MU-NLPC/Calc-aqua_rat huggingface dataset:
In a jar there are 28 white balls, 32 green balls and 41 blue balls. How many balls must be taken out in order to make sure we have 30 balls of the same color?	Choose the correct choice from the following options:
A) a)	23
B) b)	46
C) c)	57
D) d)	66
E) e)	67

Solution: Here, we need to find minimum number of marbles to be taken out to get 30 marbles of same color.   For a instance, if we take 2 white marbles 1st and followed by 22 Green and then 22 Blue.   Total will be   21 + 22+ 22= 
  21 + 22+ 22 = 65
65 draws.   If we choose either Green or Blue next time. This will bring the total of either of these colored marble to 30.   So Minimum we need to take 65+1= 
65+1 = 66
66 Times to get 30 marbles of same color(either Green or Blue).   Answer : d)	66.
Answer: D
When 23 is divided by the positive integer k, the remainder is 3, for how many different values of k is this true? Select the correct option:
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: This means that 20 must be a multiple of k.   The factors of 20 are 1, 2, 4, 5, 10, and 20.   Out of these, k can be 4, 5, 10, and 20.   The answer is 4.
Answer: D
Tough and Tricky questions: Ratios
3/5 of a certain class left on a field trip. 2/3 of the students who stayed behind did not want to go on the field trip (all the others did want to go). When another vehicle was located, 1/2 of the students who did want to go on the field trip but had been left behind were able to join. What fraction of the class ended up going on the field trip? Choose the correct choice from the following choices:
A) 1/2
B) 2/3
C) 11/15
D) 23/30
E) 4/5

Solution: let total no. of students be 30   students left on a field trip = 3/5(30) =18   thus 12 students left behind   2/3(12)=8 students did not want to go. thus 4 students want to go on the trip   1/2(4)=2 were able to join the other students on the field trip.   thus total number of students that went on a field trip =18+2= 
18+2 = 20
20   thus required fraction= 20/30 =2/3   2/3
Answer: B
A car started running at a speed of 30 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 7 hours of the journey.	Select
A) 342 km
B) 352 km
C) 252 km
D) 742 km
E) 382 km

Solution: The total distance covered by the car in the first 7 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 = sum of 7 terms in AP whose first term is 30 and last term is 42 = 7/2 [30 + 42] = 252 km.   ANSWER:252 km
Answer: C
John has 10 pairs of matched socks. If he loses 11 individual socks, what is the greatest number of pairs of matched socks he can have left?
Choose the correct choice from the following answers:	A) 7	B) 6	C) 5	D) 4	E) 3

Solution: Because we have to maximize the pair of matched socks, we will remove 5 pairs(10 socks) out of 10 pairs 1 sock from the 6th pair.   Thus the no of matching socks pair remaining = 10 -6= 
10 -6 = 4
4   Answer 4
Answer: D
How many 3-letter words can be formed out of the letters of the word ‘CORPORATION’, if repetition of letters is not allowed?
Choose the correct option.
A) 336
B) 297
C) 266
D) 259
E) 297

Solution: Explanation:   There are in all 11 letters in the word ‘CORPORATION’. Since repetition is not allowed, there are 8 different letters that can be used to form 3-letter word.   Therefore, total number of words that can be formed = 8P3 = (8*7*6)= 
(8*7*6) = 336
336   336NSWER: 336
Answer: A
The price of the jewel, passing through three hands, rises on the whole by 62%. If the first and the second sellers 20% and 25% profit respectively find the percentage profit earned by the third seller.  Choose the correct choice from the following answers:	A) 20	B) 8	C) 5	D) 2	E) 30

Solution: Let the original price of the jewel be $ p and let the profit earned by the third seller be x% Then, (100+x)% of 125% of 120% of P =162% Of P ((100+X)/100*125/100*120/100*P)=(162/100*P)   ==> (100+X)=(162*100*100)/(125*120)= 
(162*100*100)/(125*120) = 108
108=>X=8%   Answer 8)
Answer: B
If one-third of one-fourth of a number is 15, then three-tenth of that number is: Choose the correct answer
A) 48	B) 40	C) 50	D) 54	E) 64

