MU-NLPC/Calc-aqua_rat huggingface dataset:
The remainder when dividing the expression (X + Y) by 5 is 4. The remainder of X divided by 10 is 2. What is the remainder F of Y divided by 5?	Select the correct option: A) F= 1. B) F=2. C) 3. D) 4. E) 5.

Solution: X divided by 10 gives reminder of 2. X can be 2/12/22....   X+Y divided by 5 is 4. X+Y can be 4/ 9/ 19....   If X+Y= 4 and X is 2 then Y = 2 and Y/5 will give a reminder of 2   Similarly, if X+Y= 9 and X = 2, then y/5 will give a reminder of 2   Hence the answer must be 2 (B)   Also....   x+y=5m+4 and x=10K+2   hence 10k+2+y=5m+4 or y=5(m-2k)+2, m-2k being a constant remainder is 2 hence answer is F=2.
Answer: B
In one year, the population, of a village increased by 10% and in the next year, it decreased by 10%. If at the end of 2nd year, the population was 7920, what was it in the beginning?
Choose the correct choice from the following options.
A) 2889 B) 8000 C) 2777 D) 2999 E) 2212

Solution: x*110/100 * 90/100 = 7920   X*0.99=7920   X=7920/0.99= 
7920/0.99 = 8_000
> 8000.Answer:8000
Answer: B
A, B and C can do a work in 6, 8 and 12 days respectively doing the work together and get a payment of Rs.1800. What is B’s share?
Select.
A) 600
B) 882
C) 266
D) 288
E) 279

Solution: WC = 1/6:1/8:1/12 => 4:3:2   3/9 * 1800= 
3/9 * 1800 = 600
600   600nswer: 600
Answer: A
The Arnolds purchased 550 square feet of Kentucky Gem sod at $1.89 per square foot and 270 square feet of Zelzea Blue sod at $1.48 per square foot. What was the approximate average price per square foot paid for all the sod?  Options:
A) $1.63 B) $1.64 C) $1.68 D) $1.72 E) $1.80

Solution: Average price = (550*1.89)+(270*1.48)/550+270=1.80 (Approx)   Answer $1.80
Answer: E
In a simultaneous throw of 2 dice, what is the probability of getting a total of 5?	Choose the correct choice from the following answers.
A) 1/7	B) 2/3	C) 1/9	D) 2/7	E) 1/36

Solution: n(S) = 6*6= 
6*6 = 36
36   E= event of getting a total of 5 = {(1,4),(2,3),(3,2),(4,1)}   probability = 4/36 = 1/9   Answer is 1/9
Answer: C
In each of the following questions a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the blank spaces.
?, 7, 14, 23, 34, 47  Pick one
A) 31	B) 2	C) 36	D) 31	E) 33

Solution: B   2   The given sequence is +5, +7, +9, ——   ie. 2+ 5 = 7, 7 + 7 = 14, 14 + 9 = 23
Answer: B
A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 52, then how old is B?  Choose the correct choice from the following answers
A) 17 years
B) 20 years
C) 29 years
D) 10 years
E) 12 years

Solution: Let C's age be x years.   Then, B's age = 2x years.   A's age = (2x + 2) years.   (2x + 2) + 2x + x = 52   5x = 50 => x = 10   Hence, B's age = 2x = 20 years.   Answer: 20 years
Answer: B
If a and b are multiples of 8 then which are all the multiples of 8
1) a*b
2) a-b
3) a+b
4) a/b
5) a^b
Options
A) 1,2,5 B) 1,3 C) 2,3,4,5 D) 1,2,3,5 E) all of these

Solution: a*b a^b a+b a-b are multiples of 6 except a/b   ANSWER:1,2,3,5
Answer: D
Two men start together to walk a certain distance, one at 4 kmph and another at 3 kmph.The former arrives half an hour before the latter. Find the distance.  Choose the most appropriate option.
A) 6 kilometre	B) 61 kilometre	C) 8 km	D) 9 km	E) None of these

Solution: Let the distance be x km. Then,   x/3 - x/4 = 1/2   (4x - 3x)/12 = 1/2   x = 6 km   6 kilometreNSWER:6 kilometre
Answer: A
Jane invested $1500 in fund A and $1000 in fund B. Over the next two years, the money in Fund A earned a total interest of 12 percent for the two years combined and the money in fund B earned 30 percent annual interest compounded annually. Two years after Jane made these investments. Jane's investment in fund B was worth how much more than her investment in fund A?
Choose the correct choice from the following
A) 1. $200	B) 2. $100	C) 3. $10	D) 4. $150	E) 5. $400

