MU-NLPC/Calc-aqua_rat huggingface dataset:
If x and y are different prime numbers, each greater than 8, which of the following must be true? I. x+y is an even integer II. xy is an odd integer III. (x/y) is not an integer  Choose the most appropriate option:	A) I,II only	B) I,III only	C) II,III only	D) I,II and III	E) II only

Solution: Given: x and y are different prime numbers, both greater than 8   Statement I: x+y is an even integer   Since x and y are prime numbers greater than 8, they will be odd   Therefore sum will be even.   Correct   Statement II: xy is an odd integer   Since x and y are prime numbers greater than 8, they will be odd   Therefore multiplication will be odd.   Correct   Statement III: (x/y) is not an integer   Since x and y are prime integers, therefore they will not have any common factor apart from 1   Hence (x/y) will not be an integer   Correct   Hence all three statements I, II and III are correct   Answer : I,II and III
Answer: D
In an examination, 25% of total students failed in Hindi, 35% failed in English and 40% in both. The percentage of these who passed in both the subjects is : Choose the correct choice from the following answers:
A) 10%  B) 20%  C) 60%  D) 80%  E) 50%

Solution: pass percentage = 100 - (25+35-40) = 100-20= 
100-20 = 80
80   ANSWER:80%
Answer: D
Ramesh starting from a fixed point goes 15 km towards North and then after turning to his right he goes 15 km. then he goes 10, 15 and 15 metres after turning to his left each time. How far is he from his starting point?
Choose the correct answer
A) 8 km B) 9 km C) 10 km D) 11 km E) 12 km

Solution: he will be 10 km. away from his starting point.   ANSWER:10 km
Answer: C
Copper is 7 times as heavy as water and gold is 13 times as heavy as water. In what ratio should these be mixed to get an alloy 11 times as heavy as water ?	Choose the correct choice from the following
A) 2 : 1 B) 1 : 2 C) 2 : 3 D) 3 : 2 E) 3 : 1

Solution: Explanation :   Solution: C = 7W and G = 13W.   Let 1 gm of copper be mixed with x gm of gold to get (1+x)gm of alloy.   (1gm copper)+(xgm gold) = (x+1)gm of alloy.   =>7W+13W*x = (x+1)*11W   => 7+13x = 11(x+1)   => 2x = 4 => x = 2.   .'. Ratio of copper and gold = 1 : 2   Answer : 1 : 2
Answer: B
A train running at the speed of 60 km/hr crosses a pole in 12 seconds. What is the length of the train?	Choose the correct choice from the following choices.
A) 200 metres B) 180 metres C) 324 metres D) 228 metres E) 150 metres

Solution: Speed= 60 x	5/18	m/sec	= 50/3	m/sec.   Length of the train = (Speed x Time).   Length of the train = 50/3	x 9	m = 200 m.   Option 200 metres
Answer: A
The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, what is the weight of B? Choose one
A) 31 kg  B) 28 1/2 kg  C) 32 kg  D) 30 1/2 kg  E) 32 kg

Solution: Explanation:   Let the weight of A, B and C are a,b and c respectively.   31 kgverage weight of 31 kg,B and C = 45   a + b + c = 45 × 3 = 135 --- equation(1)   31 kgverage weight of 31 kg and B = 40   a + b = 40 × 2 = 80 --- equation(2)   31 kgverage weight of B and C = 43   b + c = 43 × 2 = 86 --- equation(3)   equation(2) + equation(3) - equation(1)   => a + b + b + c - (a + b + c) = 80 + 86 - 135   => b = 80 + 86 -135 = 166 - 135= 
166 - 135 = 31
31   Weight of B= 31 Kg   31 kgnswer: Option 31 kg
Answer: A
A milk man sells the milk at the cost price but he mixes the water in it and thus he gains 9.09%. The quantity of water in the mixture of 1 liter is?	Choose the correct choice from the following answers:
A) 83.33 ml B) 12.33 ml C) 77.33 ml D) 22.33 ml E) 18.33 ml

Solution: Profit (%) = 9.09 % = \inline \frac{1}{11}   Since the ratio of water and milk is 1 : 11,   Therefore the ratio of water is to mixture = 1:12   Thus the quantity of water in mixture of 1 liter =   {1}/{12} = 83.33 ml   83.33 mlnswer: 83.33 ml
Answer: A
Three years ago the average age of a class of six members was 23 years. A boy have been added, the average age of the class is the same today. What is the age of the boy?
Select:
A) A)1	B) B)2	C) C)3	D) D)4	E) E)5

