MU-NLPC/Calc-aqua_rat huggingface dataset:
In an entrance test, Deepika came across a mathematical patter problem.
If
6 / 7 = 2,
3 / 9 = 7,
8 / 2 = 6,
Then
4 / 5 = ?
She was able to solve it in less than a minute. Can you?	Choose one
A) 0	B) 1	C) 2	D) 3	E) 4

Solution: Solution:   The answer is 0.   As   6 / 7 = 42 but the answer is written as 2   3 / 9 = 27 but the answer is written as 7   8 / 2 = 16 but the answer is written as 6   If we look at the answers, the second digit has been used in the problem.   Now, as   4 / 5 = 20 and the second digit is 0, the answer is 0.   0nswer 0
Answer: A
How many numbers from 9 to 79 are exactly divisible by 11?	Choose one:
A) 5 B) 7 C) 9 D) 11 E) 12

Solution: 9/11 = 0 and 79/11 = 7 ==> 7 - 0= 
7 - 0 = 7
7 Numbers   Answer : 7
Answer: B
A ship sails 4 degrees north, then 14 S. then 17 N. then 19 S. and has finally 11 degrees of south latitude. What was her latitude at starting ? Choose the correct choice from the following choices:
A) 0	B) 1	C) 2	D) 3	E) None of these

Solution: Let x = the latitude sought.   Then marking the northings +, and the southings -;   By the statement x + 4 - 14 + 17 - 19 = -11   And x = 1.   Answer 1
Answer: B
In a group of hats consisting of only blue hats, green hats, and purple hats, the ratio of blue hats to green hats to purple hats is 7:4:12. If there are a total of 46 hats in this group, how many of these hats are not blue?
Choices.
A) 28  B) 22  C) 48  D) 64  E) 76

Solution: B:G:P = 7:4:12 --> total of 23 parts.   Not blue = (G + P)/(total)*92 = 16/23*46= 
16/23*46 = 32
32.   Answer: 22.
Answer: B
In how many different number of ways 4 boys and 3 girls can sit on a bench?	Answers:  A) 5040  B) 710  C) 720  D) 730  E) 740

Solution: npn = n!   7p7 = 7 X 6 Ã— 5 Ã— 4 Ã— 3 Ã— 2 Ã— 1 = 5040   5040
Answer: A
Two trains start from p and q respectively and travel towards each other at a speed of 50km/hr and 40km/hr respectively. By the time they meet, the first train has travelled 1ookm more than the second. The distance between p and q is Select the correct option:	A) 500km	B) 600km	C) 700km	D) 900km	E) 400km

Solution: Explanation:   At the time of meeting, let the distance travelled by the second train be x km   Then, distance covered by the first train is (x+100)km   => x/40 = (x+100)/50 => 50x = 40x+4000 => x=400km   so, distance between p and q = (x+x+100)km = 900km   Answer: Option 900km
Answer: D
At 3:00 pm, a car has driven 20 miles east. It will continue to drive east at 0.8 minutes per mile and then turn around and drive at 0.8 minutes per mile back to its original starting point. How far can it drive before turning around in order to arrive back to its original starting point by 3:40 pm?	Choose the correct option: A) a) 10 B) b) 11 C) c) 12 D) d) 15 E) e) 14

Solution: 0.8 minutes --> 1 mile   1 minute --> 1/0.8 = 10/8= 
10/8 = 5/4 = around 1.25
1.25 miles/minute   d) 15istance covered in 40 minutes= 1.25 * 40 = 12.5 * 4= 
12.5 * 4 = 50
50 miles   d) 15istance covered in the current direction= d) 15istance covered from the opposite direction (since car returns back to starting point)   Let x be the miles driven before turning   20 + x = 50 - x   2x = 30   x = 15   Answer: d) 15
Answer: D
Lucy deposited $31250 in an investment fund that provided 16 percent annual return compounded quarterly. If she made no other transactions with the fund, in how much time, in months, did her investment earn a total interest of $2550?	Choose the correct choice from the following options:	A) 0.5	B) 2	C) 12/4	D) 12/2	E) 6.1