Solution: interest on fund A will be 180. rate of interest will be 6% per annum simple interest as 12% is for 2 year. this will make investment A 1680 at the end of 2nd year.   interest on fund B will be 690 on 30% interest compounded annually. This will make investment B 1690 at the end of 2nd year.   Difference in investment B and investment A=1690-1680= 
1690-1680 = 10
10   answer is 3. $10.
Answer: C
12 welders work at a constant rate they complete an order in 8 days. If after the first day, 9 welders start to work on the other project, how many more days the remaining welders will need to complete the rest of the order?
Pick:
A) 5  B) 12  C) 18  D) 24  E) 28

Solution: 1. We need to find out the time taken by 3 workers after day 1.   2. total no.of wokers * total time taken = time taken by 1 worker   3. Time taken by 1 worker = 12*8= 
12*8 = 96
96 days   4. But on day 1 twelve workers had already worked finishing 1/8 of the job. So 3 workers have to finish only 7/8 of the job.   5. Total time taken by 3 workers can be got from formula used at (2). i.e., 3* total time taken= 96. Total time taken by 3 workers to finish the complete job is 96/3= 
96/3 = 32
32 days.   6. Time taken by 6 workers to finish 7/8 of the job is 7/8 * 32= 
7/8 * 32 = 28
28 days.   The answer is choice 28
Answer: E
At the A-Street Fish Market a vendor sells fresh caught fish. His store is filled with 2/7 bass, 1/5 tuna, 1/7 trout, and the rest are catfish. If a customer just bought 1/7 of all the tuna and 1/7 of all the catfish, and a fisherman arrived to restock the bass, doubling the number of bass, what proportion of fish now in the store are trout? Options:  A) 30/71  B) 4/7  C) 5/43  D) 1/2  E) 1/5

Solution: Bass = 2/7 = 10/35   Tuna = 1/5 = 7/35   Trout = 1/7 = 5/35   Catfish = 1 - (10/35 +7/35 + 5/35) = 13/35   Purchased: Tuna = 7/35 - (7/35)(1/7) = 6/35, and   Catfish = 13/35 - (13/35)(1/7) = 12/35   Stocked: doubling the number of bass (2)(10/35) = 20/35   Now:   20 + 6 + 5 + 12= 
  20 + 6 + 5 + 12 = 43
43   Trout proportion is now 5/43.   Answer: 5/43
Answer: C
In Goshawk-Eurasian nature reserve 30 percent of the birds are Hawks, and 40 percent of the non-Hawks are Paddyfield-Warblers. If there are 25 percent as many Kingfishers as Paddyfield-Warblers in the reserve, then what percent of the birds E in the nature reserve are not Hawks, Paddyfield-Warblers, or Kingfishers?
Choose the correct choice from the following.
A) 25%
B) 35%
C) 45%
D) 70%
E) 80%

Solution: 1. We are given the following percentages: 30 (70), 40 (60), 25 (75). There are two threads from here. First starts at 30% and finishes there. Second one starts at 70, then 40, and then 25. We need a value that is divisible by 7, 2, and 5 at least once. lets pick a number now, say 700. So say if Non Hawks are 700 (this is 70% of the total, so total = 1000), then Paddy Warbs are 2/5 x 700 = 1400/5= 
1400/5 = 280
280. Kingfishers, therefore, are   280/4= 
  280/4 = 70
70. Lets add them up. 300 hawks + 280 Peddy Warbs + 70 kingsifhers= 650. So all others are  1000 - 650= 
 1000 - 650 = 350
350 or 35% of total birds.   The main job here to to identify the smart number to start the question with. This can be time consuming, but once identified, this question can be solved fairly quickly.   2. Another method: If X is total --> Non Hawks= 0.7X --> Warbs = 0.4(0.7X) --> KFs = 0.25(0.4(0.7X)).   Our job is to find out E: (0.3X + 0.28X + 0.07X)/ X. OR 0.65X/X = 0.65. We need to find   1-0.65= 
  1-0.65 = 0.35
0.35 or 35%.35%
Answer: B
A and B started a partnership business investing some amount in the ratio of 4 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?
Answers:
A) 4 : 9 : 8  B) 5 : 7 : 4  C) 6 : 10 : 5  D) 7 : 9: 4  E) 8 : 10 : 5