Solution: 6 * 26= 
6 * 26 = 156
156   7 * 23= 
7 * 23 = 161
161   `5   5
Answer: E
A train 220 m long is running with a speed of 90 km/hr. In what time will it pass a bus that is running with a speed of 60 km/hr in the direction opposite to that in which the train is going?	Select:	A) 4.37	B) 5.28	C) 6.75	D) 8	E) 3.1

Solution: Speed of train relative to bus = 90 + 60= 
90 + 60 = 150
150 km/hr.= 150 * 5/18 = 125/3 m/sec.   Time taken to pass the bus = 220 * 3/125= 
220 * 3/125 = 132/25 = around 5.28
5.28 sec.   Answer: 5.28
Answer: B
50 litres of diesel is required to travel 600 km using a 800 cc engine. If the volume of diesel required to cover a distance varies directly as the capacity of the engine, then how many litres of diesel is required to travel 800 km using 1200 cc engine?	Choose the correct choice:  A) 80 litres  B) 90 litres  C) 100 litres  D) 170 litres  E) None of these

Solution: Explanatory Answer   To cover a distance of 800 kms using a 800 cc engine, the amount of diesel required = 800/600*50 = 66.67 litres.   However, the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity.   i.e., for instance, if the capacity of engine doubles, the diesel requirement will double too.   Therefore, with a 1200 cc engine, quantity of diesel required = 1200/800*66.67 = 100 litres.   Answer 100 litres
Answer: C
There are 5 bags three of which each contains 4 white and 2 black balls, and remaining 2 bags each contains 1 white and 4 black ball; a white ball has been drawn, find the chance that it came from first group. Answers:
A) 2/7 B) 6/35 C) 8/25 D) 5/6 E) 3/5

Solution: Please go through my solution and suggest any mistake.   Chances of selecting a white ball from group 1: 2/3---------------------Chances of selecting a white ball from group 2: 1/5   Thus combined probability of section of white ball from group 1:   3/5 x 2/3 = 2/5   Thus combined probability of section of white ball from group 2:   2/5 x 1/5 = 2/25   Out of these chances, chance of occurrence of first case : (2/5) / (2/5 + 2/25) = 5/6   5/6
Answer: D
In an office in Singapore there are 60% female employees. 50 % of all the male employees are computer literate. If there are total 62% employees computer literate out of total 1400 employees, then the no. of female employees who are computer literate ? Select the correct option.
A) 588
B) 674
C) 672
D) 960
E) None

Solution: Solution: Total employees,   = 1400   Female employees, 60% of 1400.   = (60 *1400) /100= 
(60 *1400) /100 = 840
840.   Then male employees,= 560   50 % of male are computer literate,   = 280 male computer literate.   62 % of total employees are computer literate,   = (62 *1400) /100= 
(62 *1400) /100 = 868
868 computer literate.   Thus, Female computer literate= 868 - 280= 
868 - 280 = 588
588.   588nswer: Option 588
Answer: A
a product of ages of ankit and nikita is 240. if twice the age of nikita is more than ankit's by 4 years. what is the nikita's age? Choose the correct choice from the following choices.
A) 12yrs
B) 13yrs
C) 14yrs
D) 15yrs
E) 11yrs

Solution: if ankit age=x   nikita age=240/x   then (2*(240/x))-x=4 so,x=20   ankit age=20yrs   nikita age=(240/20)= 
(240/20) = 12
12yrs   12yrsNSWER:12yrs
Answer: A
The average weight of 22 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. Choose the correct option:
A) 48.89
B) 42.25
C) 50
D) 51.25
E) 52.25

Solution: Explanation:   48.89verage weight of 22 boys = 50.25   Total weight of 22 boys = 50.25 × 22   48.89verage 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 × 16)+ (45.15 × 8)   Total boys = 22 + 8= 
22 + 8 = 30
30   48.89verage weight of all the boys= ((50.25×22)+(45.15×8))/30   =48.89   48.89nswer: Option 48.89
Answer: A
An seller earns an income of Re 3 on the first day of his business. On every subsequent day, he earns an income which is just thrice of that made on the previous day. On the 15th day of business, he earns an income of:  Choose the correct choice from the following answers.
A) 19	B) 22	C) 25	D) 20	E) 36