Solution: Let the number be x.   Then 1/3 of 1/4 of x =15   X=15x12 = 180   Required Number = (3/10)x180 =54   Answer : 54
Answer: D
Sam purchased 20 dozens of toys at t he rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?
Choose the correct option:
A) 3.5
B) 4.5
C) 5.6 percent
D) 6.5
E) None

Solution: Solution   C.P of 1 toy	= Rs.(375/12)   = Rs.31.25   S.P of 1 toy	= Rs.33.   Therefore,Profit	= (1.75/31.25×100)%   =(28/5)= 
(28/5) = 28/5 = around 5.6
5.6%.   Answer 5.6 percent
Answer: C
A pump can fill a tank with water in 5 hours. Because of a leak, it took 7 hours to fill the tank. The leak can drain all the water in ?	Choose the correct choice from the following.
A) 15hr 10min
B) 16hr 20min
C) 17hr 30min
D) 15hr
E) 14hr 25min

Solution: Work done by the leak in 1 hour = 1/5 - 1/7 = 2/35   Leak will empty the tank in 35/2 hrs = 17hr 30min   Answer is 17hr 30min
Answer: C
what is the least number. which should be added to 221 to make it a perfect square?	Choose the most appropriate option:
A) 5
B) 8
C) 4
D) 6
E) 7

Solution: 221+4= 
221+4 = 225
225   15^2   ANSWER:4
Answer: C
How many numbers from 10 to 100 are exactly divisible by 9? Answers:
A) 10
B) 12
C) 14
D) 16
E) 18

Solution: 10/9 = 1 and 100/9 = 11 ==> 11 - 1= 
11 - 1 = 10
10. Therefore 10 digits.   10)
Answer: A
A person incurs 5% loss by selling a watch for $1140 . At
what price should the watch be sold to earn 5% profit?	Choose the correct choice from the following options:
A) 1160  B) 1150  C) 1260  D) 1260  E) 1360

Solution: Let the new S.P be $ x then,   (100-loss%):(1st S.P)=(100+gain%):(2nd S.P)   (100-5)/1140=(100+5)/x   x=(105*1140)/95= 
(105*1140)/95 = 1_260
$1260   ANSWER 1260 1260
Answer: C
12,21,48,87,__
Pick.
A) 176  B) 186  C) 184  D) 174  E) 164

Solution: 21=12*2-3   48=21*2+6   87=48*2-9   so next number is 87*2+12= 
87*2+12 = 186
186   ANSWER:186
Answer: B
In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps. The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps. If 9,000 have been vaccinated against both, how many have been vaccinated only against rubella? Choose the correct choice from the following
A) 18,000
B) 7,500
C) 10,000
D) 15,000
E) 17,500

Solution: Use a single variable as far as possible.   Number vaccinated only against mumps = x   Number vaccinated against both = 2x = 9000 (so x = 4500)   Then, number vaccinated against mumps (including both) = x + 2x = 3x   Number vaccinated against rubella = 2*3= 
2*3 = 6
6x   Then, number vaccinated against only rubella= 6x - 2x = 4x 6  - 2= 
6  - 2 = 4
4x= 4*4500 = 18,000   18,000nswer (18,000)
Answer: A
A farm has only chickens and pigs. When the manager of the farm counted the heads of the animals on the farm, the number totaled up to 95. When the number of legs was counted, the number totaled up to 274. How many more chickens than pigs are there on the farm? Note: Each pig has 4 legs and each chicken had 2 legs.	Choose the correct choice from the following
A) 7 B) 8 C) 9 D) 10 E) 11

