MU-NLPC/Calc-aqua_rat huggingface dataset:
It is being given that (2^32 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
Choose the correct option:
A) (2^90 - 1)	B) (2^90 + 1)	C) (2^96 - 1)	D) (2^96 + 1)	E) (2^95 + 1)

Solution: Let 232 = x. Then, (232 + 1) = (x + 1).   Let (x + 1) be completely divisible by the natural number N. Then,   (296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.   (2^96 + 1))
Answer: D
Arabica coffee costs $0.4 per ounce while Robusta coffee costs $0.3 per ounce. If the blend of Arabica and Robusta costs $0.33 per ounce, what is the share of Arabica in this blend?
Choose the correct choice:  A) 20%  B) 24%  C) 30%  D) 33%  E) 40%

Solution: a= amount of arabica coffee   1-a = amount of robusta coffee. because if you subtract a from the 1 ounce, the remaining amount is robusta   therefore:   .4a + .3(1-a) = .33   .4a + .3 - .3a = .33   a= .3   therefore: .3/1 ounce = 30%. Therefore, the answer should be 30%
Answer: C
Dacid obtained 91, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?	Choose the correct choice.
A) 29 B) 78 C) 39 D) 37 E) 75

Solution: Average = (91 + 65 + 82 + 67 + 85)/5= 
(91 + 65 + 82 + 67 + 85)/5 = 78
78   Answer: 78
Answer: B
The cost price of 20 books is the same as the selling price of x books. If the profit is 25%, then the value of x is?	Choose the correct choice from the following answers:
A) 14
B) 16
C) 18
D) 22
E) 24

Solution: Let C.P. of each book be Re. 1 C.P. of x articles = Rs. x.   S.P. of x booksv= Rs. 20.   Profit = Rs. (20 - x).   20 - x	x 100 = 25   x   2000 - 100x = 25x   125x = 2000   x = 16.   16)
Answer: B
What is the next number of the following sequence
3,5,15,75,?
Choose the correct choice from the following options.
A) 1125
B) 1200
C) 1000
D) 1100
E) 1500

Solution: 3*5= 
3*5 = 15
15   5*15= 
5*15 = 75
75   15*75= 
15*75 = 1_125
1125   therefore next no. is 1125   1125NSWER:1125
Answer: A
Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?
Choose the correct choice from the following answers
A) 729  B) 561  C) 456  D) 354  E) 163

Solution: The first ring can be worn in any of the 3 fingers (3 ways).   Similarly each of the remaining 5 rings also can be worn in 3 ways.   Hence total number of ways   =3×3×3×3×3×3=36=729   729ns:729
Answer: A
If the sum of one-half of a number exceeds one-third of that number by 7 1/3, the number is: Choose the correct choice from the following:  A) 15  B) 18  C) 20  D) 25  E) 30

Solution: Let the number be x. Then,   (1/2 x + 1/5 x) - 1/3 x = 22/3   11/30 x = 22/3   x = 20   ANSWER:20
Answer: C
A relay has a series of 5 circuits in a line. The even-numbered circuits are control circuits; the odd are buffer circuits. If both a control circuit and the buffer circuit immediately following it both fail in that order, then the relay fails. The probability of circuit one failing is 3/8; circuit two, 1/8; circuit three, 3/10; circuit four, 3/4; and circuit five, 2/5 .What is the probability that the relay fails? Choices:	A) 9/80	B) 3/10	C) 261/800	D) 35/80	E) 497/800

Solution: The first circuit doesn't matter.   Prob(relay fails) = 1 - Prob(relay succeeds)   Prob(2+3 work) = 1 - 3/80 = 77/80   Prob(4+5 work) = 1 - 3/10 = 7/10   Prob(relay fails) = 1 - Prob(2+3 work AND 4+5 work) = 1 - (77/80)(7/10) = 1 - 539/800 = 261/800   261/800
Answer: C
Coins are to be put into 12 pockets so that each pocket contains at least one coin. At most 8 of the pockets are to contain the same number of coins, and no two of the remaining pockets are to contain an equal number of coins. What is the least possible number of coins needed for the pockets?  Choices
A) 7	B) 13	C) 17	D) 22	E) 28

Solution: Since at most 3 of the pockets are to contain the same number of coins then minimize # of coins in each, so let each contain just 1 coin;   Next, we are told that no two of the remaining 4 pockets should contain an equal number of coins, so they should contain 2, 3, 4, and 5 coins each (also minimum possible);   Total:   1+1+1+1+1+1+1+1+2+3+4+5= 
  1+1+1+1+1+1+1+1+2+3+4+5 = 22
22   Answer: 22.
Answer: D
The sum of n terms of a series in A.P is 6n2 + 6n. What is the 4 th term of the series?	Choose the correct answer.
A) 38 B) 49 C) 60 D) 48 E) 50

