MU-NLPC/Calc-aqua_rat huggingface dataset:
Ram purchased a flat at Rs. 1 lakh and Prem purchased a plot of land worth Rs. 1.1 lakh. The respective annual rates at which the prices of the flat and the plot increased were 10% and 5%. After two years they exchanged their belongings and one paid the other the difference. Then  Choose the correct option
A) Ram paid Rs. 275 to Prem  B) Ram paid Rs. 475 to Prem  C) Ram paid Rs. 375 to Prem  D) Prem paid Rs. 475 to Ram  E) None of these

Solution: Explanation :   After 2 years the price of the flat will be (1)(1.10)2 = Rs. 1.21 lakh.   Correspondingly the price of the land will be (1.1)(1.05)2 = Rs. 1.21275 lakh.   Hence, the price of the plot is Rs. (1.21275 – 1.21) lakh = Rs. 275 more than that of the flat. Hence, if they exchange, Ram will have to pay Prem this amount.   Ram paid Rs. 275 to Premnswer : Ram paid Rs. 275 to Prem
Answer: A
How many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 50 percent butterfat to obtain milk that is 20 percent butterfat?  Choose the correct answer.
A) 6 B) 12 C) 14 D) 24 E) 28

Solution: Equate the fat:   0.1x + 0.5*8 = 0.2(x + 8) --> x = 24.   Answer: 24.
Answer: D
If x and y are positive odd integers, then which of the following must also be an odd integer? I. x^(y+2) II. x(y+4) III. (y+1)^(x-1) + 2 Choose the most appropriate option:  A) II,III only  B) I,II only  C) I only  D) II only  E) III only

Solution: let x= 5, y= 3   I. 5^5 = > Odd   II. 5*7 = > Odd   III. 4^4 +2= > Even   Answer : I,II only
Answer: B
The present worth of Rs.1404 due in two equal half-yearly instalments at 8% per annum. Simple interest is:
Choose the correct choice from the following:
A) 1320
B) 1300
C) 1325
D) 120
E) None of these

Solution: Explanation:   Required Sum = PW of Rs.702 due 6 months hence +PW of Rs.702 due 1 year hence   =Rs.[100×702/100+(8×12)+100×702/100+(8×1)]   = Rs. 1325   Answer: 1325
Answer: C
A train overtakes two persons who are walking in the same direction to that of the train at 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. What is the length of the train?  Pick:
A) 62 m  B) 54 m  C) 50 m  D) 55 m  E) 56 m

Solution: Explanation:   Let x is the length of the train in meter and v is its speed in kmph   x/9 = ( v-2)(10/36) ---(1)   x/10 =( v-4) (10/36) --- (2)   Dividing equation 1 with equation 2   10/9 = (v-2)/(v-4)   => 10v - 40 = 9v - 18   => v = 22   Substituting in equation 1, x/9 = 200/36 => x = 9×200/36 = 50 m   Answer: Option 50 m
Answer: C
If Q = {1, 7, 18, 20, 29, 33}, how much less is the mean of the numbers in Q than the median of the numbers in Q?
Choose the most appropriate option.
A) 1.0	B) 1.5	C) 2.0	D) 2.5	E) 3.0

Solution: This is a good question to understand the difference between mean and median.   Mean: Average of all the numbers. (Sum of all the elements divided by the number of elements)   Median: Arrange the elements of the set in increasing order. If the number of terms is odd, the middle term is the median. If the number of terms is even, the average of middle two terms is the median   Coming to this question,   Mean = (1 + 7 + 18 + 20 + 29 + 33)/6= 
(1 + 7 + 18 + 20 + 29 + 33)/6 = 18
18   Median= (18 + 20)/2= 
(18 + 20)/2 = 19
19   Difference= 1   Option 1.0
Answer: A
4 persons a, b, c, d are to be lined up in a row. If a, b, and c adhere always together, how many possible cases are there?
Choose the correct choice from the following options
A) 12 B) 36 C) 48 D) 72 E) 144