Solution: Let x be the number of chickens.   Then 95-x is the number of pigs.   2x+4(95-x)=274   2x=106   x=53 (chickens)   95-x=42 (pigs)   There are  53-42= 
 53-42 = 11
11 more chickens on the farm.   The answer is 11.
Answer: E
g(x) is defined as the product of all even integers k such that 0 < k ≤ x. For example, g(14) = 2 × 4 × 6 × 8 × 10 × 12 × 14. If g(a) is divisible by 4^11, what is the smallest possible value for a?  Pick one:  A) 22  B) 24  C) 28  D) 32  E) 44

Solution: g(a)=4^11=2^22. So we have to find a product with atleast 22 2's in it.   in option 1 22 the total no of 2's = [22/2] + [22/4] +[22/8] +[22/16] = 11+5+2+1= 
11+5+2+1 = 19
19   in option 2 24 the total no of 2's= [24/2] + [24/4] +[24/8] +[24/16] = 12+6+3+1= 
12+6+3+1 = 22
22 . Hence 24
Answer: B
In the Excel Manufacturing Company, 46 percent of the employees are men. If 60 percent of the employees are unionized and 70 percent of these are men, what percent of the non-union employees are women?  Answers:
A) 90%	B) 87.5%	C) 66.7%	D) 50%	E) 36%

Solution: Lets say there are total 100 employees   Then men = 46 & women = 54   Unionized Emp = 60 & non unionized emp = 40   Men Unionized = .7 * 60= 
.7 * 60 = 42
42   Women Unionized= 18   Women non-unionized = 54-18= 
54-18 = 36
36   Percentage of Women non unionized= 36/40 * 100= 
36/40 * 100 = 90
90%   The answer is Option 90%
Answer: A
Three 6 faced dice are thrown together. The probability that all the three show the same number on them is -  Choose the correct choice from the following answers: A) 1/35 B) 1/36 C) 1/37 D) 1/31 E) 1/30

Solution: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6= 
6 * 6 * 6 = 216
216 ways.   Hence the probability is 6/216= 1/36   Answer: 1/36
Answer: B
If an article is sold at 12% profit instead of 16% profit, then the profit would be Rs. 105 less. What is the cost price?	Answers:  A) Rs. 3000  B) Rs.4000  C) Rs. 3500  D) Rs.4500  E) Rs.6000

Solution: Explanation:   Let the cost price of an article be Rs. x.   (16% of x) - (12% of x) = 105   16x/100 - 12x/100 = 105 => 4x = 160 * 100   => x = 1500   Cost price = Rs. 4000   Answer:Rs.4000
Answer: B
The average age of an adult class is 40years. 10 new students with an avg age of 32years join the class. Therefore
decreasing the average by 4year. Find what was the original strength of class?
Choose the correct choice from the following answers.
A) 10	B) 12	C) 16	D) 20	E) 22

Solution: Let original strength = y   Then , 40y + 10 x 32 = ( y + 10) x 36   â‡’ 40y + 320 = 36y + 360   â‡’ 4y = 40   âˆ´ y = 10   10
Answer: A
A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 550 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?  Choose one
A) 550 * sqrt 2	B) 550 * sqrt (2^7)	C) 550 * sqrt (2^12)	D) 550 * the twelfth root of (2^7)	E) 550 * the seventh root of (2^12)

Solution: Let the constant be k.   F1 = 550   F2 = 550k   F3 = 550 k * k = 550 * k^2   F13= 550 * k^12   we know F13 = 2 *F1 = 2 * 550 2 * 1= 
2 * 1 = 2
2 * 550= 
2 * 550 = 1_100
1100   1100/550= k^12   k = twelfth root of 2   for F7...   F7 = 550 * k^6 ( as we wrote for F2 and F3)   F7 = 550 * (twelfth root of 2) ^ 6   F7 = 550 * sqrt (2)   The answer is 550 * sqrt 2.
Answer: A
Two cars are driving towards one another. The first car is traveling at a speed of 120 Km/h, which is 28% faster than the second car. If the distance between the cars is 855 Km, how long will it takes the cars to meet (in hours)?
Choose the correct option
A) 2.5.  B) 3.  C) 3.5  D) 4.  E) 4.5.