Solution: 2nd day he earns = 3(2 – 3)   3rd day he earns = 3(3 – 3)   On 15th day he earns 3(15 -3) = 36 rupees   ANSW36R:36
Answer: E
It rained as much as on Wednesday as on all the other days of the week combined. If the average rainfall for the whole week was 3 cms, How much did it rain on Wednesday? Select the correct option:
A) 10.9  B) 10.5  C) 10.2  D) 10.1  E) 10.6

Solution: Explanation:   Let the rainfall on wednesday = 6x.   ∴ Rainfall on the remaining days = 6x   Given,   (6x + 6x )/7 = 3   ⇒12x = 21   ⇒6x = 10.5   Answer: 10.5
Answer: B
Find the value of x from the below equation? : 3x^2+5x+2 = 0 Choose the correct choice
A) -1
B) 1
C) 2
D) 3
E) 4

Solution: a = 3, b = 5, c = 2   x1,2 = (-5 ± √(52 - 4×3×2)) / (2×3) = (-5 ± √(25-24)) / 6 = (-5 ± 1) / 6   x1 = (-5 + 1)/6 = -4/6 = -2/3   x2 = (-5 - 1)/6 = -6/6 = -1   -1
Answer: A
Of the science books in a certain supply room, 50 are on botany, 55 are on zoology, 90 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 area science?
Choose the most appropriate option
A) 81  B) 159  C) 166  D) 285  E) 314

Solution: The worst case scenario is to remove all the books on botany, zoology, and geology.   Also we can remove 79 books each from physics and chemistry.   The total is  50 + 55 + 50 + 79 + 79= 
 50 + 55 + 50 + 79 + 79 = 313
313.   The next book removed must either be physics or chemistry, ensuring 80 books in that subject.   The answer is 314.
Answer: E
The average weight of 8 girlsincreases by 2.5 kg when a new gitl comes in place of one of them weighing 65 kg. What might be the weight of the new girl?  Choose the correct choice from the following options:
A) 65 kg
B) 75 kg
C) 85 kg
D) 90 kg
E) 92 kg

Solution: Total weight increased = (8 x 2.5) kg = 20 kg.   Weight of new person = (65 + 20)= 
(65 + 20) = 85
85 kg   85 kg
Answer: C
If money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested $ 7000 in a long term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of investment 18 years later, when Pat is ready for college?  Choose the correct answer
A) $28000	B) $15000	C) $12000	D) $10000	E) $9000

Solution: Since investment doubles in 70/r years then for r=8 it'll double in 70/8=~9 years (we are not asked about the exact amount so such an approximation will do). Thus in 18 years investment will double twice and become ($7,000*2)*2=$28,000 (after 9 years investment will become $7,000*2=$14,000 and in another 9 years it'll become $14,000*2=$28,000).   $28000nswer: $28000.
Answer: A
From a Group of 9 People, Including George and Nina, 4 people are to be selected at random to work on a certain project. What is the probability that 4 people selected will include George but not Nina
Choose the correct choice from the following choices:
A) 5/56  B) 9/56  C) 15/56  D) 35/120  E) 25/56

Solution: Number of ways of selecting 4 people out of 9 people = 9C4   In the three members George will always be there in the team. At this step we have vacancy for 3 more members and 8 members are available. Nina cannot be there in the team. So 3 members have to be selected and the number of available members = 8 - Nina = 7   Number of ways to form a 4 member team that includes George and excludes Nina = 7C3   Probability = 7C3/9C4 = 35/120   Answer: 35/120
Answer: D
A train crosses a platform in 25 sec, same train crosses another platform of length 400 m in 30 sec. If the length of the train is 200m , find the length of the platform?  Choose the correct choice from the following choices:
A) 280m
B) 180m
C) 350m
D) 300m
E) 267m

Solution: Length of the platform be ‘X’   (X + 200)/25 = (200 + 400)/30   6X + 1200 = 3000   X = 300m   Answer: 300m
Answer: D
In a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class?  Select:
A) 12.9  B) 12.1  C) 12.3`  D) 12.6  E) 12.5

Solution: Total age of 50 students   (30X 13+20 X 12) = 630   Average = 630/50= 
630/50 = 63/5 = around 12.6
12.6 Years   Answer: 12.6
Answer: D
A number x is 6 times another number y. The percentage that y is less than x is Select:
A) 12.5% B) 83.3% C) 80% D) 11% E) 1%