Solution: firstly it is not GEOMETRY but COMBINATIONS, so changing the TAG accordingly..   total 4 are there..   take a,b, and c as one,so total =2..   these 2 can be arranged in 2! ways..   a,b, and c can be arranged within themselves in 3! ways ..   TOT12L = 2!*3!=12   12
Answer: A
At Company X, senior sales representatives visit the home office once every 20 days, and junior sales representatives visit the home office once every 15 days. The number of visits that a junior sales representative makes in a 2-year period is approximately what percent greater than the number of visits that a senior representative makes in the same period? Choose the correct choice from the following answers
A) 10%
B) 25%
C) 33%
D) 50%
E) 67%

Solution: Each 60-day period, senior representatives visit the home office 3 times while junior representatives visit 4 times, thus 33% more.   The answer is 33%.
Answer: C
Otto and Han are driving at constant speeds in opposite directions on a straight highway. At a certain time they are driving toward each other and are 10 miles apart. One and a half hours later, they are again 10 miles apart, driving away from each other. If Otto drives at a speed of x miles per hour, then, in terms of x, Han drives at a speed of how many miles per hour?
Pick one:  A) a) 13.33-x  B) b) 40-x  C) c) 80-2x  D) d) 120-x  E) e) 40-x/2

Solution: Let's say the two cars have speeds V1 and V2. The fact that they are moving in opposite direction means that their relative speed is (V1 + V2). In other words, any gap between them will be changing in size at a rate of (V1 + V2). It doesn't matter whether they are moving toward each other or away from each other. If they are approaching each other, the gap between them is decreasing at a rate of (V1 + V2). If they are moving away from each other, the gap between them is increasing at a rate of (V1 + V2). Either way, the number for the rate of change remains the same.   Here, the two cars approach a distance 10 mi, then move away from each other another distance of 10 miles. That's a total distance of 20 miles in 1.5 hr, which gives a rate of:   R = (20 mi)/(1.5) = 13.33 mph   That's the rate of change of the gap, so it must equal the sum of the speeds of the two cars.   One of the speeds is x, and let's call the other y. We want y.   x + y = 13.33   y = 13.33 - x   a) 13.33-xnswer =(a) 13.33-x)
Answer: A
At 11:00 a.m., Tom begins traveling on a certain bike path from Riverdale at a constant rate of 10 mph. If, at 3:00 p.m., Jim begins traveling from Riverdale on the same path at a constant rate of 20 mph, at what time will he catch up to Peter?
Choose the correct choice from the following.
A) 6:00 p.m.	B) 7:00 p.m.	C) 8:00 p.m.	D) 9:00 p.m.	E) 10:00 p.m.

Solution: 7:00 p.m.y the time Jim starts, Tom has already covered = 4 hr * 10 mph = 40 miles   Relative speed = 20- 10= 
20- 10 = 10
10mph   To catch up, Jim needs to cover 40 miles which can be covered in= 40/10= 
40/10 = 4
4 hours   If Jim leaves at 3 pm, he will catch Tom at 7 pm   Answer: 7:00 p.m.
Answer: B
A train 125 m long pass a telegraph pole in 5 seconds. Find the speed of the train
Select the correct option.
A) 90 km/hr
B) 68.4 km/hr
C) 72 km/hr
D) 79.2 km/hr
E) None

Solution: Sol.   Speed = [125/5] m/sec = [25 * 18/5] km/hr = 90 km/hr.   90 km/hrnswer 90 km/hr
Answer: A
Express 25 mps in kmph?
Select
A) 77 kmph B) 55 kmph C) 90 kmph D) 56 kmph E) 17 kmph

Solution: 25 * 18/5= 
25 * 18/5 = 90
90 kmph   Answer: 90 kmph
Answer: C
How many shots of 1cm radius can be prepared from a sphere of 3cm radius?  Answers:	A) 33	B) 88	C) 27	D) 88	E) 99

Solution: 4/3 π * 3 * 3 * 3 = 4/3 π * 1 * 1 * 1 * x   x = 27   Answer: 27
Answer: C
If a quarter kg of potato costs 60 paise, how many paise does 200 gm cost?  Choose the correct answer.
A) 65 paise  B) 70 paise  C) 52 paise  D) 48 paise  E) None of these