Solution: 4 th term = sum of 4 terms - sum of 3 terms   = ( 6* 42 + 6*4 ) -( 6* 32 +6*3 ), = ( 96+24 ) – ( 54+18 )   = 120 - 72= 
120 - 72 = 48
48   ANSWER:48
Answer: D
In covering a distance of 120 km, A takes 2 hours more than B. If A doubles his speed, then he would take 1 hour less than B. A's speed is:	Select:
A) 5 km/h	B) 8 km/h	C) 10 km/h	D) 15 km/h	E) 20 km/h

Solution: Let A's speed be X km/hr.   Then, 120/x - 120/2x = 3   6x = 120   x = 20 km/hr.   Answer : 20 km/h.
Answer: E
39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work? Select the correct option:
A) 11  B) 13  C) 55  D) 76  E) 81

Solution: Explanation:   Let the required number of days be x.   Less persons, More days (Indirect Proportion)   More working hours per day, Less days (Indirect Proportion)   \inline {\color{13lue} \left.\begin{matrix} persons &30:39 \\ working\; hours/day & 6:5 \end{matrix}\right\}::12:x}   \inline {\color{13lue} \therefore } 30 x 6 x x = 39 x 5 x 12   => x= \inline {\color{13lue}\frac{39\times 5\times 12}{30\times 6}}   => x= 13   Answer: 13
Answer: B
How many seconds does Sandy take to cover a distance of 600 meters, if Sandy runs at a speed of 15 km/hr?	Select the correct option.
A) 128  B) 136  C) 144  D) 152  E) 160

Solution: 15 km/hr = 15000 m / 3600 s = (150 / 36) m/s = (25 / 6) m/s   time = 600 / (25/6)= 
600 / (25/6) = 144
144 seconds   The answer is 144.
Answer: C
How many different subsets of the set {10, 14, 15, 24} are there that contain an odd number of elements?	Pick one
A) 8 B) 6 C) 18 D) 10 E) 12

Solution: 8nswer = 8 = 8   {10}   {14}   {15}   {24}   {10, 14, 15}   {14, 15, 24}   {10, 15, 24}   {10, 14, 24}
Answer: A
The radius of a semi circle is 6.3 cm then its perimeter is? Choose the correct option:
A) 32.6
B) 32.4
C) 32.9
D) 32.2
E) 32.1

Solution: 36/7 r = 6.3 = 32.4   Answer:32.4
Answer: B
From a group of boys and girls, 15 girls leave. There are then left 2 boys for each girl. After this, 45 boys leave. There are then 5 girls for each boy. Find the number of girls in the beginning? Choose the correct choice from the following
A) 40	B) 30	C) 50	D) 60	E) 10

Solution: Let at present there be x boys.   Then,no of girls at present=5x   Before the boys had left:no of boys=x+45   40nd no of girls=5x   X+45=2*5x   9x=45   x=5   no of girls in the beginning=25+15= 
25+15 = 40
40   40nswer is 40.
Answer: A
Find the average of first 10 natural numbers.  Choose the correct choice
A) 20.5  B) 18  C) 19.5  D) 19  E) 5.5

Solution: Exp. Sum of first n natural numbers = n( n+1)/2   So, sum of first 10 natural numbers = 10*11/2= 
10*11/2 = 55
55   Required average=55/10= 
55/10 = 11/2 = around 5.5
5.5   Answer:5.5
Answer: E
Two partners in a business (Miles and King) invested $1200 and $2000 in a business respectively. At the end of the year they made a profit of $1500. Find share of each partner? Pick one
A) $562.5,$677.5 B) $555.5,$937.5 C) $562.5,$939.5 D) $662.5,$937.5 E) $562.5,$937.5

Solution: A:B = 1200:2000   A:B = 3 : 5   A's share = 1500*3/8= 
1500*3/8 = 1_125/2 = around 562.5
$562.5   B's share= 1500*5/8= 
1500*5/8 = 1_875/2 = around 937.5
$937.5   Answer is $562.5,$937.5
Answer: E
Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120?	Choose the correct choice.
A) Rs.1000	B) Rs.1100	C) Rs.1050	D) Rs.1200	E) Rs.1500

