MU-NLPC/Calc-aqua_rat huggingface dataset:
A certain research group plans to create computer models of x% of a list of 10,000 bacterial species known to inhabit the human body. After a budget cut, the group finds it must reduce this selection by (x − 6)%. In terms of x, how many species of bacteria will the group be able to model?	Choose the correct choice from the following.
A) (x)*(106 - x)
B) (x)(105 – x)
C) (100)(105 – x)
D) (100)(95 – x)
E) (x-5)/100

Solution: Initial: (x/100)*10000 = 100x (bacterial species)   (x)*(106 - x)fter reduce BY (x - 6)%, the percentage of bacterial species = 1 - (x - 6)% = 1 - (x - 6)/100 = (106 - x)/100   Note: Difference between reduce to[means: the remain] and reduce by[means: the remain = 1 -reduce by]   So, the number of bacterial species after reducing: 100x*(106 - x)/100 = (x)*(106 - x)   (x)*(106 - x)ns is (x)*(106 - x).
Answer: A
In Township K each property is taxed at 8 percent of its assessed value. If the assessed value of a property in Township K is increased from $18,000 to $28,000, by how much will the property tax increase?  Choose the correct option
A) $320 B) $800 C) $320 D) $600 E) $850

Solution: Increase in house value = $28,000 - $18,000 =$10000   So, tax increase = 8% of$10000=$800   Answer: $800
Answer: B
The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 24. What is the rate of interest per annum?
Choose the correct choice from the following answers.
A) 8	B) 2	C) 9	D) 4	E) 6

Solution: Explanation:   [15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 104   15000[(1 + R/100)2 - 1 - 2R/100] = 24   15000[(100 + R)2 - 10000 - 200R]/10000 = 24   R2 = (24 * 2)/3= 
(24 * 2)/3 = 16
16=> R = 4   Rate = 4%   Answer: Option 4
Answer: D
A sum of Rs. 2691 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?	Choose the correct answer: A) 1629 B) 1656 C) 1277 D) 6298 E) 1279

Solution: (x*8*3)/100 = ((2691 - x)*3*5)/100   24x/100 = 40365/100 - 15x/100   39x = 40365 => x = 1035   Second sum = 2691 â€“ 1035 = 1656   Answer:1656
Answer: B
Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?	Choose the most appropriate option.
A) 876  B) 268  C) 269  D) 600  E) 278

Solution: Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.   BE2 + AE2 = AB2   252 = 152 + AE2 AE = √(625 - 225)= 
(625 - 225) = 400
√400= 20,   AC = 20 + 20= 
20 + 20 = 40
40 cm.   Area of a rhombus= 1/2 * d1d2   = 1/2 * 40 * 30= 
1/2 * 40 * 30 = 600
600 sq.cm.   Answer:600
Answer: D
There are 4 runners on a track team who run an average of 4.5 seconds per 40 yards. If another runner joins their team who runs 4.3 seconds per 40 yards, what will the new average 40 yard time be?  Pick:	A) 4.46	B) 4.39	C) 4.42	D) 4.49	E) 4.33

Solution: (sum of the 4 times)/4 = 4.5   sum of the 4 times = 18   new sum = 18+4.3= 
18+4.3 = 22.3
22.3   new average= 22.3/5= 
22.3/5 = 4.46
4.46   ans: 4.46
Answer: A
Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 15 inches by 20 inches and Jordan's rectangle is 6 inches long, how wide is Jordan's rectangle, in inches? Choose the correct answer:
A) 20	B) 30	C) 40	D) 50	E) 60

Solution: Area of first rectangle is 15*20= 
15*20 = 300
300 hence area of second would be 6x=300x   x=50   answer is 50
Answer: D
A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 7 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
Choose the correct option:
A) 2.9 hrs
B) 8.9 hrs
C) 9.3 hrs
D) 7.2 hrs
E) 8.6 hrs

Solution: Net part filled in 1 hour = (1/4 - 1/7)   = 3/28   The cistern will be filled in 28/3 hrs i.e., 9.3 hrs.   Answer:9.3 hrs
Answer: C
The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?  Choose the correct choice from the following answers
A) 6 kmph
B) 9 kmph
C) 8 kmph
D) 10 kmph
E) 1 kmph