Solution: Explanation :   Let 200 gm potato costs x paise   Cost of ¼ Kg potato = 60 Paise   => Cost of 250 gm potato = 60 Paise (∵ 1 Kg = 1000 gm => ¼ Kg = 1000/4= 
1000/4 = 250
250 gm)   More quantity, More Paise (direct proportion)   Hence we can write as   Quantity200:250}::x:60   ⇒200×60=250×x⇒4×60=5×x⇒4×12=x⇒x=48 . Answer : Option 48 paise
Answer: D
What will come in place of the x in the following Number series? 5,28,57,88,125  Choose the correct choice: A) 120 B) 145 C) 166 D) 170 E) 189

Solution: 28=23+5   57=29+28   88=31+57   125=37+88   166=41+125= 
41+125 = 166
166   166
Answer: C
If m is an odd integer and n an even integer, which of the following is definitely odd?	Choose the correct choice:
A) (2m+n)(m-n)  B) (m+n2)+(m+n2)  C) m2+mn+n2  D) m +n  E) None

Solution: m+n because the sum of an even and an odd number is always an odd number.   Ex: 3 is an odd number and 6 is an even number. Now, 3+6=9, is an odd number.   ANSWER:m +n
Answer: D
Daniel is playing a dice game in which a dice is rolled 5 times. If a number turns up exactly 3 times then the game is won. Daniel has thrown the dice two times and got number 4 both times. What is the probability that Daniel will win the game ?
Note: the dice is an unbiased die with numbers 1 to 6	Pick
A) 1/216  B) 75/216  C) 80/216  D) 90/216  E) 100/216

Solution: Probability of any number from 1 to 6 = 1/6.   Given that you already have 2 4s , leaving you with 3 more slots to determine if you will win or not.   2 scenarios for a win:   Scenario 1: 4 4 T N N , with T= 4 , N= not 4   Probability of this scenario = 1*1*(1/6)*(5/6)*(5*6)*3!/2!=75/216 .... (3!/2! to show the arrangement of TNN in 3 slots)   Scenario 2: 4 4 N N N , with N = any particular number but 4 and in this case for a 'win' all 'N's are the same number.   Probability of this scenario = 1*1*(5/6)*(1/6)*(1/6) = 5/216 ...(with 1/6 shows the probability of choosing that same number out of 6 possible)   Thus the final probability = 75/216 + 5/216 = 80/216   80/216 is the correct answer.
Answer: C
The price of commodity X increases by 30 cents every year, while the price of commodity Y increases by 20 cents every year. If in 2001, the price of commodity X was $4.20 and the price of commodity Y was $4.40, in which year will commodity X cost 70 cents more than the commodity Y? Choose one
A) 2010 B) 2011 C) 2012 D) 2013 E) 2014

Solution: The cost of commodity X increases by 10 cents per year relative to commodity Y.   The price of X must gain  20 + 70= 
 20 + 70 = 90
90 cents on commodity Y, which will take 9 years.   The answer is 2010.
Answer: A
In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 30,870,000, how many red beads were removed?  Choose the correct choice from the following answers: A) 1 B) 2 C) 3 D) 4 E) 5

Solution: 30,870,000   = 2^4 * 5^4 * 3087   = 2^4 * 3 * 5^4 * 1029   = 2^4 * 3^2 * 5^4 * 343   = 2^4 * 3^2 * 5^4 * 7^3   The answer is 3.
Answer: C
In the xy-coordinate system, what is the slope of the line that goes through the origin and is equidistant from the two points P = (4, 6) and Q = (6, 2)?  Choose the correct answer.
A) 0.8  B) 1.0  C) 1.2  D) 1.4  E) 1.6

Solution: First, get the middle coordinate between (4,6) and (6,2).   x = 4 + (6-4)/2= 
4 + (6-4)/2 = 5
5   y= 2 + (6-2)/2= 
2 + (6-2)/2 = 4
4   Second, get the slope of (5,4) and (0,0). m= 4-0 / 5-0= 
4-0 / 5-0 = 4
4/5= 
4/5 = 4/5 = around 0.8
0.8   0.8nswer: 0.8
Answer: A
Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 50 percent on clothing, 20 percent on food, and 30 percent on other items. If Jill paid a 4 percent tax on the clothing, no tax on the food, and an 8 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes?	Choose the correct choice from the following:
A) 2.8%
B) 3.6%
C) 4.4%
D) 5.2%
E) 6.0%

