20 more chickens, he will run out of feed 1 day earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have? Pick one:
A) 15
B) 20
C) 20/3
D) 25
E) 10

Solution: Let x = total feed required for the planned period   n= number of chicken   t = total time of the planned feed   x = nt   1) x = (n-5) * (t+4)   2) x = (n+20) * (t-1)   equating 1 &2   (n-5) * (t+4) = (n+20) * (t-1)   5n = 25t   n =5t   x= n * n/5   substituting this value in 1   n * n/5 = (n-5) * (n/5+4)   15n = 100   n =20/3   20/3
Answer: C
A can do a piece of work in 20 days which B can do in 12 days. B worked at it for 9 days. A can finish the remaining work in ?	Pick one
A) 3 days	B) 5 days	C) 6 days	D) 7 days	E) 11 days

Solution: B's 9 day's work = 9 x (1/12) = 3/4   Remaining work = (1 - 3/4) = 1/4   1/4 work is done by A in = 20 x (1/4) = 5 days.   answer : 5 days
Answer: B
The difference between the local value and the face value of 4 in the numeral 98625147 is  Select:
A) 36  B) 63  C) 34  D) 30  E) 33

Solution: Explanation:   (Local value of 4) - (Face value of 4) = (40 - 4)= 
(40 - 4) = 36
36   36)
Answer: A
3 buffaloes eat as much as 4 cows or 2 oxen. At a farm there are 15 buffaloes, 8 oxen and 24 cows. The fodder for these cattle is available for 24days. If 8 more cows & 9 more buffaloes are brought in, how long will the fodder last?	Pick:
A) 10 B) 13 C) 15 D) 18 E) 21

Solution: Sol. 2 oxen = 3 buffaloes = 4 cows 8 oxen = 16 cows and 15 buffaloes = 20 cows 16 cows + 20 cows + 24 cows = 60 cows Since fodder is available for 60 cows for 24 days   So fodder will be available for  (60 + 8 + 12)= 
 (60 + 8 + 12) = 80
80 cows c 24x60 .0 .   for-^—=18 days.   18
Answer: D
Consider below info to be a table:
AMOUNT OF BACTERIA
TIME - AMOUNT
1PM - 10gms
4PM - x gms
7PM - 12.1 gms
Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same factor during each of the two 3-hour periods shown, how many grams of bacteria were present at 4PM ?
Pick:
A) 12.0
B) 12.1
C) 12.2
D) 12.3
E) 11.0

Solution: let say the factor is x, the at 7PM quantity = 10 (i.e. quantity @1PM)* x^2 =12.1 => x^2 =1.21 or x = 1.1 => @4PM quantity = 10x =10*1.1= 
10*1.1 = 11
11.   Answer 11.0
Answer: E
There were 36,000 hardback copies of a certain novel sold before the paperback version was issued. From the time the first paperback copy was sold until the last copy of the novel was sold 8 times as many paperback copies as hardback copies were sold. If a total of 441,000 copies of the novel were sold in all, how many paperback copies were sold?  Select the correct option
A) 45,000
B) 360,000
C) 364,500
D) 392,000
E) 405,000

Solution: Say x was the # of hardback copies sold from the time the first paperback copy was sold.   Then the total # of paperback copies sold was 9x;   Hence the total # of copies sold was (hardback)+(paperback)=(36+x)+(8x)=441 --> x=45.   So, the total # of paperback copies sold was 9x=9*45= 
9*45 = 405
405 or 405,000.   Answer: 405,000.
Answer: E
If two dice are thrown together, the probability of getting a doublet on the dice is	Choose the correct choice from the following answers.
A) 1/6
B) 1/5
C) 1/4
D) 1/3
E) 1/2

Solution: The number of exhaustive outcomes is 36.   Let E be the event of getting doublet on the dies is 6/36 = 1/6   P(E) = 1/6.   1/6)
Answer: A
The number obtained by interchanging the two digits of a two-digit number is less than the original number by 45. If the sum of the two digits of the number so obtained is 13, then what is the original number?  Choose the correct option:
A) 22  B) 94  C) 27  D) 19  E) 11

Solution: Explanation:   Let the number be in the form of 10a + b   Number formed by interchanging a and b = 10b + a.   a + b = 13 --- (1)   10b + a = 10a + b - 45   45 = 9a - 9b => a - b = 5 --- (2)   Adding (1) and (2), we get   2a = 18 => a = 9 and b = 4   The number is: 94.   Answer:94
Answer: B
An office manager must choose a five-digit lock code for the office door. The first and last digits of the code must be odd, and no repetition of the digits is allowed. How many different lock codes are possible.?  Options
A) 3120  B) 3250  C) 3275  D) 3860  E) 3980

Solution: However, I think 6720 (the answer given in MGMAT) is wrong. Here's my reasoning. If you have (an) odd number(s) for your 2nd, 3rd and/or 4th digits, you cannot repeat that(those) numbers for the last digit. Therefore, this problem needs to be partitioned into 4 groups.   1) ODD (1st digit); 3 EVENs (2nd, 3rd, 4th digits); ODD (5th digit)   5 x 5x 4 x 3 x 4 = 1200   2) ODD (1st digit); 2 EVEN, 1 ODD (2nd, 3rd, 4th digits); ODD (5th digit)   5 x 5 x 4 x 4 x 3 = 1200   3) ODD (1st digit); 1 EVEN, 2 ODDs (2nd, 3rd, 4th digits); ODD (5th digit)   5 x 5x 4 x 3 x 2 = 600   4) ODD (1st digit); 3 ODDs (2nd, 3rd, 4th digits); ODD (5th digit)   5 x 4 x 3 x 2 x 1 = 120   Then the total # of combinations would be 1200 + 1200 + 600 + 120= 
1200 + 1200 + 600 + 120 = 3_120
3120.   3120NS:3120
Answer: A