Solution: S = 4   M = x   DS = x + 4   US = x - 4   6/(x + 4) + 6/(x - 4) = 2   x = 8   Answer:8 kmph
Answer: C
On his drive to work, Leo listens to one of three radio stations A, B or W. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to W. If W is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.30 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?
Pick.
A) 0.027
B) 0.09
C) 0.417
D) 0.657
E) 0.9

Solution: Probability he hears a song is like:   Tune to A and likes what he is hearing = 0.3   Tune to A, don't find he like what they are airing, then tune to B and likes what he finds there = 0.7 * 0.3= 
0.7 * 0.3 = 0.21
0.21   Tune to A, finds crap there, Tune to B, hears a similar crap, Tune to W and finally falls in love with the program= 0.7^2 * 0.3 = 0.147   Total = 0.657   Ans 0.657
Answer: D
is twice as fast as B. If B alone can do a piece of work in 30 days, in what time can A and B together complete the work?
Choose the correct choice from the following answers
A) 13 days B) 10 days C) 16 days D) 11 days E) 18 days

Solution: B   10 days   A can do the work in 30/2 i.e., 15 days.   A and 10 days's one day's work = 1/15 + 1/30 = (2 + 1)/30 = 1/10   So A and 10 days together can do the work in 10 days.
Answer: B
If the President and Vice President must sit next to each other in a row with 6 other members of the Board, how many different seating arrangements are possible?	Choose the correct choice from the following choices
A) 120	B) 240	C) 300	D) 10080	E) 720

Solution: We need to take President and VP as one unit. Therefore we have 7 people to arrange=7! ways   Also, we both President and VP can be arranged in 2 ! ways.   Reqd no of ways=7!*2!=10080 ways   Answer 10080
Answer: D
Of the science books in a certain supply room, 50 are on botany, 62 are on zoology, 83 are on physics. 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science? Choose the correct choice from the following answers:
A) 321
B) 159
C) 166
D) 285
E) 324

Solution: First, you can take all 50 Botany books, all 62 zoology books and all 50 geology books because you're sure to never pick 80 of them.   There are still 83 on physics and 110 on chemistry   The worst case could be that we pick 79 physics and 79 chemistry. So that the next book picked will necessary complete 80 books picked, either in physics or chemistry.   Minimum number of books picked to reach 80 in the same science should be : 50 + 62 + 50 + 79 +79 + 1= 
50 + 62 + 50 + 79 +79 + 1 = 321
321   321
Answer: A
The present worth of Rs.169 due in 2 years at 4% per annum compound interest is Choose the correct choice from the following options.
A) Rs 155.25 B) Rs 156.25 C) Rs 157.25 D) Rs 158.25 E) None of these

Solution: Explanation:   In this type of question we apply formula   Amount=P /(1+R/100)n   Amount=169 /(1+4/100)2   Amount=169∗25∗25/26∗26   Amount=156.25   Option Rs 156.25
Answer: B
For prime numbers x and y, x^3*y^5=z^4. How many positive factors does positive integer z have?	Choose the most appropriate option: A) One B) Two C) Three D) Four E) Five

Solution: Solution: given x^3*y^5=z^4; here if x and y are two different prime numbers then z = x^3/4 * y^5/4   in this case z can not be and integer.   now to make z = (x^3*y^5)^1/4 an integer it is required to have x=y then equation will become z=x^2 or z=y^2   hence total positive factors will be 3.	ANSWER:Three
Answer: C
A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 30. Find the profit percentage?  Choose the most appropriate option:  A) 20%  B) 40%  C) 50%  D) 80%  E) 30%

Solution: C   50%   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: C
A and B together can complete a work in 12 days. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work?	Pick one:	A) 10 days	B) 11 days	C) 15 days	D) 20 days	E) None of these

Solution: B's 1 day's work=(1/12-1/20)=2/60=1/30   Now, (A+B)'s 1 day's work=(1/20+1/60)=4/60=1/15   So, A and B together will complete the work in 15 days.   15 daysorrect Option: 15 days
Answer: C
Mike has forty-five cents. If mike gives away two nickles and a dime, how much money does he have left?  Choose the correct choice from the following options.
A) 10 cents
B) 16 cents
C) 35 cents
D) 25 cents
E) 40 cents