Solution: Let amount spent by Jill = 100   4.4%lothing=50, Food=20, others=30   Tax on clothing= 2   Tax on others=2.4   Percentage= 4.4/100 4.4%   Answer: 4.4%
Answer: C
The ratio of a to b to c is 2 to 3 to 4, and a, b, c are positive integers. If the average (arithmetic mean) of the three numbers is 51, what is the value of a? Pick one: A) 24 B) 25 C) 28 D) 32 E) 34

Solution: Let a=2k, b=3k, and c=4k.   a+b+c = 2k+3k+4k = 9k   Since the average is 51:   9k/3 2 +3 +4= 
2 +3 +4 = 9
9k   Since the average is 51:   9k/3= 51   3k = 51   k=17   Then a=34.   The answer is 34.
Answer: E
Two pipes can fill a tank in 12 minutes and 20 minutes respectively. Both pipes are opened together and after some time the first pipe is closed and the tank is full in totally 10 minutes. For how many minutes was first pipe open?	Choose the correct answer
A) 8 minutes	B) 6 minutes	C) 7 minutes	D) 10 minutes	E) 9 minutes

Solution: Second pipe is opened for 10 minutes. So , part of tank filled by the second pipe = 10/20=1/2.   So, 1 -1/2 = 1/2 tank is filled by first pipe.   First pipe can fill 1/2 of tank in 1 * 12/2= 
1 * 12/2 = 6
6minutes.   So, the first pipe is opened for 6minutes.   ANSWER:6 minutes
Answer: B
If Rani earns a raise of between 5% and 11%, non-inclusive, by what fraction could her salary have increased?	Choose the correct choice from the following.
A) 1/4  B) 1/5  C) 1/70  D) 1/10  E) 1/20

Solution: Perhaps it is also easy to just translate the % into fractions:   6%: 6/100 = 3/50   7%: 7/100   8%: 8/100 = 4/50 =2/25   9%: 9/100   10%:10/100=1/10   Only 1/10 exists in the answer choices, so ANS 1/10
Answer: D
How many days will there be from 29th January,1996 to 15th May,1996(both days included)?	Options
A) 102 B) 103 C) 111 D) 120 E) 108

Solution: 108xplanation:   Number of days from 29-Jan-1996 to 15-May-1996 (both days included)   = 3(Jan) + 29(Feb) + 31 (Mar) + 30(Apr)+ 15(May) = 108   Answer: Option 108
Answer: E
The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square.	Choose the most appropriate option:
A) 488
B) 776
C) 481
D) 480
E) 412

Solution: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.   4a = 2(l + b)   2a = l + b   l . b = 480   We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .   Area of the square cannot be found.Answer:480
Answer: D
There are 36 people in a certain community who belong to the local golf club, tennis club or both clubs. If twice as many people belong to the tennis club as belong to the golf club, what could be the number of people who belong to both clubs?  Choose the correct option
A) 4  B) 7  C) 17  D) 21  E) 27

Solution: let's find the range of Both and hence the range of x. Minimum value of Both: Say there is no overlap in the two sets. 36 = x + 2xx = 12In this case Both = 0 Maximum value of Both: Say there is maximum overlap between the two sets. One set has x so it could be a subset of the set 2x.36 = 2xx = 18 So Both lies between 0 and 18 Only option (C) satisfies this condition. ANSWER:17
Answer: C
Spanish Language Broadcast records last 90 min on each of two sides. If it takes 3 hours to translate one hour of broadcast, how long will it take to translate 16 full records? Choose the correct choice from the following choices:
A) 144 hours  B) 124 hours  C) 134 hours  D) 154 hours  E) 164 hours

Solution: Records last 90 min on each of 2 sides,   ==> record last 90*2= 
90*2 = 180
180 min= 3 hours   16 full records--> 16*3 = 48 hour broadcast   Given, 3 hours to translate 1 hour of broadcast   Let x be the time required to translate 48 hour broadcast(16 full records)   x  --  16*3= 
 --  16*3 = 48
48 hour broadcast   Given, 3 hours to translate 1 hour of broadcast   Let x be the time required to translate 48 hour broadcast(16 full records)   x= 48*3= 
48*3 = 144
144 hours   144 hoursNSWER:144 hours
Answer: A
In a race where 12 cars are running, the chance that car X will win is 1/6, that Y will win is 1/10 and that Z will win is 1/8. Assuming that a dead heat is impossible, find the chance that one of them will win. Choose one
A) 1/140
B) 1/180
C) 27/410
D) 47/120
E) 57/120