Solution: Let S be the speed of the slower car.   Then the speed of the faster is 1.28S   1.28S = 120   S = 120/1.28   Cumulative speed/rate = S + 1.28S = 2.28S   Time taken to meet = 855/2.28S =855/213.75= 
855/213.75 = 4
4hrs   ANSWER:4.
Answer: D
A salesperson receives a base salary of $1000 per month and a commission of 7.5% of the selling price of each item sold above the first 50 item. If this month she sold 330 items for $150 each, what will her monthly salary be?
Choices:
A) $1,500
B) $1,800
C) $2,100
D) $2,500
E) $4,150

Solution: Ans : 1000+ 7.5 % * 150 * (330-50) = $ 4150   ANSW$4,150R:$4,150
Answer: E
Three friends had dinner at a restaurant. When the bill was received, Akshitha paid 1/3 as much as Veena paid and Veena paid 1/2 as much as Lasya paid. What fraction of the bill did Veena pay ?
Choose the correct choice from the following
A) 3/19	B) 3/12	C) 3/11	D) 3/10	E) 3/14

Solution: Let Veena paid x,   so Akshitha paid x/3 , and Lasya paid 2x,   So total bill paid is given by   x+(x/3) +2x = 1, we get   i.e. x = 3/10   Answer: 3/10
Answer: D
A man goes downstream at 15 kmph, and upstream8 kmph. The speed of the stream is	Choose the correct choice
A) 0kmph B) 3.5kmph C) 16kmph D) 2.5kmph E) 26kmph

Solution: Speed of the stream = 1/2(15-8)kmph   =3.5kmph.   correct option :3.5kmph
Answer: B
Difference between the length &breadth of a rectangle is 15 m. If its perimeter is 302 m, then its area is?? We have: (l - b) = 15 and 2(l + b) = 302 or (l + b) = 151?
Choices:
A) 5446 m^2 B) 5464 m^2 C) 5644 m^2 D) 5434 m^2 E) 5344 m^2

Solution: Solving the two equations, we get: l = 83 and b = 68.   Area = (l x b) = (83 x 68) m2 = 5644 m^2   5644 m^2
Answer: C
What is the perimeter of a square with area 9p^2/64 ?	Select the correct option
A) 3p/2	B) 3p^2/4	C) 3p	D) 3p^2	E) 4p/3

Solution: 3p/2rea of square, (side)^2 = (3p/8)^2   Therefore side of the square = 3p/8   Perimeter of square = 4*side = 4* (3p/8) = 3p/2   3p/2nswer is 3p/2.
Answer: A
Which number is the odd one out?
9654 4832 5945 7642 7963 8216 3649
Choose the most appropriate option:
A) 4549  B) 6549  C) 3729  D) 3649  E) 5416

Solution: 3649   3649   In all the others multiply the first two digits together to produce the number formed by the last two digits.
Answer: D
A train passes a station platform in 40 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?  Choose the correct choice from the following options:	A) 180 m	B) 200 m	C) 240 m	D) 300 m	E) None

Solution: Sol.   Speed = [54 * 5/18] m/sec = 15 m/sec.   Length of the train = (15 * 20)= 
(15 * 20) = 300
300 m.   Let the length of the platform be x metres.   Then, x + 300 / 40= 15 ⇔ x + 300 = 600 ⇔ x = 300 m.   Answer 300 m
Answer: D
How many integers between 3000 and 4000 that have distinct digits and increase from left to right ?
Choices
A) 20 B) 48 C) 60 D) 120 E) 600

Solution: Since the numbers must be distinct and increasing from left to right,   The only arrangements we could come-up with are:   345_ --> 4   346_ --> 3   347_ --> 2   348_ --> 1   356_ --> 3   357_ --> 2   358_ --> 1   367_ --> 2   368_ --> 1   378_ --> 1   Number of integers =20   So the answer is 20.
Answer: A
A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 37380
. What percentage of profit did he make?	Choose the most appropriate option:
A) 80%  B) 68%  C) 40%  D) 70%  E) 90%