Solution: Say y=1 and x=6.   Then y=1 is less than x=6 by (6-1)/6*100=5/6*100=83.3%.   Answer: 83.3%.
Answer: B
A football player scores 4 goals in his fifth match thus increasing his average goals score by 0.2. The total number of goals in his 5 matches would be Choose the correct choice from the following answers.
A) 4
B) 6
C) 8
D) 10
E) 16

Solution: While this question can be solved with a rather straight-forward algebra approach (as the other posters have noted), it can also be solved by TESTing THE ANSWERS. One of those numbers MUST be the total number of goals...   From a tactical standpoint, it's best to TEST either Answer B or Answer D, so if the answer is not correct, then you would have a gauge for whether you should gohigherorlowerwith your next TEST.   Here, I'll start with Answer E = 16 goals   If....   Total goals = 16 goals   5th game = 4 goals   1st 4 games = 12 goals   Avg. for 1st 4 games = 12/4= 
12/4 = 3
3 goal/game   Avg. for all 5 games= 6/5 = 3.2 goals/game   This is an 16XACT MATCH for what we're told in the prompt, so Answer 16 MUST be the answer.
Answer: E
Rs.1200 divided among P, Q and R. P gets half of the total amount received by Q and R. Q gets one-third of the total amount received by P and R. Find the amount received by R ?
Select.
A) 377
B) 500
C) 287
D) 179
E) 112

Solution: Let the amounts to be received by P, Q and R be p, q and r.   p + q + r = 1200   p = 1/2 (q + r) => 2p = q + r   Adding 'p' both sides, 3p = p + q + r = 1200   => p = Rs.400   q = 1/3 (p + r) => 3q = p + r   Adding 'q' both sides, 4q = p + q + r = 1200   => q = Rs.300   r = 1200 - (p + q) => r = Rs.500.   Answer: 500
Answer: B
Rahul can do a work in 3 days while Rajesh can do the same work in 2days. Both of them finish the work together and get $170. What is the share of Rahul?
Pick
A) $68  B) $40  C) $60  D) $100  E) $90

Solution: Rahul's wages: Rajesh's wages = 1/3 : 1/2 = 2:3   Rahul's share = 170*2/5= 
170*2/5 = 68
$68   $68nswer is $68
Answer: A
The function F(n) is defined as the product of all the consecutive positive integers between 2 and n^2, inclusive, whereas the function G(n) is defined as the product of the squares of all the consecutive positive integers between 1 and n, inclusive. The exponent on 2 in the prime factorization of F(3)/G(3) is
Choose the correct choice from the following:
A) 1	B) 2	C) 3	D) 4	E) 5

Solution: F(3)/G(3)   =product(1 to 3 ^2) / 1.2^2.3^2   =1.2.3.4.5.6.7.8.9/1.4.9   =1.2.3.(2^2).5.(2.3).7.(2^3).9/1.(2^2).9   =1.(2^7).3.5.7.9/1.(2^2).9   Loof for 2^7/2^2=2^5 ----Exponent 3   Answer: 3
Answer: C
S is a set of 85 consecutive multiples of 5. If the smallest number in S is 90, then the greatest number in S is	Choose the correct choice from the following choices:
A) 158  B) 597  C) 599  D) 402  E) 510

Solution: last term =first term +(total no. of terms-1)consecutive difference   S is a set of 85 consecutive multiples of 5. If the smallest number in S is 90, then the greatest number in S is   first term = 90 ; total terms =85 ; difference = 5   90+(84)5 = 510   Ans 510
Answer: E
Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 9. What is the value of x? Options:
A) 20 B) 60 C) 100 D) 120 E) 150

Solution: y = 0.5*0.5*x = x/4   y%*x = 9   (y/100)*x = 9   (x/400)*x = 9   x^2 = 9*400   x = 60   The answer is 60.
Answer: B
One day a car rental agency rented 3/4 of its cars, including 2/3 of its cars with CD players. If 3/5 of its cars have CD players, what percent of the cars that were not rented had CD players?	Pick:  A) 1/2  B) 2/3  C) 3/4  D) 4/5  E) 5/6