Solution: Required probability = P(X) + P(Y) + P(Z) (all the events are mutually exclusive).   = 1/6 + 1/10 + 1/8   = 47/120   ANSWER:47/120
Answer: D
I remember during the school days , the teacher asked the class "can you tell me the sum of the first 50 odd numbers ?".
I ran quickly to the teacher and told her "the answer is 2500". The teacher replied "lucky guess".
She then asked me "can you tell me the sum of first 71 odd numbers ?".
I wait for approx 10 seconds and replied with the correct answer.
How can i answer so quickly and whats the correct answer ?
Options
A) 8715  B) 0152  C) 3581  D) 5041  E) 9126

Solution: D   5041   n^1   71 * 71 = 5625 (sum of first 71 odd numbers).   50 * 50= 
50 * 50 = 2_500
2500 (sum of first 50 odd numbers).
Answer: D
A can do a piece of work in 10 days, while B alone can do it in 15 days. They work together for 5 days and the rest of the work is done by C in 2 days. If they get 450 for the whole work, how should they divide the money ?  Choose the correct choice from the following answers.
A) 225, 150, 75  B) 250, 100, 100  C) 200, 150, 100  D) 175, 175, 100  E) None of these

Solution: Work done by 225, 150, 75 and B in 5 days = (1⁄10 + 1⁄15) × 5 = 5⁄6   Work remaining = 1 - 5⁄6 = 1⁄6   ∴ C alone can do the work in 6 × 2 = 12 days   Ratio of their share work = 5⁄10 : 5⁄15 : 2⁄12 = 3 : 2 : 1   Share of wages = 225, 150, 75   225, 150, 75nswer 225, 150, 75
Answer: A
The average of 8 numbers is 25, that of the first 2 is 20 and of the next three is 26. The sixth number is less than the seventh by 4, and less than the eighth by 6. The last number is  Choose the most appropriate option
A) 30
B) 32
C) 40
D) 36
E) 38

Solution: Explanation :   Sum of all the numbers = 25*8= 
25*8 = 200
200   Sum of first two numbers= 40   Sum of next three numbers(i.e., 3rd, 4th and 5th) = 78   So, sum of first five numbers = 118 and sum of 6th, 7th and 8th number = 82   Assuming sixth number to be x, we get 7th number = x+4 and 8th number = x+6.   So, x + (x+4) + (x+6) = 82   => x = 24.   Hence, last number(8th number) = 30.   30nswer : 30
Answer: A
In a hostel there were 100 students. To accommodate 20 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now? Choose the correct choice from the following choices: A) 54888 B) 2777 C) 5400 D) 1278 E) 2881

Solution: 100x + 400 = 12(x – 5)   x = 50   100 * 50 + 400= 
100 * 50 + 400 = 5_400
5400   Answer: 5400
Answer: C
Find number which is 80% less than 80. Choose the correct choice from the following options
A) 18 B) 22 C) 28 D) 26 E) 16

Solution: Explanation:   80% less is 20% of the given number   Therefore, 20% of 80 is 16.   ANSW16R: 16
Answer: E
The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table?	Choose the correct choice from the following options:
A) 2266	B) 2987	C) 2678	D) 6725	E) 2677

Solution: CP = SP * (100/(100 + profit%))   = 8339(100/124) = Rs. 6725.   Answer: 6725
Answer: D
By using the numbers 1, 3, 4, 6 and 9 only once, how many five digit numbers can be made that are divisible by 8?	Choose the correct option
A) 3	B) 12	C) 6	D) 18	E) 42

Solution: A number to be divisible by 8 must end with 08, 16, 24,32 ,40 or 72.   So, there are the following cases possible:   349-16 --> the first three digits can be arranged in 3=6 ways.   Total = 6 = 6.   Answer: 6.
Answer: C
In certain year in Country C, x sets of twins and y sets of triplets were born. If there were z total babies born in Country C in this year, and x and y were both greater than 0, which of the following represents the fraction Q of all babies born who were NOT part of a set of twins or triplets?  Choose the correct answer
A) z - 2x - 3y	B) (2x+3y)/z	C) (x+y)/z	D) 1 - (2x+3y)/z	E) 1 - (x+y)/z