Solution: Nickle = 5 cents   25 centsime = 10 cents   45-(2)5-10 = 25   25 cents.25 cents
Answer: D
The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is : Choose the correct choice
A) Rs. 113.5	B) Rs. 119.7	C) Rs. 124.75	D) Rs. 130.75	E) Rs. 134.45

Solution: For an income of Rs.756, investment = Rs.9000   For an income of Rs., investment = = Rs.125   For a Rs.100 stock, investment = Rs.125.   Market value of Rs. 100 stock = = Rs. 124.75   Rs. 124.75
Answer: C
Life expectancy is defined by the formula 2SB/G, where S = shoe size, B = average monthly electric bill in dollars, and G = GMAT score. If Melvin's GMAT score is twice his monthly electric bill, and his life expectancy is 60, what is his shoe size?  Choose the correct option
A) 25 B) 60 C) 35 D) 40 E) 50

Solution: Solution -   Given that, G = 2B and Life expectancy(L) = 60   L=2SB/G -> 60 = 2SB/2B --> S=60.   ANS 60
Answer: B
A car gets 60 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 170 kilometers?
Choose the most appropriate option: A) 3.5 gallons B) 2.37 gallons C) 5.7 gallons D) 4.25 gallons E) 2.83 gallons

Solution: Each 60 kilometers, 1 gallon is needed. We need to know how many 60 kilometers are there in 170 kilometers?   60 Ã· 170 = 2.83 Ã— 1 gallon = 2.83 gallons   correct answer is 2.83 gallons) 2.83 gallons
Answer: E
Look at this series: 70, 71, 76, __, 81, 86, 70, 91, ... What number should fill the blank? Choose the correct choice from the following choices.
A) 70
B) 71
C) 80
D) 90
E) 96

Solution: 70
Answer: A
The manager at a health foods store mixes a unique superfruit juice cocktail that costs $1399.45 per litre to make. The cocktail includes mixed fruit juice and açai berry juice, which cost $262.85 per litre and $3104.35 per litre, respectively. The manager has already opened 33 litres of the mixed fruit juice. How many litres of the açai berry juice does he need to add?
Choose the correct option: A) 17 litres B) 22 litres C) 11 litres D) 07 litres E) 38 litres

Solution: 262.85(33)+3,104.35x = 1,399.45(33 + x)   Solve the equation.   262.85(33)+3,104.35x = 1,399.45(33 + x)   8,674.05 + 3,104.35x = 46181.85 + 1,369.45x   8,674.05 + 1,704.9x = 46181.85   1,704.9x = 37,507.8   x = 22   Answer is 22 litres.
Answer: B
A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.11 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost?  Choose one
A) 1276	B) 1200	C) 2832	D) 1299	E) 1320

Solution: 1320xplanation:   l * 30 = 1200 è l = 40   40 + 30 + 50= 
40 + 30 + 50 = 120
120   120 * 11= 
120 * 11 = 1_320
1320   Answer: Option 1320
Answer: E
189. The inside dimensions of a rectangular wooden box
are 12 inches by 14 inches by 16 inches. A cylindrical
canister is to be placed inside the box so that it stands
upright when the closed box rests on one of its six
faces. Of all such canisters that could be used, what is
the radius, in inches, of the one that has maximum
volume? Choose the correct choice.
A) 3 B) 4 C) 5 D) 6 E) 7

Solution: Since the radius is squared, the biggest volume cylinder will have the biggest possible radius. To achieve that, let the smaller dimension of the rectangular box be the height. So, it will have 16x14width x length. The biggest cylinder must fit both dimensions, so it must have at most a diameter of 14, so the radius will be 7.   7
Answer: E
If a fair coin is tossed six times, what is the probability of getting exactly five heads in a row?  Choose the correct choice from the following answers.
A) 1/64 B) 1/32 C) 1/16 D) 3/64 E) 3/32