Solution: The cars with CD players which were not rented is (1/3)(3/5) = 1/5 of all the cars.   The cars which were not rented is 1/4 of all the cars.   The percent of non-rented cars which had C4/5 players is (1/5) / (1/4) = 4/5   The answer is 4/5.
Answer: D
To produce an annual income of Rs. 1200 from a 12 % stock at 90,the amount of stock needed is : Select the correct option.
A) Rs. 10,000	B) Rs. 10,800	C) Rs. 14,400	D) Rs. 16,000	E) Rs. 46,000

Solution: Solution   For an income of Rs. 12, stock needed = Rs. 100.   For an income of Rs. 1200, stock needed = Rs. 10/12x12000=10,000   Rs. 10,000nswer Rs. 10,000
Answer: A
.007/?= .01 Select the correct option:	A) .7	B) .07	C) .007	D) .0007	E) None of them

Solution: Let .007/x = .01;   Then x = .007/.01= 
.007/.01 = 0.7
.7/1= 
.7/1 = 0.7
.7   .7nswer is .7
Answer: A
A and B have monthly incomes in the ratio 5:6 and monthly expenditures in the ratio 3:4. If they save Rs. 1800 and Rs. 1600 respectively, find the monthly income of B	Choose the correct choice from the following choices.
A) Rs. 3400  B) Rs. 2700  C) Rs. 1720  D) Rs. 7200  E) Rs. 8200

Solution: Explanation:   Incomes of A and B=5x and 6x and expenses of A and B = 3y and 4y   Then, savings of A = 5x-3y = 1800—?(1)   Savings of B = 6x-4y = 1600—?(2)   By solving equations (1) and (2)   y = 1400   Monthly income of B = Expenses of B + savings of B   = 4y+1600 = 4(1400) + 1600 = Rs. 7200   Answer: Rs. 7200
Answer: D
John has 10 pairs of matched socks. If he loses 9 individual socks, what is the greatest number of pairs of matched socks he can have left?  Pick one.
A) 7	B) 6	C) 5	D) 4	E) 3

Solution: Because we have to maximize the pair of matched socks, we will remove 4 pairs(8 socks) out of 10 pairs 1 sock from the 5th pair.   Thus the no of matching socks pair remaining = 10 -5= 
10 -5 = 5
5   Answer 5
Answer: C
Jim takes a seconds to swim d meters at a constant rate from point P to point Q in a pool. Roger, who is faster than Jim, can swim the same distance in b seconds at a constant rate. If Jim leaves point P the same time that Roger leaves point Q, how many fewer meters will Jim have swum than Roger when the two swimmers pass each other?  Choose the correct choice from the following answers:
A) c(b-a)/ a+b  B) d(a-b)/a+b  C) c(a+b)/a-b  D) ab(a-b)/a+b  E) ab(b-a)/a+b

Solution: Both JimRoger are travelling at constant speedin opposite direction:   So, speed of Jim = d/a speed of Roger = d/b   Let say Jim travelled distance x from P where it met Roger, it means that Roger travelled (c-x) from point Q   [x would be less than (c-x) as Jim is travelling slow]   From above, time taken by Jim to travel x = xa/d....................... (1)   Also, time taken by Roger to travel (c-x) = (d-x)b/d.....................(2)   Time taken by both JimRoger is same, so (1) = (2)   xa/d = (d-x)b/d,   Solving further, x = bd/(a+b).................... (3)   We require to find how many fewer meters will Jim have swum i.e   additional distance travelled by Roger = (d - x) - x   = d-2x   Substituting value of x from (3)solving the equation further, we get Answer = d(a-b)/a+b   Answer = (d(a-b)/a+b)
Answer: B
In the first 10 overs of a cricket game, the run rate was only 3.4. What should be the run rate in the remaining 40 overs to reach the target of 282 runs? Choose the correct choice.
A) 4.25
B) 5
C) 6.2
D) 7
E) 7.5

Solution: Required run rate = 282 - (3.4 x 10) =	248   248/40= 
248/40 = 31/5 = around 6.2
6.2   6.2)
Answer: C
Which of the following equations describes a line that is perpendicular to y=x-7?	Choose the most appropriate option:
A) y = x + 7 B) y = −5 − x C) y = 7x D) y = 7x+1 E) y = 1/x - 7