Solution: X set of twins implies 2x babies of twin category.   Y set of triplets means 3y babies of triplet category.   Let K be the babies other than twin or triplet category.   Total babies = z = 2x+3y+k.   or K=Z-(2x+3y)   => Fraction of babies other than twin or triplet categories = K/Z = Z-(2x+3y)/Z.   Q= 1- (2x+3y)/Z. Hence answer is 1 - (2x+3y)/z.
Answer: D
Diane find 1 can of paint are just enough to paint one third of her room. How many more cans of paint will she need to finish her room and paint a second room of the same size? Choose the correct choice from the following:  A) 5  B) 7 and a half  C) 10  D) 12 and a half  E) 15

Solution: She will need 2 cans to paint the rest of this room and 3 for the next room for a total of 5 cans.   5
Answer: A
The sum of two numbers is 216 and their H.C.F. is 27. The number are:	Choose the correct choice from the following options:	A) 27, 189	B) 81,189,	C) 108, 108	D) 154, 162	E) none of these

Solution: Let the required numbers be 27a and 27b.Then, 27a+27b=216   a+b=8   Now, co-primes with sum 8 are(1, 7)and(3,5).   required numbers are (27*1*, 27*7) and (27*3,27*5)   i.e., (27, 189)and (81,135)   out of these, the given one in the answer is the pair(27,189).   correct Option:27, 189
Answer: A
A committee has 6 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?
Choose the correct choice from the following answers:
A) 127
B) 300
C) 882
D) 272
E) 323

Solution: The number of ways to select two men and three women   = 6C₂ * ⁶C₃   = (6*5)/(2 * 1) * (6 * 5 * 4)/(3 * 2)= 
(6*5)/(2 * 1) * (6 * 5 * 4)/(3 * 2) = 300
300   Answer: 300
Answer: B
The sum E of the arithmetic sequence a, a+d, a+2d,..., a+(n-1)d is give by En = (n/2)*(2a + n-1)d. What is the sum of the integers 1 to 100 inclusive, with the even integers between 25 and 63 omitted.  Choose the correct answer:
A) 4345	B) 4302	C) 4258	D) 4214	E) 4170

Solution: a method to do it under one minutes is to take advantage of the choices given...   lets work on the last digit as we have different units digit in each choice...   total sum of 1 to 100 inclusive will have 0 as the last digit..   this is so because the resultant will be 10*(sum of all single digits)... and since we are multiplying by 10,units digit will be 0...   now for single digit in sum E of even number from 25 to 63..   25 to 65 will have 4 times sum of single digit even int, 4*(2+4+6+8+0)=4*20..   here too the units digit is 0, but 64 has to be excluded from the total..   two ways from here on..   1) we are subtracting 0 from 0   so units digit should be 0, but we have to add 64..   so last/units digit =4..   2)we subtract 64 from sum of even int..   so units digit=80-4=76..   or units digit =6...   so our answer should have units digit as 10-6=4..   only D has 4 as units digit..   ans 4214
Answer: D
In how many ways can Ann, Bob, Chuck, Don and Ed be seated in a row such that Ann and Bob are not seated next to each other?	Select the correct option:
A) 24  B) 48  C) 56  D) 72  E) 96

Solution: These 5 people can be arranged in 5! ways. These are the total number of ways you get.   Now, when we tie 2 people together, we have only 4 entities to arrange. We can do this in 4! ways. But in each of these entities, the two people can sit in two different ways (AB and BA). So number of ways in which these two people sit together is 4!*2!.   Now, the ways in which these two people will not be together will be 5!- 4!*2! = 4!(5 - 2) = 72   ANSWER:72
Answer: D
The original price of a car was $25,200. Because the car owner thought he could get more money for the car, he increased the price of the car to 110% of its original price. After a week, the car had not sold, so the owner then discount ed the price by 10%, and the car was finally sold. What price was the car sold for?	Pick one
A) $25,200	B) $25,000	C) $24,948	D) $24,542	E) $23,658

Solution: The car is sold for 1.1*0.9*25200   =0.99 * 25200   =(1 - 0.01) * 25200   =25200 - 252= 
25200 - 252 = 24_948
24948   $24,948 is the answer
Answer: C