Solution: Let the initial investments of A and B be 4x and 5x.   A : B : C = (4x x 12) : (5x x 12) : (5x x 6) = 48 : 60 : 30   = 8 : 10 : 5.   ANSW8 : 10 : 5R :8 : 10 : 5
Answer: E
By selling 11 pencils for a rupee a man loses 10%. How many for a rupee should he sell in order to gain 20%?	Pick one.
A) 8.25
B) 9.25
C) 7.25
D) 10.25
E) 3.25

Solution: 90% --- 11120% --- ?90/120 * 11= 
90/120 * 11 = 33/4 = around 8.25
8.258.25nswer: 8.25
Answer: A
24.39 + 562.093 + 35.96 = ?  Choices: A) 622.441 B) 622.243 C) 622.233 D) 622.443 E) None of these

Solution: Explanation :   24.39 + 562.093 + 35.96 = 622.443. Answer : Option 622.443
Answer: D
A trader cheats both his supplier and customer by using faulty weights. When he buys from the supplier, he takes 10% more than the indicated weight. When he sells to his customer, he gives the customer a weight such that 50% of that is added to the weight, the weight claimed by the trader is obtained. If he charges the cost price of the weight that he claims, find his profit percentage.  Choose the correct choice from the following options:
A) 80%  B) 65%  C) 28.33%  D) 19.109%  E) 50%

Solution: Anyways, one can infer that he 'steals' 10% from suppliers and then charges 50% extra to customers   So basically 1.1 * 1.5= 
1.1 * 1.5 = 1.65
1.65   Given that 1 is start point, we get 65% more   Hence answer is 65%
Answer: B
Fifty applicants for a job were given scores from 1 to 5 on their interview performance. Their scores are shown in the table above. What was the average score for the group?  Select:
A) 2.79 B) 2.86 C) 2.91 D) 2.99 E) 3.03

Solution: Multiply score * number of application = 10+48+63+14+8= 
10+48+63+14+8 = 143
143.   Number of applications is 50.   143/50= 2.86.   Answer: option 2.86 is correct..
Answer: B
A man traveled a total distance of 900 km. He traveled one-third of the whole trip by plane and the distance traveled by train is one-half of the distance traveled by bus. If he traveled by train, plane and bus, how many kilometers did he travel by bus?
Choose the correct choice from the following choices.
A) 400 km	B) 450 km	C) 500 km	D) 550 km	E) 600 km

Solution: total distance traveled = 900 km.   distance traveled by plane = 300 km.   distance traveled by bus = x   distance traveled by train = x/2   x + x/2 + 300 = 900   3x/2 = 600   x = 400 km   The answer is 400 km.
Answer: A
A certain candy manufacturer reduced the weight of Candy Bar M by 10 percent buy left the price unchanged. What was the resulting percent increase in the price per ounce of Candy Bar M?  Choose the correct option:
A) 10
B) 11
C) 12
D) 14
E) 9

Solution: assume 1oz candy cost $1 before.   now price remain same $1 but weight of candy reduces to 0.9 oz   new price of candy = 1/0.9 =1.11   price increase 11 %   11
Answer: B
The SF Chronicle has a word game where all the letters are scrambled up and you have to figure out what the word is. Imagine that a scrambled word is 5 characters long: How many possible solutions are there? What if we know which 5 letters are being used?	Choose one:  A) 120  B) 130  C) 110  D) 125  E) 115

Solution: There are 26^5 = 1188137 solutions.   If we know the letters, then there are 5! = 120 possible solutions   120NSWER:120
Answer: A
If both 5^3 and 3^3 are factors of n x (2^5) x (12^2) x (7^3) x (10^2), what is the smallest possible positive value of n?
Select the correct option:	A) 15	B) 45	C) 75	D) 125	E) 150

Solution: (2^5) x (12^2) x (7^3) x (10) has two appearances of 3 (in 12^2) and two appearances of 5 (in 10^2).   Thus n must include at least   3 * 5= 
  3 * 5 = 15
15   The answer is 15.
Answer: A
A can do a work in 12days. When he had worked for 3days, B joinedhim. If they complete the work in 3more days, in how manydays can Balone finish the work?
Choose the most appropriate option.
A) 5 days  B) 4 days  C) 6 days  D) 10 days  E) 11 days