Solution: A = P + I = 31250 + 2550= 
31250 + 2550 = 33_800
33800   33800= 31250(1 + 16/4*100)^(4t)   (676/625) = (104/100)^(4t)   (26/25)^2 = (26/25)^4t   t = 1/2 yrs = 12/2 months   Answer: 12/2
Answer: D
What number comes next in this Number series.
5 5 3 4 4 6 9 ?
*Hint: check calender	Choose the correct choice from the following:
A) 7 B) 8 C) 6 D) 1 E) 8

Solution: 7   7 (the number of letters in the month October)   March : 5 letters   7pril : 5 letters   May : 3 letters   June : 4 letters   July : 4 letters   7ugust: 6 letters   September : 9 letters
Answer: A
If 2 pounds of dried apricots that cost x dollars per pound are mixed with 2 pounds of prunes that cost y dollars per pound, what is the cost, in dollars, per pound of the mixture?
Choose the correct choice from the following options:	A) (2x + 2y)/5	B) (2x + 2y)/(x + y)	C) (2x + 2y)/(xy)	D) 5(2x + 2y)	E) 2x + 2y

Solution: Total Cost = Weight(in pounds) * Price/pound;   To find Total cost/pound, Divide by total pounds.   Cost of Dried apricots = 2x;   Cost of prunes = 2y;   Cost per pound = (2x + 2y)/5;   (2x + 2y)/5ns is ((2x + 2y)/5).
Answer: A
AA is two digit number then m times its cube of AA has 1 in its tens place then what is m.	Choose the correct choice from the following.
A) 3  B) 4  C) 5  D) 6  E) 7

Solution: when AA=11   7*(11)^3= 7*1331= 
7*1331 = 9_317
9317   m=7   ANSW7R:7
Answer: E
If the line L passes through the point (3,n) and (n,3), where n is not equal to 3, which of the following must be true?
1. The slope of L is negative
2.Line L must passes through the first quadrant
3. Line L does pass the origin.	Select:
A) I only B) II only C) III only D) I and II E) II and III

Solution: Slope of the given line= 3-n/n-3   Given information is that n is not equal to 3, that means n <3 or n>3. In both these conditions the slope will be negative.   1) n<3 (n=2)   3-2/2-3= -1   2) n<3 (n= 0)   3-0/0-3= -1   3) n<3 (n=-3)   3+3/ -3-3= -2/3   4) n>3   3-4/4-3= -1   I onlynswer I only
Answer: A
In a certain sequence of 7 numbers, each number after the first is 1 more than the previous number. If the first number is −5, how many of the numbers in the sequence are positive?  Choose the correct option:	A) None	B) One	C) Two	D) Three	E) Four

Solution: Non - Negative ( zero to positive infinity )   Solution to the question :   -5,-4,-3,-2,-1,0 , 1   Hence ans is 1 ..option One
Answer: B
Each customer of a networking company subscribes to one of two plans: Plan A or Plan B. Plan A costs $75 per month and Plan B costs $250 per month per customer. If the company’s average revenue per customer per month is $200, then what percent of the company's revenue comes from customers with Plan A? Choose the correct answer:
A) 10.7%  B) 30%  C) 37.5%  D) 56.25%  E) 75%

Solution: If there are A customers with plan A, and B customers with plan B, then the total revenue is $75A + $250B.   Since the average customer pays $100, we know that   $200 = ($75A + $250B) / (A + B)   $200(A + B) = ($75A + $250B)   $200A + $200B = $75A + $250B   $125A = $50B   A = 2/5*B.   Since there are 2/5 times as many $75 clients as $250 clients, for every $250 received from Plan B customers, 2/5*($75) = $30 is received from Plan A customers, and the percent of revenue from customers with Plan A is:   $30/($30 + $250) = $30/$280 = 10.7%.   The correct answer is choice (10.7%).
Answer: A
In Town X, 64 percent of the population are employed, and 50 percent of the population are employed males. What percent of the employed people in Town X are females?  Options:	A) 16%	B) 22%	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 50 are employed males, hence 14% are employed females.   (employed females)/(total employed people)=14/64=22%   Answer: 22%.
Answer: B
Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 12? Choices:
A) 6	B) 8	C) 4	D) 3	E) 2