Solution: Explanation:   1120 = P [1 + (5*12/5)/100]   P= 1000   Rs.1000NSWER IS Rs.1000
Answer: A
The average weight of 18 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.	Choices.
A) 48.68077	B) 42.25983	C) 50	D) 51.25388	E) 52.25

Solution: Explanation:   48.68077verage weight of 18 boys = 50.25   Total weight of 18 boys = 50.25 × 18   48.68077verage weight of remaining 8 boys = 45.15   Total weight of remaining 8 boys = 45.15 × 8   Total weight of all boys in the class = (50.25 × 18)+ (45.15 × 8)   Total boys = 18 + 8= 
18 + 8 = 26
26   48.68077verage weight of all the boys= (50.25×18)+(45.15×8)/26   =48.68077   48.68077nswer: Option 48.68077
Answer: A
The CP of 20 apples are the same as the SP of y apples. If the profit is 25%, then the value of y is?
Pick
A) 8	B) 12	C) 16	D) 18	E) 20

Solution: Let C.P. of each article be Re. 1 C.P. of x articles = Rs. x.   S.P. of x articles = Rs. 20.   Profit = Rs. (20 - x).   20 - x	x 100 = 25   x   2000 - 100x = 25x   125x = 2000   x = 16   16
Answer: C
If x and y are positive integers and 42x=56y what is the least possible value of xy?  Select the correct option:
A) 14
B) 28
C) 63
D) 196
E) 252

Solution: 42x=56y   => x/y = 4/3   => 3x=4y   3(14)=4(14) => x*y=196   252
Answer: E
The greatest possible length which can be used to measure exactly the length 8m, 4m 84cm, 11 m 90 cm is
Pick.
A) 11 cm
B) 12 cm
C) 5 cm
D) 2 cm
E) 43 cm

Solution: Explanation:   Required Length = H.C.F of 800 cm, 484 cm and 1190 c   = 2 cm. Answer: 2 cm
Answer: D
What is the diagonal of a square field whose perimeter is 24m?	Pick one:
A) 8 m  B) 2 m  C) 7 m  D) 10 m  E) 6√2 m

Solution: Sol:   Let the side of the square be x meters.   Therefore,   4x=24   x=6   Diagonal of the square is= √2*(6)^2=6√2   Answer: 6√2 m
Answer: E
If 13 and 17 are prime numbers, which of the following CANNOT be the sum of a and b?	Choose the correct option
A) 30	B) 60	C) 90	D) 120	E) 31

Solution: ans: 31
Answer: E
A bag contains 6 green balls and 7 white balls. If two balls are drawn simultaneously, what is the probability that both balls are the same colour?	Select.
A) 2/7
B) 3/10
C) 5/11
D) 6/13
E) 11/21

Solution: The total number of ways to draw two balls is 13C2 = 78   The number of ways to draw two green balls is 6C2 = 15   The number of ways to draw two white balls is 7C2 = 21   P(two balls of the same colour) = 36/78 = 6/13   The answer is 6/13.
Answer: D
a man purchased earphone on friday.but he forgot how much it cost.the data he have are mean expenditure of all 7 days is 500.expenditure on mon,tue,wed,thurs,sat,sun are 450,600,400,500,550,300.on friday he purchased three things one earphone,one pen and one notebook.pen cost 30 and notebook cost 50.then what is cost of earphone?	Pick one:	A) 620	B) 530	C) 450	D) 470	E) 500

Solution: solution   let expenditure on Friday be x   (450+600+400+500+x+550+300)/7=500   2800+x=3500   x=700   pen+notebook+earphone=700   earphone=700-80= 
700-80 = 620
620   answer 620
Answer: A
A, B and C completed a piece of work, A worked for 6 days, B for 9 days and C for 4 days. Their daily wages were in the ratio of 3:4:5. Find the daily wages of C, if their total earning was Rs.1850? Choose the correct choice from the following
A) s.125	B) s.108	C) s.100	D) s.103	E) s.102

Solution: 3x 4x 5x   6 9 4   18x + 36x + 20x = 1850   74x = 1850 => x = 25   5x = 125 Rs.   s.125nswer:s.125
Answer: A
xy=1 then what is (5^(x+y)^2) / (5^(x-y)^2)  Choose the correct option.
A) 2 B) 625 C) 8 D) 16 E) 32

Solution: (x+y)^2 - (x-y)^2   (x+y+x-y)(x+y-x+y)   (2x)(2y)   4xy   4   5^4 = 625   Answer 625
Answer: B
The diagonals of a rhombus are 12 cm and 20 cm. Find its area?
Choose the correct choice:  A) 120  B) 266  C) 150  D) 288  E) 212