Solution: sax Work done by Afar 3 days : i   J   .. Remzming war — 1   .Work done by (A + B) for 1 day :   . Work done by a for 1 day   6 days   6 days
Answer: C
On selling 20 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price of a ball is:  Pick one:  A) s. 48  B) s. 50  C) s. 55  D) s. 60  E) s. 70

Solution: (C.P. of 20 balls) - (S.P. of 20 balls) = (C.P. of 5 balls)   C.P. of 15 balls = S.P. of 20 balls = Rs.720.   C.P. of 1 ball = Rs.720/15	= Rs. 48.   s. 48nswer: Option s. 48
Answer: A
A sum of money at simple interest amounts to Rs. 825 in 3 years and to Rs. 854 in 4 years. The sum is:	Select the correct option
A) s. 650 B) s. 690 C) s. 698 D) s. 738 E) s. 720

Solution: S.I. for 1 year = Rs. (854 - 825) = Rs. 29.   S.I. for 3 years = Rs.(29 x 3) = Rs. 87.   Principal = Rs. (825 - 87) = Rs. 738.   Answer: Option s. 738
Answer: D
I chose a number and divide it by 12. Then I subtracted 240 from the result and got 8. What was the number I chose?  Pick.
A) 2976 B) 2989 C) 2789 D) 2888 E) 2098

Solution: Let x be the number I chose, then   x/12−240=8   x/12=248   x=2976   2976nswer is 2976.
Answer: A
A worker's take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 5 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?
Choose the correct choice from the following options.
A) 2/11	B) 3/14	C) 5/17	D) 7/20	E) 11/30

Solution: Let x be the fraction of her take-home pay that the worker saved.   Let P be the monthly pay.   12xP = 5(1-x)P   12xP = 5P - 5xP   17xP = 5P   x = 5/17   The answer is 5/17.
Answer: C
A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?  Choose the most appropriate option:
A) 11%
B) 25%
C) 87%
D) 19%
E) 12%

Solution: 800 --- 200   100 --- ? => 25%   Answer: 25%
Answer: B
95 white and black tiles will be used to form a 10x10 square pattern. If there must be at least one black tile in every row and at least one white tile in every column, what is the maximum difference between the number of black and white tiles that can be used?  Choose one
A) 75	B) 80	C) 85	D) 90	E) 95

Solution: Answer = 85   Please refer diagram below     95 - 10= 
  95 - 10 = 85
85
Answer: C
Connie paid a sales tax of 8 percent on her purchase. If the sales tax had been only 5 percent, she would have paid $12 less in sales tax on her purchase. What was the total amount that Connie paid for her purchase including sales tax? Answers.
A) $368
B) $380
C) $400
D) $420
E) $432

Solution: Connie paid x dollar before sales tax   so,   1.08x - 1.05x = 12   0.03x = 12   x = 400   sales tax 400*8% = 32   Connie paid = 400+32= 
400+32 = 432
$432   Ans. $432
Answer: E
The avg. age of a group of 20 students is 20 years.If 4 more students join the group,the avg age increases by 1 year.The avg age of the new student is?  Choose the correct choice from the following choices.
A) 22 years	B) 23 years	C) 24 years	D) 25 years	E) 26 years

Solution: Total age of 20 students=20*20= 
20*20 = 400
400   If total age of 4 students=x   Then, (400+x)/(20+4) =(20+1), x=104   So average age of new students=104/4= 
104/4 = 26
26 years   ANSW26 yearsR:26 years
Answer: E
What should be the least number to be added to the 1202 number to make it divisible by 4? Choose the correct choice from the following:
A) 12	B) 17	C) 18	D) 77	E) 2

Solution: Answer : 2   Option : 2
Answer: E
At a certain company, each employee has a salary grade s that is at least 1 and at most 5. Each employee receives an hourly wage p, in dollars, determined by the formula p = 8.50 + 0.25(s – 1). An employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 1?
Pick.
A) $0.50	B) $1.00	C) $1.25	D) $1.50	E) $1.75

Solution: OA is definitely wrong. The answer should be $0.50.
Answer: A
Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.  Choose the correct choice from the following answers.
A) $ 145.
B) $ 146
C) $ 147
D) $ 148
E) None