Solution: You should consider the worst case scenario: if you pick numbers 0, 1, 2, 3, 4,5 and 6 then no two numbers out of these 7 add up to 12.   Now, the next, 8th number whatever it'll be (7, 8, or 9) will guarantee that two number WILL add up to 12. So, 8 slips must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 12.   Answer: 8
Answer: B
If k and y are integers, and 10k + y is odd, which of the following must be true? Choose the correct choice from the following answers:
A) k is odd B) k is even C) y is odd D) y is even E) both k and y are odd

Solution: 10k will be always even as 10 has 2 as one of its factors   if 10k+y is odd, then the only possible explanation is that y is odd   correct answer y is odd
Answer: C
Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn
randomly. If it is known that the number on the drawn card is more than 3, what is the probability
that it is an even number?  Choose one
A) 3/5 B) 3/7 C) 4/7 D) 4/9 E) 5/3

Solution: Let A be the event ‘the number on the card drawn is even’ and B be the   event ‘the number on the card drawn is greater than 3’. We have to find P(A|B).   Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}   Then A = {2, 4, 6, 8, 10}, B = {4, 5, 6, 7, 8, 9, 10}   and A n B = {4, 6, 8, 10}   Also P(A) = 5/2, P(B) = 7/10 and P(A n B) = 4/10   Then P(A|B) = P(A n B)/P(B) = (4/10)/(7/10) = 4/7   4/7)
Answer: C
A dishonest dealer claims to sell a product at its cost price. He uses a counterfeit weight which is 20% less than the real weight. Further greed overtook him and he added 30% impurities to the product. Find the net profit percentage of the dealer?  Answers:
A) 44%
B) 40%
C) 50%
D) 56.25%
E) 37.5%

Solution: The dealer uses weight which is 20% less than the real weight. or (1- 1/5) or 4/5 of real weight.   It means that he is selling $4 worth of product for $5.   The dealer then further added 30% impurities to the product.   It means that he is selling $5 worth of product for $5.5.   So his profit is $5.5-$4 = $1.5   and his profit percent is   (1.5/4)*100 5.5- 4= 
5.5- 4 = 1.5
$1.5   and his profit percent is    (1.5/4)*100= 
 (1.5/4)*100 = 37.5
37.5%   Answer:- 37.5%
Answer: E
A basketball coach will select the members of a five-player team from among 11 players, including John and Peter. If the five players are chosen at random, what is the probability that the coach chooses a team that includes both John and Peter? Choose the correct choice from the following choices:	A) 1/9	B) 1/6	C) 2/11	D) 5/18	E) 1/3

Solution: straight forward way is to group J and P as always present on the team and as order does not matter so we just need to find the total number of ways to select rest three players = 9c3   total number of ways of selecting 5 players out of 11 = 11c5   probability = 9c3/11c5 =2/11   2/11
Answer: C
A batsman makes a score of 64 runs in the 16th innings and thus increased his average by 3. Find his average after the 16th inning?
Choices:	A) 15	B) 14	C) 18	D) 19	E) 20

Solution: Let the average after the 16th inning be P.   So, the average after the 15th inning will be   (P-3) Hence, 15(P-30) + 64 = 16P => P = 19.   Answer:19
Answer: D
Every day, Fred takes the train to travel from his work back to Alkmaar, his place of residence. Usually, he arrives at the station of Alkmaar at six o'clock, and exactly at that moment, his wife picks him up by car. Yesterday evening, Fred took an earlier train, without informing his wife, and therefore he already was at the station of Alkmaar at five o'clock. He decided to walk part of the way to meet his wife. When he met the car with his wife, he drove home with her. In this way, they were home ten minutes earlier than normal. Fred's wife always drives the entire way between home and station at the same constant speed.How long did Fred walk yesterday evening?
Choose the most appropriate option:
A) 55	B) 45	C) 58	D) 65	E) 59