Solution: P(HHHHHT) = 1/64   P(THHHHH) = 1/64   The sum of these probabilities is 2/64 = 1/32   The answer is 1/32.
Answer: B
If an integer r is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that r(r + 1)(r + 2) will be divisible by 8? Select the correct option.
A) 1/4	B) 3/8	C) 1/2	D) 5/8	E) 3/4

Solution: for r Total numbers 8*12   There are 12 numbers divisible by 8 -> 3*12 (if 8 is an example - (6,7,8), (7,8,9), (8,9,10))   and 12 numbers divisible by 4 but not divisible by 8 -> 2*12 (if 4 is an example (2,3,4) and (4,5,6))   The answer 5/8 -> 5/8
Answer: D
there are two sections A and B of a class consisting of 36 and 44 students respectively. If the average weight of section A is 40kg and that of section B is 35kg, find the average weight of the whole class?  Choose the correct choice from the following options
A) 15.42 B) 37.25 C) 12.54 D) 32.37 E) 23.47

Solution: Sol: total weight of(36+44) students=(36*40+44*35)= 
(36*40+44*35) = 2_980
2980kg.   Therefore weight of the total class=(2980/80)= 
(2980/80) = 149/4 = around 37.25
37.25kg.   Ans: 37.25
Answer: B
One side of a rectangle is 3 cm shorter than the other side. If we increase the length of each side by 1 cm, then the area of the rectangle will increase by 18 cm2. Find the lengths of all sides. Choices:
A) 10 and 3  B) 7 and 10  C) 10 and 7  D) 3 and 10  E) 10 and 10

Solution: Let x be the length of the longer side x>3, then the other side's length is x−3 cm. Then the area is S1 = x(x - 3) cm2. After we increase the lengths of the sides they will become (x+1) and (x−3+1)=(x−2) cm long. Hence the area of the new rectangle will be A2=(x+1)⋅(x−2) cm2, which is 18 cm2 more than the first area. Therefore   A1+18=A2   x(x−3)+18=(x+1)(x−2)   x2−3x+18=x2+x−2x−2   2x=20   x=10. So, the sides of the rectangle are 10 cm and (10−3)=7 cm long.   So answer is 10 and 7.
Answer: C
Ella leaves her home and walks toward Ed's house. Two hours later, Ed leaves his home and walks toward Ella's house. The distance between their homes is 42 kilometers, Ella's walking speed is 5 km/h, and Ed's walking speed is 3 km/h. How many kilometers will Ella walk before she meets Ed? Answers
A) 28
B) 29
C) 30
D) 31
E) 32

Solution: Ella walks 10 km in the first two hours so there are 32 km remaining.   When Ed starts walking, they complete a total of 8 km per hour.   They will meet four hours after Ed starts walking.   Since Ella walks for 6 hours, she walks 30 km.   The answer is 30.
Answer: C
John bought 9.25m of cloth for $407. Find the cost price per metre.  Select:	A) 46	B) 47	C) 58	D) 44	E) 54

Solution: Cloth bought by John = 9.25 m   Cost of 9.25 m = $407   Cost per metre = 407 ÷ 9.25   The cost of the cloth per metre = $ 44   Answers: 44
Answer: D
A crate of mangoes contains one bruised mango for every thirty mango in the crate. If three out of every four bruised mango are considerably unsaleble and there are 11 unsaleable mangoes in the crate then how msny mango are there in the crate?
Choose the correct answer
A) 100 mangoes B) 110 mangoes C) 120 mangoes D) 130 mangoes E) 125 mangoes

Solution: 110 mangoes   ANSWER:110 mangoes
Answer: B
four children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Children AB must sit next to each other, and child C must be somewhere to the right of AB. How many possible configurations are there for the children?
Choose the correct choice from the following options
A) 560  B) 720  C) 1440  D) 4320  E) 4800