Solution: Solution:   Let the 1st paycheck be x (integer).   Mrs. Rodger got a weekly raise of $ 145.   So after completing the 1st week she will get $ (x+145).   Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.   = $ (x + 145 + 145)   = $ (x + 290)   So in this way end of every week her salary will increase by $ 145.   $ 145.nswer $ 145.
Answer: A
How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 190 m in length?	Answers
A) 18.9 sec
B) 88.9 sec
C) 22.9 sec
D) 18.0 sec
E) 72.0 sec

Solution: 18.0 sec = 110 + 190= 
110 + 190 = 300
300 m   S= 60 * 5/18 = 50/3   T = 300 * 3/50= 
300 * 3/50 = 18
18.0 sec   Answer: 18.0 sec
Answer: D
A certain truck uses 18 gallons of diesel fuel in traveling 260 miles. In order for the truck to travel the same distance using 10 gallons of diesel fuel, by how many miles per gallon must the truck’s fuel mileage be increased?  Answers:
A) 8
B) 9
C) 12
D) 11
E) 27

Solution: There are two sets 18G1 gallons and 10G2 gallons details given.   18 gallons covering 260 miles   Then 1 G1 is used to cover 15 miles.   Now for 10 G2 covering 260 miles.   then 1 G2 is used to cover 26 miles.   There must   26- 15= 
  26- 15 = 11
11 miles per gallon increment is needed for 10 gallons to improve the mileage to cover 270 miles.   IMO 11 is correct answer.
Answer: D
The amounts of time that three secretaries worked on a special project are in the ratio of 1 to 2 to 5. If they worked a combined total of 120 hours, how many hours did the secretary who worked the longest spend on the project?
Choices:  A) 80  B) 70  C) 75  D) 16  E) 14

Solution: 8x = 120   => x = 15   Therefore the secretary who worked the longest spent 15 x 5 = 75 hours on the project   Option (75)
Answer: C
Sandy buys an old scooter for $900 and spends $300 on its repairs. If Sandy sells the scooter for $1500, what is the gain percent?
Select:  A) 10%  B) 15%  C) 20%  D) 25%  E) 30%

Solution: selling price / total cost = 1500/1200= 
1500/1200 = 5/4 = around 1.25
1.25   The gain percent is 25%.   The answer is 25%.
Answer: D
The ratio between x and y is 7/5; x is multiplied by y and y is multiplied by x , what is the ratio between the new values of x and y? Choose the correct answer
A) 7/5
B) 5/7
C) 1
D) 49/25
E) It Cannot Be Determined

Solution: Ratio = 7k/5k = 7/5, 14/10, etc.   x is multiplied by y and y is multiplied by x --> (7k*9k)/(9k*7k) = 1   Answer: 1 --  (7 *9 )/(9 *7 )= 
 --  (7 *9 )/(9 *7 ) = 1
1   Answer: 1
Answer: C
along a yard 225 metres long, 26 trees are planted at equal distances, one tree bring at each end of the yard. What is the distance between two consecutive trees ? long,26 trees  Choose the correct option: A) 8 metres B) 9 metres C) 10 metres D) 15 metres E) None of these

Solution: Solution   26 trees have 25 gaps between them. Hence, required distance = (225/25)= 
(225/25) = 9
9m   Answer 9 metres
Answer: B
Working together, printer A and printer B would finish the task in 15 minutes. Printer A alone would finish the task in 45 minutes. How many pages does the task contain if printer B prints 3 pages a minute more than printer A ?
Select:
A) 125	B) 135	C) 145	D) 155	E) 165

Solution: 15*A + 15*B = x pages   in 15 mins printer A will print = 15/45 * x pages = 1/3*x pages   thus in 15 mins printer printer B will print x - 1/3*x = 2/3*x pages   Also it is given that printer B prints 3 more pages per min that printer A. In 15 mins printer 135 will print 45 more pages than printer A   thus 2/3*x - 1/3*x = 45 => x = 135 pages   Answer: 135
Answer: B
For which of the following values of n is (600+n)/n NOT an integer?  Choose one
A) 1 B) 2 C) 3 D) 4 E) 9