Solution: Fred's wife needed to drive ten minutes less than usual, which is five minutes less in the direction of the station and five minutes less back home. Therefore, Fred met his wife at five minutes to six. He had walked already since five o'clock, so he walked 55 minutes in total.   55nswer 55
Answer: A
What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 48? Options:	A) A)Rs.3944	B) B)Rs.3948	C) C)Rs.3264	D) D)Rs.3949	E) E)Rs.3923

Solution: Let the side of the square plot be a ft.   a2 = 289 => a = 17   Length of the fence = Perimeter of the plot = 4a = 68 ft.   Cost of building the fence = 68 * 48 = Rs.3264.   Answer: Rs.3264
Answer: C
The city of Boston decided to reconstruct its major tunnels. It estimated the job would require 612 mini projects spread evenly over an 18 month plan of completion. Only 108 mini projects had been successfully completed after 8 months. At this time, the construction was behind schedule by how many projects?
Choose the correct answer:	A) 34	B) 96	C) 198	D) 164	E) 504

Solution: Project/month :   612/18= 
  612/18 = 34
34   Project in 6 month to be completed= 34*8= 
34*8 = 272
272   Lag :  272-108= 
  272-108 = 164
164   164 is the answer
Answer: D
In an election, candidate A got 65% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favor of candidate?
Choose the correct choice from the following answers:
A) 355600	B) 355800	C) 356500	D) 309400	E) 357000

Solution: Total number of invalid votes = 15 % of 560000   = 15/100 × 560000   = 8400000/100= 
8400000/100 = 84_000
84000   Total number of valid votes 560000 – 84000= 476000   Percentage of votes polled in favour of candidate A = 65 %   Therefore, the number of valid votes polled in favour of candidate A = 65 % of 476000   = 65/100 × 476000   = 30940000/100= 
30940000/100 = 309_400
309400   309400)
Answer: D
If xy = 2 and x^2 + y^2 = 12, then x/y + y/x =  Select
A) 6 B) 3 1/7 C) 5 1/3 D) 7 E) 60

Solution: We can make simplifying of question and get it in view: (x^2 + y^2) / xy and as we know the meaning of this parts:   x^2 + y^2 = 12   xy = 2   we can calculate the answer 12/2 -> 6 so answer is 6
Answer: A
If $25,000,000 is the initial amount placed in an account that collects 7% annual interest, which of the following compounding rates would produce the largest total amount after two years?  Choose one:
A) compounding daily	B) compounding quarterly	C) compounding monthly	D) compounding annually	E) All four of these would produce the same total

Solution: This will produce the maximum yield as the interest accured each day will be added the very next day to the Principal amount for further computation of interest.   This process will be repeated every day till the amount matures   Compounding annually will give least returns   compounding dailynswer = compounding daily
Answer: A
Each of the integers from 3 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10?
Choose the correct choice from the following answers:
A) 3	B) 4	C) 5	D) 6	E) 7

Solution: Answer is 4. In the worst case, you could end up drawing 3,4,5. 7th draw will result in either of 6,7,8,9 which would result in the numbers adding to 10.   4
Answer: B
The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is:  Choose the correct choice from the following:	A) 266	B) 288	C) 245	D) 211	E) 776

Solution: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m.Answer: 245
Answer: C
One fourth of one third of two fifth of a number is 10. What will be40% of that number Pick one:
A) A)140
B) B)150
C) C)120
D) D)200
E) E)220

Solution: Explanation:   (1/4) * (1/3) * (2/5) * x = 10   then x = 10 * 30= 
10 * 30 = 300
300   40% of 300= 120   Answer: Option 120
Answer: C
The value of (2.502+0.064)^2 - (2.502-0.064)^2/2.502*0.064	Pick one.
A) .25	B) .235	C) 4	D) 3	E) 2