Solution: A, B, C, D, E, F, G- seven children, of which AB must sit next to each other. Considering them as one X (A, B), we have X, C, D, E, F, G. These can be arranged in 6! ways. But A,B can arrange themselves in 2! ways. So a total of 6!*2! ways = 1440. Since in exactly half of them, C will be to the right of AB, and exactly half, C will be to the left of AB, therefore 1440/2 = 560.   560 is the right answer.
Answer: A
John was thrice as old as Tom 6 yrs back. He will be 5/3 times as old as Tom 6 years hence. How old is Tom today?	Choose the correct choice from the following choices
A) 10	B) 11	C) 12	D) 15	E) 19

Solution: Sol. RMBflSk -6 = 3 (Ravi - 6) ...(j)   and Rupesh + 6 = | (Ravi + 6) ...(ii)   Solving both the equations we get,   Ravi = 12 years.   12
Answer: C
A bank pays interest to its customers on the last day of the year. The interest paid to a customer
is calculated as 10% of the average monthly balance maintained by the customer. John is a
customer at the bank. On the last day, when the interest was accumulated into his account, his
bank balance doubled to $6840. What is the average monthly balance maintained by John in his
account during the year?	Select: A) 2840 B) 5680 C) 6840 D) 7540 E) 34200

Solution: Soln:-   Bank balance is doubled with accumulation of interest to 6840..   this means INTEREST is   6840/2= 
  6840/2 = 3_420
3420 for entire year..   although since interest is 10% of avg MONthly balance, it becomes 34200..   ANSW34200R:34200
Answer: E
n is a positive integer and k is the product of all integers from 1 to n inclusive. If k is a multiple of 1680, then what is the smallest possible value of n? Choose the correct choice from the following options.
A) 4  B) 6  C) 7  D) 10  E) 12

Solution: 3360=2^4*3*5*7   2^4 means that n must be at least 6. That is, We need 2, 4, and 6.   However, we also need 7, so n must be at least 7.   The answer is 7.
Answer: C
The average of first 16 even numbers is?  Select the correct option:	A) 19	B) 18	C) 16	D) 11	E) 17

Solution: Sum of 16 even numbers = 16 * 17= 
16 * 17 = 272
272   Average= 272/16= 
272/16 = 17
17   Answer:17
Answer: E
The number of students in the three sections of a class are in the ratio 2:3:4. The average marks scored in each of these sections is in the ratio 4:3:1. By what percent is the average mark of the second section more than the class average?	Answers
A) 23.27%	B) 28.57%	C) 32.38%	D) 36.74%	E) 38.74%

Solution: Let the number of students be 2x, 3x, 4x.   Let the average marks be 4y,3y,y.   Average mark of class = ( 8xy+9xy+4xy)/(2x+3x+4x)   =21xy/9x=7y/3   Percentage difference = ( 3y - 7y/3)/7y/3 *100   = 28.57%   ANSWER:28.57%
Answer: B
If a*b=2a-3b+ab,then3*5+5*3 is equal to Choose the correct option:
A) 22
B) 24
C) 26
D) 28
E) 30

Solution: 3*5+5*3= (2x3-3x5+3x5)+(2x5-3x3+5x3)   =22   22NSWER 22 22
Answer: A
A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. The difference between the profit shares of A and C is?	Choose the correct answer.
A) 299	B) 277	C) 298	D) 600	E) 271

Solution: Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6   And also given that, profit share of B is Rs. 1500   => 5 parts out of 15 parts is Rs. 1500   Now, required difference is 6 - 4= 
6 - 4 = 2
2 parts   Required difference= 2/5 (1500) = Rs. 600   Answer: 600
Answer: D
The average of a non zero number and its square is 5 times the number. The number is Choose the correct choice from the following answers:
A) 9  B) 17  C) 29  D) 295  E) None

Solution: Sol.   Let the number be x. Then,   x + x2 / 2 = 5x   ‹=› x2 – 9x = 0   ‹=› x (x - 9) = 0   ‹=› x = 0 or x = 9.   So, the number is 9.   9nswer 9
Answer: A
If the mean of numbers 38, x, 70, 88 and 110 is 69, what is the mean of 50, 72, 97, 125,147 and x? Choose the correct choice from the following
A) 73.5
B) 77.86
C) 86.67
D) 66.69
E) 70.56