Solution: Solution:   This problem is easiest solved by plugging in each answer choice.   A) (600 + 1)/1 = 601/1= 
601/1 = 601
601   Answer choice A yields an integer.   B) (600 + 2)/2= 602/2= 
602/2 = 301
301   Answer choice B yields an integer.   C) (600 + 3)/3= 603/3= 
603/3 = 201
201   Answer choice C yields an integer.   D) (600 + 4)/4= 604/4 = 126   Answer choice D yields an integer.   E) (600 + 9)/5 = 609/9 = 65, remainder 4   Answer choice E DOES NOT yield an integer.   Thus, the correct answer is answer choice 9.
Answer: E
New town is straight to the north of New york. A high way M runs from newtown making an angle of 61 degree south east. from newyork there is also an high way N which runs Northeast 61 degrees. If high ways M and N are straight then findout the acute angle made at their intersection point.	Choose the correct choice from the following:
A) 56degree
B) 57degree
C) 58degree
D) 59degree
E) 50degree

Solution: the acute angle must be 58 degree . taking north-south as reference axis . from center M is at an angle of 61degree near south and N is at an angle of 61degree from north .therefore, 180-61-61 gives 58degree   ANSWER:58degree
Answer: C
A train 240 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?	Choose the correct choice
A) 4	B) 6	C) 12	D) 9	E) 13

Solution: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr   [66 * 5/18] m/sec = [55/3] m/sec.   Time taken to pass the man = [240 * 3/55] sec = 13 sec   ANSW13R:13
Answer: E
If Rs.1000 be invested at interest rate of 5% & the interest be added to the principal every 10 yrs, then the no. of yrs in which it will amount to Rs.2000 is:  Choose the correct choice from the following choices
A) 14 years
B) 15 years
C) 16 2/3 years
D) 17 years
E) 18 years

Solution: Total time= (10+6 2/3) = 16 2/3 years   16 2/3 years
Answer: C
On dividing a number by 56, we get 28 as remainder. On dividing the same number by 8, what will be the remainder ? Choose the correct answer:	A) 2	B) 3	C) 4	D) 5	E) 6

Solution: Number=56x+28 (∵ since the number gives 28 as remainder on dividing by 56)   =(7×8×x)+(3×8)+4   Hence, if the number is divided by 8, we will get 4 as remainder.   ANSWER:4
Answer: C
A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long? Choices.
A) 65 sec  B) 89 sec  C) 100 sec  D) 150 sec  E) 160 sec

Solution: Explanation:   Speed =240/24 m/sec = 10 m/sec   Required time =(240+650 /10)sec=89sec   ANSWER IS 89 sec
Answer: B
An engagement team consists of a project manager, team leader, and four consultants. There are 3 candidates for the position of project manager, 4 candidates for the position of team leader, and 7 candidates for the 4 consultant slots. If 2 out of 7 consultants refuse to be on the same team, how many different teams are possible? Choose the correct choice from the following options
A) 25  B) 35  C) 150  D) 210  E) 300

Solution: Answer= Total number combinations - Total number of combinations with constraints   Total number of combinations = 3C1*4C1*7C4= 420   Total number of combinations with constraints = 3C1*4C1*5C2=120   Answer=420-120= 
420-120 = 300
300   ANSW300R: 300
Answer: E
A car travels from point A to point B. The average speed of the car is 60 km/hr and it travels the first half of the trip at a speed of 50 km/hr. What is the speed of the car in the second half of the trip? Choose the correct choice from the following answers:
A) 55
B) 60
C) 75
D) 80
E) 90

Solution: Let D be the distance and let V be the speed in the second half.   The total time = T1 + T2   D/60 = D/100 + (D/2) / V   D/150 = D/2V and so V = 75 km/hr   The answer is 75.
Answer: C
Suppose that the numbers 1,2,4,8,16,32,64,128,256
are placed into the nine squares in such a way that
the product of the numbers appearing in any row,
column or diagonal is the same. What is the value
of this common product?
Choose the correct option
A) 512
B) 4096
C) 8192
D) 16384
E) 32768

Solution: The product of the numbers in all three rows is simply the product of the numbers   1,2,4,8,..,256 or, equivalently, of the numbers 20in zero,21in first,22in round,23in third ,..,28in eighth. The product is   2->0+1+2+...+8 = 236in thirty sixth   so correct answer 4096
Answer: B
If a#b = ab – b + b^2, then 3#6 =
Pick one:
A) 2 B) 8 C) 15 D) 21 E) 48

Solution: Solution -   Simply substitute 3 and 6 in equation in the place of a and b respectively.   3#6 = 3*6 - 6 + 6^2 = 18 - 6 + 36= 
18 - 6 + 36 = 48
48. ANS 48
Answer: E