Solution: (2.502+0.064)2 - (2.502-0.064)2/2.502*0.064 = (a+b)2 - (a-b)/ab   = 4ab/ab   = 4   ANSWER:4
Answer: C
A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:	Pick one:
A) 588 apples B) 600 apples C) 672 apples D) 700 apples E) 720 apples

Solution: Explanation:   Suppose originally he had x apples.   Then, (100 - 40)% of x = 420.   60	x x = 420   100   x =(420*100 /60)= 
(420*100 /60) = 700
700.   ANSWER IS 700 apples
Answer: D
What percentage of numbers from 1 to 95 have squares that end in the digit 0? Choose the correct choice from the following choices
A) 1 B) 14 C) 9.47 D) 21 E) 22

Solution: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 95 are 10,20,30,40,50,60,70,80,90.   Number of such numbers = 14.   Required percentage = (9/95 * 100) = 9.47%   ANSWER:9.47
Answer: C
What is the angle between the 2 hands of the clock at 8:24 pm?	Pick
A) 100° B) 107° C) 106° D) 108° E) None of these

Solution: Required angle = 240 – 24 × (11/2)   = 240 – 132 = 108°   Answer 108°
Answer: D
A man can do a piece of work in 9 days, but with the help of his son he can do it in 3 days. In what time can the son do it alone ?
Pick:
A) 7 1/2 days
B) 6 1/2 days
C) 5 1/2 days
D) 4 1/2 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 =   (1/3−1/9)=(6−2)/18=2/9   So son will do whole work in 9/2 = 4 1/2 days   Answer: 4 1/2 days
Answer: D
The average of 20 numbers is zero. Of them, How many of them may be greater than zero, at the most? Select the correct option
A) 1
B) 20
C) 0
D) 19
E) 20

Solution: Explanation:   Average of 20 numbers = 0   => Sum of 20 numbers/20= =0   => Sum of 20 numbers = 0   Hence at the most, there can be 19 positive numbers.   (Such that if the sum of these 19 positive numbers is x, 20th number will be- x)   Answer: Option 19
Answer: D
A meal cost $ 48.75 adn there was no tax. If the tip was more than 5 pc but less than 20pc of the price, then the total amount paid should be:  Choose the correct answer:
A) 60-65
B) 55-58
C) 51-59
D) 39-41
E) 38-40

Solution: 5%(48.75) = 2.4375   20%(48.75) = 9.75   total amount could have been 48.75+2.4375 and 48.75+9.75   => could have been between 51.1875 and 58.5   => approximately between 51 and 59   Answer is 51-59.
Answer: C
Solve below question 2x + 1 = -17
Choose the correct answer:	A) -8	B) -9	C) -5	D) -4	E) 1

Solution: 1. Subtract 1 from both sides:   2x + 1 - 1 = -17 - 1   2. Simplify both sides:   2x = -18   3. Divide both sides by 2:   4. Simplify both sides:   x = -9   -9
Answer: B
The units digit of (35)^(87) + (93)^(46) is:
Select the correct option:
A) 2	B) 4	C) 6	D) 8	E) 0

Solution: Step 1: (35)^(87) can be broken up into (5)^87 x (7)^87. Each power of 7 ends in a units digit of either a 7,9,3 or 1. Each power of 5 ends in a 5. When you multiply 5 by any odd number you will end up with a units digit of 5.   Step 2: (93)^(46) can be broken up into (3)^46 x (31)^46. Each power of 31 ends in a units digit of 1. Each power of 3 ends in a units digit of either 3,9,7 and 1. Since there is a pattern here where every 4th power of 3 ends in a units digit of 3, the 46th power of 3 would end in a units digit of 9. When you multiply 1 by 9 you end up with a units digit of 9.   Therefore, the units digit we are looking for is 5 + 9= 
5 + 9 = 14
14. Units digit will be 4. Answer 4.
Answer: B
Maths, Physics and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability T, that a book selected at random is either a hard cover book or a chemistry book?  Choose the correct choice
A) 1/10  B) 3/20  C) 1/5  D) 1/4  E) 9/20