Solution: 1/2 * 12 * 20= 
1/2 * 12 * 20 = 120
120   120nswer: 120
Answer: A
k, l, m together started a business. k invested Rs.6000 for 5 months l invested Rs.3600 for 6 months and m Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of l ?  Pick
A) Rs. 1640	B) Rs. 2500	C) Rs. 2160	D) D) Rs. 3000	E) NONE OF THESE

Solution: Explanation:   => 60x5 : 36x6 : 75x3   => 100 : 72 : 75   => 72/247 x 7410 = Rs. 2160   ANSWER IS Rs. 2160
Answer: C
Divide Rs. 1200 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?  Choose the correct choice
A) 300	B) 368	C) 375	D) 337	E) 639

Solution: 300+B+C = 1200   300 = 1/3(B+C); B = 2/3(300+C)   300/(B+C) = 1/3   300 = 1/4 * 1200= 
1/4 * 1200 = 300
> 300   300nswer:300
Answer: A
The side of a cube is 12 m, find the lateral surface area?
Pick one:	A) 816	B) 516	C) 716	D) 216	E) 916

Solution: Lateral surface = 4 a(power)2   4 × 12(power)2 = 4 × 144 => 516 m(power)2   Answer is 516.
Answer: B
Subtracting 4% of A from A is equivalent to multiplying A by how much ? Select
A) 0.96	B) 9.4	C) 0.094	D) 94	E) None

Solution: Answer   Let A - 4% of A = AB.   ⇒ (96 x 0.96) / 100 = 0.96B   ∴ B = 0.96   Correct Option: 0.96
Answer: A
The ratio of pens to pencils is 5 to 6. There are 6 more pencils than pens. How many pencils are there? Pick:
A) 32  B) 36  C) 40  D) 44  E) 48

Solution: Let the number of pens be 5x and the number of pencils be 6x.   6x - 5x = 6   x = 6   The number of pencils is 36.   The answer is 36.
Answer: B
A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price? Select
A) 18%
B) 13%
C) 12%
D) 32%
E) 15%

Solution: Original price = 100   12%P = 80   S = 80*(140/100)= 
80*(140/100) = 112
112   100 - 112= 12%   Answer: 12%
Answer: C
The number of positive integer solutions for the equation x +y +z + t = 21 is	Select the correct option
A) 1140
B) 1145
C) 1240
D) 1340
E) 15640

Solution: The number of positive integer solutions for the equatio fx1+x2+⋯+xn=k   (k-1)C(n-1)- where k is the number and n is number of variable in the equation.   21-1 C 4-1 = 20C3 = 1140   1140nswer : 1140
Answer: A
In ΔPQS above, if PQ =4 and PS = 5, then  Choose the correct choice from the following:
A) 9/4
B) 12/5
C) 16/5
D) 15/4
E) 10/3

Solution: there are two ways to calculate area of PQS. area remains same, so both are equal.   4*5/2 = PR*6/2   PR = 10/3   10/3
Answer: E
If 4 men working 10 hours a day earn Rs. 1400 per week, then 9 men working 6 hours a day will earn how much per week?	Choose the correct choice from the following options:
A) Rs 840 B) Rs 1320 C) Rs 1620 D) Rs 1890 E) None of these

Solution: Explanation :   (Men 4:9) : (Hrs/Rs 1890ay 10:6) :: 1400 : x   hence 4 * 10 *x = 9 * 6 * 1400   or x = 9*6*1400/ 4*10 = 1890   Answer : Rs 1890
Answer: D
A contractor hires 100 men to finish a job in 50 days. After 20 days, n men leave. After some more days, the contractor hires 2n more men to complete the job on time. For how many days did these 2n men work?
Choose the most appropriate option:  A) 20  B) 18  C) 15  D) 12  E) 8

Solution: Step1: Find Each day what % of work is finished ; it requires 50 days to complete which means each day 1/50= 2% work will be completed.   Step 2 : After 20 Days = 20* 2= 
20* 2 = 40
40% of work is finished. remaining is 60% ( which means if same 100 men were about to complete the job they would have required 30 more days)   Step3: Let us assume all people have left job. therefore contractor hires 2n people. initially it was taking 30 days to compete for n people. at present 2n people are present to finish job. hence 15 more days.   15
Answer: C
A sum of Rs. 1550 was lent partly at 5% and partly at 8% p.a. simple interest. The total interest received after 3 years was Rs. 300. The ratio of the money lent at 5% to that lent at 8% is:	Pick:
A) 16 : 15
B) 15 : 16
C) 15 : 8
D) 8 : 15
E) 8 : 17