Solution: Mean = (Sum of all no. in series)/(no. in series)   M1 = 69 = (X+38+70+88+110)/(5)   69 x 5 = 290 + X   X = 39   Therefore mean of 2nd series   M2 = (X+50+62+97+125+147)/6   M2 = 86.67   Answer = 86.67
Answer: C
What is the ratio whose terms differ by 40 and the measure of which is 2⁄7	Choose the most appropriate option: A) 16 : 56 B) 14 : 56 C) 15 : 56 D) 16 : 72 E) None of these

Solution: Let the ratio be x: (x + 40).Then,   x/(x+40)=2/7 ⇒ 2x + 80 ⇒ x = 16.   ∴ Required ratio = 16 : 56.   16 : 56nswer 16 : 56
Answer: A
Find the greatest number which leaves the same remainder when it divides 21, 57 and 105. Choose the correct answer
A) 18 B) 8 C) 12 D) 16 E) None of these

Solution: 105 - 57= 
105 - 57 = 48
48   57 - 21= 
57 - 21 = 36
36   105 - 21= 
105 - 21 = 84
84   The H.C.F of 36, 48 and 84 is 12.   ANSWER:12
Answer: C
Two pipes A and B can fill a tank in 15 min and 20 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank?
Choose the correct choice from the following options:
A) 10 min 20 sec  B) 11 min 45 sec  C) 12 min 30 sec  D) 14 min 40 sec  E) 15 min 40 sec

Solution: Part filled in 4 minutes = 4(1/15 + 1/20) = 7/15   Remaining part = 1 - 7/15 = 8/15   Part filled by B in 1 minute = 1/20   1/20 : 8/15 :: 1 ; x   x = 8/15 * 1 * 20 = 10 2/3 min = 10 min 40 sec.   The tank will be full in (4 min. + 10 min. 40 sec) = 14 min 40 sec.   ANSWER:14 min 40 sec
Answer: D
Tommy makes a bet that a coin will land on heads 2 times out of 8. After the first 6 tosses, the coin has landed on heads twice and tails four times. What is the probability that Tommy will win the bet? Choose the correct choice from the following answers
A) 1/4 B) 1/2 C) 1/8 D) 1/3 E) 1/6

Solution: For Tommy to win, the coin must land on tails for both the remaining two tosses.   The probability of this happening given a fair coin is 1/2 * 1/2 = 1/4   1/4nswer:1/4
Answer: A
what is the remainder when 7894104 is divided by 72
Choose the correct choice from the following choices.
A) 8 B) 25 C) 32 D) 4 E) 24

Solution: 7894104 / 72   7894104 / 9*8   986763 / 9 => rem = 3   we have cancelled it by 8   reqd remainder = 8*3= 
8*3 = 24
24   ANSW24R:24
Answer: E
If c and d are prime numbers, which of the following CANNOT be the sum of c and d?
Select.
A) 5  B) 9  C) 13  D) 23  E) 33

Solution: All answer choices but D are odd. In order odd number to be the sum of two prime numbers one must be even, so 2, and another odd.   Now, 23=2+21. Since 21 is not a prime then 23 cannot be written as the sum of two prime numbers.   Answer: 23
Answer: D
Two trains are running in opposite directions with the same speed. If the length of each train is 180 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:	Choose the correct choice from the following answers:
A) 31 km/hr.
B) 52 km/hr.
C) 34 km/hr.
D) 54 km/hr.
E) 36 km/hr.

Solution: Let the speed of each train be x m/sec.   Then, relative speed of the two trains = 2x m/sec.   So, 2x = (180 + 180)/12   2x = 30   x = 15.   Speed of each train = 15 m/sec = 15 x 18/5 km/hr = 54 km/hr.   answer :54 km/hr.
Answer: D
Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 50% Vermouth by volume. How many ounces of Gin must he add?	Choose the correct choice from the following choices:  A) n/6  B) n/3  C) 3n/5  D) 5n/6  E) 8n/5

Solution: 4 ounces is vermouth   6 ounces of gin...   Total volume 10.   To make vermouth account for 50% of total volume the new volume must be....   x*0.5=4   x=8 ounces....   So now you see that he must add 2 ounces of gin...   Plug in 6 for n in the answer choices and look for answer 2   n/3
Answer: B