Solution: First phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf. To do so, you have the equations:   m + p + c = 20 (since 4/5 of the 25 spots are full of books)   m = 2p   p = 4 + c   From that, you can use Substitution to get everything down to one variable.   c = p - 4   m = 2p   p = p   Then (p - 4) + 2p + p = 20, so 4p = 24 and p = 6. That means that there are 12 math, 6 physics, and 2 chemistry books on the shelf.   With those numbers, you also know that there are 8 total hardcovers, 1 of which is chemistry. So if your goal is to get either a hardcover or a chemistry, there are 9 ways towin- either one of the 7 hardcovers that aren't chemistry or the two chemistry books. So out of the 20 total, T=9 provide the desired outcome, making the answer 9/20.
Answer: E
80% of the population of a village is 32000. The total population of the village is? Choices:
A) 40000  B) 24000  C) 26682  D) 29973  E) 12312

Solution: X * (80/100) = 32000   X = 400 * 100= 
400 * 100 = 40_000
40000   40000nswer: 40000
Answer: A
What is the % change in the area of a rectangle when its length increases by 20% and its width decreases by 20%?  Select
A) 0%  B) 20% increase  C) 20% decrease  D) 4% decrease  E) Insufficient data

Solution: (12/10)*(8/10) = 96/100 of original area   96/100 is a 4% decrease from 100/100 ->4% decrease
Answer: D
In a class of 45 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German?	Choose the correct choice
A) 30
B) 10
C) 18
D) 23
E) 32

Solution: Total=English+German-Both+Neither --> 45=English+22-12+0 --> English=35 --> Only English=English-Both=35-12= 
35-12 = 23
23.   Answer: 23.
Answer: D
A 160 meter long train crosses a man standing on the platform in 12 sec. What is the speed of the train?	Options
A) 48 kmph B) 54 kmph C) 92 kmph D) 86 kmph E) 76 kmph

Solution: S = 160/12 * 18/5= 
160/12 * 18/5 = 48
48 kmph   48 kmphNSWER:48 kmph
Answer: A
Two persons start running simultaneously around a circular track of length 700 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions? Pick one
A) 63
B) 10
C) 28
D) 27
E) 12

Solution: Time taken to meet for the first time anywhere on the track   = length of the track / relative speed   = 700 / (15 + 25)5/18 = 700* 18 / 40 * 5 = 63 seconds.   63nswer: 63
Answer: A
If a 10 percent deposit that has been paid toward the purchase of a certain product is $105, how much more remains to be paid?	Choose the correct answer:
A) $945 B) $965 C) $1025 D) $1050 E) $1105

Solution: 90% remains to be paid so the remaining amount is 9*105= 
9*105 = 945
$945.   The answer is $945.
Answer: A
TATA company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?
Choose one.
A) 3,024  B) 4,536  C) 5,040  D) 9,000  E) 10,000

Solution: TATA company plans to assign identification numbers to its employeeS.The first digit can take 9 values from 1 to 9 inclusive;   The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0);   The third digit can take 8 values;   The fourth digit can take 7 values.   Total = 9*9*8*7 = something with the units digit if 6.   Answer: 4,536.
Answer: B
A first grade teacher uses eight cards, each numbered from 1 to 8, to teach her students to order numbers correctly. She has students choose four flash cards randomly, then arrange the cards in ascending order. One day, she removes the cards '2' and '4' from the deck. On that day, how many different correct arrangements of four randomly selected cards are possible?
Choose the correct answer:
A) 70 B) 15 C) 60 D) 45 E) 33

Solution: problem of combination 6C4 = 6!/4!*(6-4)! = 6*5*4!/4!*2! =15   15
Answer: B