Solution: Explanation :   Let the partial amount at 5% be x and the partial amount at 8% be (1550-x)   Interest on x at 5% for 3 years + interest on (1550-x) at 8% for 3 years = 300   x × 5 × 3 /100+(1550-x) × 8 × 3 /100=300   x × 5 /100+(1550-x) ×8 /100=100   5x+8(1550−x)=10000   5x+12400−8x=10000   3x=2400   x=800   Required Ratio = x : (1550-x) = 800 : (1550-800) = 800 : 750 = 16 : 15   16 : 15nswer : Option 16 : 15
Answer: A
A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 30. Find the profit percentage?	Choose the correct choice:
A) 80%
B) 50%
C) 59%
D) 40%
E) 53%

Solution: L.C.M of 15 and 12   = 60   CP of 60 articles   = Rs. 100 (25 * 4)   SP of 60 articles   = Rs. 150 (30 * 5)   Profit percentage   = (150 - 100)/100 * 100= 
(150 - 100)/100 * 100 = 50
50%   Answer: 50%
Answer: B
A train 280 m long passed a pole in 20 sec. How long will it take to pass a platform 720 m long? Select the correct option:	A) 12 sec	B) 59 sec	C) 71 sec	D) 61 sec	E) 66 sec

Solution: Speed = 280/20= 
280/20 = 14
14 m/sec.   Required time= (280 + 720)/14   = 71.4 sec.   Answer: 71 sec
Answer: C
Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability W that the World Series will consist of fewer than 7 games?
Pick one:
A) 12.5% B) 25% C) 31.25% D) 68.75% E) 75%

Solution: Your explanation is very close toManhattan GMAT's official answer - it's quite uncanny:   "There are many other ways this could happen. Using the permutation formula, there are 6!/(3!)(3!) = 20 ways for the two teams to split the first 6 games (3 wins for each).   There are then 2 possible outcomes to break the tie in Game 7. Thus, there are a total of 202 = 40 ways for the World Series to last the full 7 games.   The probability that any one of these 40 ways occurs can be calculated from the fact that the probability of a team winning a game equals the probability of a team losing a game = 1/2.   Given that 7 distinct events must happen in any 7 game series, and that each of these events has a probability of 1/2, the probability that any one particular 7 game series occurs is.   Since there are 40 possible different 7 game series, the probability that the World Series will last exactly 7 games is: (1/2)^7 = 1/128   40*1/128 = 40/128 = 31.25%   Thus the probability W that the World Series will last less than 7 games is 100% - 31.25% = 68.75%.   The correct answer is 68.75%." 100  - 31.25= 
 100  - 31.25 = 68.75
68.75%.   The correct answer is 68.75%."
Answer: D
If the day before yesterday was Wednesday, when will Sunday be? Choose the correct choice.
A) Day after tomorrow  B) Tomorow  C) Two days after today  D) Today  E) none

Solution: Explanation:   Day before yesterday was Wednesday   =>Yesterday was a Thursday   => Today is a Friday   => Tomorrow is a Saturday   => The day after tomorrow will be a Sunday   Day after tomorrownswer: Option Day after tomorrow
Answer: A
After taking N tests, each containing 100 questions, John had an average of 70% of correct answers. How much does John need to score on the next test to make his average equal 71%?
M13-03.
Choose the correct choice from the following options:
A) N−35  B) N+72  C) 2N+70  D) 2N+72  E) 2N−35

Solution: Say N=1.   So, after 1 test John has 70 correct answers.   In 2 tests, so in 200 questions he needs to have  0.71*200= 
 0.71*200 = 142
142 correct answers, so in the second test he must get   142-70= 
  142-70 = 72
72 questions correctly.   Now, plug N=1 into the answer choices to see which one yields 72. Only option D fits.   Answer: 2N+70.
Answer: C
A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?	Choose one:
A) 76 km	B) 16 km	C) 26 km	D) 36 km	E) 20 km

Solution: Let the distance between A and B be x km.   Total time = x/(9 + 1) + x/(9 - 1) = 4.5   => x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x   = 20 km   Answer:20 km
Answer: E
The average marks of a class of 30 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students? Choices:
A) 52.6	B) 52.4	C) 52.1	D) 52.5	E) 52.9