Solution: Two perpendicular lines have slopes that are inverse reciprocals of each other.   The slope of y=x-7 is 1 so the slope of a perpendicular line will be -1.   The answer is y = −5 − x.
Answer: B
A taxi company with a fleet of 50 taxis, plans to replace all their taxis with electric cars. Every year it retires 10 of their old taxis and buys 12 electric cars to replace them. How many years will it take to reduce their old taxi fleet to below 50% of their entire fleet if they started in 2003.	Choose the correct choice from the following choices:
A) 3  B) 4  C) 1  D) 2  E) 10

Solution: Total fleet--50   End of year 2003 -- (retires 10 and buys 12) total fleet--52(40 old 12 new).   End of year 2004 -- (retires 10 and buys 12) total fleet--54(30 old 24 new).   End of year 2005 -- (retires 10 and buys 12) total fleet--56(20 old 36 new).   3nswer is 3--after 3 years the company has a total of 56 taxis (20 old 36 new), the old taxis are already less than 50% of its fleet.
Answer: A
A group consists of 4 men, 6 women and 5 children. In how many ways can 2 men , 3 women and 1 child selected from the given group?  Choices:
A) 628 ways B) 600 ways C) 767 ways D) 762 ways E) 672 ways

Solution: Two men, three women and one child can be selected in 4C2 * 6C3 * 5C1 ways   = (4 * 3)/(2 * 1) * (6 * 5 * 4)/(3 * 2) * 5= 
(4 * 3)/(2 * 1) * (6 * 5 * 4)/(3 * 2) * 5 = 600
600 ways.   Answer:600 ways
Answer: B
If a man walks at the rate of 5 kmph, he misses a train by 7 minutes. However, if he walks at the rate of 6 kmph, he reaches the station 5 minutes before the arrival of the train. Find the distance covered by him to reach the station.  Select:	A) 10 km	B) 8 km	C) 6km	D) 4km	E) 7 km

Solution: Sol. Let the required distance be x km   Difference in the time taken at two speeds=1 min =1/2 hr   Hence x/5-x/6=1/5<=>6x-5x=6   x=6   Hence, the required distance is 6 km   Option 6km
Answer: C
If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 4-letter code words? Choose the correct choice from the following choices:
A) 5 to 4
B) 3 to 2
C) 2 to 1
D) 5 to 1
E) 6 to 1

Solution: Method #1: Using the permutation formula   # of 5 letter code words:   nPr = n! / (n – r)! = 10! / (10 – 5)! = 10*9*8*7*6   # of 4 letter code words:   nPr = 10! / (10 – 4)! = 10*9*8*7   # of 5 words / # of 4 words = (10*9*8*7*6)/(10*9*8*7)= 
(10*9*8*7*6)/(10*9*8*7) = 6
6= 6/1   Answer is 6 to 1.
Answer: E
A husband and wife can complete a certain task in 1 and 3 hours respectively. Their children, Rae and Herman, can complete the same task in 4 and 6 hours, respectively. What is the ratio of the couple's time working together to complete the task to the children's time working together to complete the task?
Options
A) a)15:46 B) b)3:10 C) c)12:23 D) d)5:16 E) e)10:3

Solution: couples one hour work=1/1+1/3=4/3   so total time=3/4.   now, kids one hour work=1/4+1/6=5/12   so total time=12/5..   ratio=3/4:12/5=5:16   ans d)5:16
Answer: D
How many different committees each composed of 2 Republicans and 3 Democrats can be formed from a group of 4 Republicans and 5 Democrats?	Choose the correct choice from the following:
A) 12  B) 24  C) 60  D) 72  E) 120

Solution: Let's take the Republicans. How many combinations of 2 can be created.   There are four total so: 4!/2!2! = 6   Democrats: 5!/3!2! = 10   6 x 10 = 60   ANSWER:60
Answer: C
10^25 - 260 is divisible by all of the following except:
Answers:  A) A.10  B) B.8  C) C.5  D) D.4  E) E.2

Solution: The last three digits ( 1000 - 260 ) 740   740 is divisible by 10,4,2,5   740 is not evenly divisible by 8 so the answer is B.8) 8
Answer: B
M = {-6, -5, -4, -3, -2}
T = {-2, -1, 0, 2, 3}
If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative?
Pick
A) 0	B) 1/3	C) 2/5	D) 1/2	E) 3/5

Solution: Answer C.   Total # of outcomes: 5*5= 
5*5 = 25
25   # of outcomes where Product is -ve : (-6,1) ,(-6,2), (-6,3)... Hence, total: 10   Probability: 10/25= 2/5
Answer: C