Solution: Sum of the marks for the class of 30 students = 30 * 40= 
30 * 40 = 1_200
1200   Sum of the marks for the class of 50 students= 50 * 60= 
50 * 60 = 3_000
3000   Sum of the marks for the class of 80 students=   1200 + 3000= 
1200 + 3000 = 4_200
4200   Average marks of all the students= 4200/80 = 52.5.Answer: 52.5
Answer: D
The average of six numbers is 30. If the average of first four is 25 and that of last three is 35, the fourth number is :
Select:  A) 25  B) 26  C) 18  D) 19  E) 10

Solution: Let the six numbers be, a, b, c, d, e, f.   a + b + c + d + e + f = 30 × 6 = 180 - - - - (1)   a + b + c + d = 25 × 4 = 100 - - - - (2)   d + e + f = 35 × 3 = 105 - - - - (3)   Add 2nd and 3rd equations and subtract 1st equation from this.   d = 25   25nswer: 25
Answer: A
A jar full of whiskey contains 40% alcohol. A part of this whisky is replaced by another containing 19% alcohols and now the percentage of alcohol was found to be 26%. The quantity of whisky replaced of whisky replaced is	Choose the correct choice from the following answers
A) 1 / 3  B) 2 / 3  C) 2 / 5  D) 3 / 5  E) None

Solution: Solution   ratio of 1st and 2nd quantities = 7 : 14 = 1 : 2.   Required quantity replaced = 2/3   Answer 2 / 3
Answer: B
How many different two-letter initials with none of the letters repeated can people have?  Pick one
A) 550  B) 650  C) 750  D) 950  E) 850

Solution: for first latter it has 26 way   and for 2 latter it has 25 way   hence  25*26= 
 25*26 = 650
650   ANSWER:650
Answer: B
During a poker game, 8 people are to be seated around a circular table. two seating arrangement are considered different only when the position of the people are different relative to each other. what is the total number of possible seating arrangements for the group?  Choose the correct choice from the following choices:	A) a.1	B) b.5,040	C) c.24	D) d.303	E) e.120

Solution: for 8 people seating arrangement around a circular table = (8-1)= 
(8-1) = 7
7!= 7*6*5*4*3*2*1   =5,040   OA is b.5,040
Answer: B
An association of mathematics teachers has 1,500 members. Only 525 of these members cast votes in the election for president of the association. What percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast?	Answers
A) 75%	B) 58%	C) 42%	D) 34%	E) 21%

Solution: Total umber of members = 1500   Number of members that cast votes = 525   Since , winning candidate received 60 percent of the votes cast   Number of votes for winning candidate = (60/100)*525= 
(60/100)*525 = 315
315   Percent of total membership that voted for winning candidate= (315/1500)*100= 
(315/1500)*100 = 21
21%   Answer 21%
Answer: E
The ratio of three numbers is 5:3:4 and their sum is 108. The second number of the three numbers is?
Pick one.
A) 25 B) 27 C) 29 D) 31 E) 32

Solution: 5:3:4   Total parts = 12   12 parts --> 108   1 part ---->9   The second number of the three numbers is = 3   3 parts ----> 27   27
Answer: B
Solve the following system of equations:
x-y-z = 0
3x+4y+3z = 4
5x+2y+7z = 22  Pick one:
A) x=1, y=2, z=3	B) x=-1, y=-2, z=1	C) x=-2, y=3, z=1	D) x=1, y=-2, z=3	E) x=3, y=-1, z=2

Solution: Solve the first equation for x.   x-y-z = 0   x = y+z   Substitute the solution for x into the second and third equations.   3*(y+z)+4y+3z = 4   3y+3z+4y+3z = 4   7y+6z = 4   5*(y+z)+2y+7z = 22   5y+5z+2y+7z = 22   7y+12z = 22   Subtract the new second equation from the new third equation and solve for z.   7y+12z = 22   - (7y+6z = 4)   6z = 18   z=3   Substitute the solution for z back into 7y+6z = 4 and solve for y.   7y+6*3 = 4   7y+18 = 4   7y = -14   y=-2   Substitute the values for y and z back into x-y-z = 0.   x-(-2)-3 = 0   x-1 = 0   x=1   x=1, y=2, z=3nswer x=1, y=2, z=3
Answer: A
Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.85. How much was lent at 5%?  Choose one:
A) 197
B) 119
C) 279
D) 500
E) 502

Solution: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 85   5x/100 + 90 – 6x/100 = 85   x/100 = 5   => x = 500   Answer:500
Answer: D