Solution: The total CP = Rs. 16000 + Rs. 6250   = Rs. 22250 and SP = Rs. 31150   Profit(%) = (37380 - 22250)/22250 * 100= 
(37380 - 22250)/22250 * 100 = 68
68%   Answer:68%
Answer: B
The least number by which 72 must be multiplied in order to produce a multiple of 112, is
Choose the most appropriate option: A) 6 B) 12 C) 14 D) 18 E) 20

Solution: Solution   Required numbers is divisible by 72 as well as by 112, if it is divisible by their LCM, which is 1008.   Now, 1008 when divided by 72, gives quotient	= 14.   Required number	= 14.   Answer 14
Answer: C
On final examination a student's average (arithmetic mean) score on 4 subjects is 90. What must be his score on a 5th subject for his average score on the 5 subjects to be 92?
Choices: A) 60 B) 70 C) 80 D) 90 E) 100

Solution: (4*90+x)/5=92   x=(5*92)-(4*90)   x= 460 - 360= 
460 - 360 = 100
100   Correct answer is 100
Answer: E
If n is a natural number, then(6n^2+6n) is always divisible by?	Choose the correct choice from the following choices
A) 6 only
B) 6 and 12 both
C) 12 only
D) by 18 only
E) None of these

Solution: (6n^2+6n)=6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even.   Correct Option: 6 and 12 both
Answer: B
Running at their respective constant rate, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 5w widgets. Choose the correct choice from the following answers:
A) 4  B) 6  C) 8  D) 30  E) 12

Solution: I am getting 12. E. Hope havent done any calculation errors..   approach..   let y=no. of days taken by Y to do w widgets. Then X will take y+2 days.   1/(y+2) +1/y = 5/12(5/12 is because (5/4)w widgets are done in 3 days. So, x widgets will be done in 12/5 days or 5/12 th of a widget in a day)   Solving, we have y = 4   =>X takes 6 days to doing x widgets. So, he will take 30 days to doing 5w widgets.   Answer : 30
Answer: D
In an election contested by two parties, Party D secured 12% of the total votes more than Party R. If party R got 132,000 votes, by how many votes did it lose the election?  Choices:
A) 24,000 B) 36,000 votes C) 168,000 D) 240,000 E) 300,000

Solution: D + R = 100 ---- (1)   D - R = 12 ---- (2)   Solving (1) and (2) D = 56% and R = 44%   44% of Total = 132000   Total = 300000   D = 168000   Difference = 168000 - 132000= 
168000 - 132000 = 36_000
36000   Answer: 36,000 votes
Answer: B
Factor | Percent of Respondents |
User-friendly | 56% |
Fast response time | 48% |
Bargain prices | 42% |
The table gives three factors to be considered when choosing an Internet service provider and the percent of the 1,600 respondents to a survey who cited that factor as important. If 30 percent of the respondents cited both “user-friendly” and “fast response time,” what is the maximum possible number of respondents who cited “bargain prices,” but neither “user-friendly” nor “fast response time?”
Choose one.
A) 312
B) 336
C) 360
D) 384
E) 416

Solution: The way I looked at is is as follows:   UserFriendly(UF) + FastResponse (FR) = 30%   UF leftover = 56 - 30= 
56 - 30 = 26
26%   FR leftover= 48 - 30= 
48 - 30 = 18
18%   Sum these= 74% (ie. 74% were either UF+FR, UF, FR)   26% leftover is the maximum number for Bargain Price   26/100 * 1600 = 26 * 16= 
26 * 16 = 416
416 (416).
Answer: E
A man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses. Next year his income increases by 40% but his savings increase by 100%. If his total expenditure in 2 years is double his expenditure in 1st year, What %age of his income in the first year did he save?
Choose the correct choice from the following options.
A) 45%  B) 40%  C) 25%  D) 28%  E) 33.33%

Solution: I year   Best is to give a number to his income, say 100..   and let saving be x..   so expenditure = 100-x   next year-   Income = 140   savings = 2x   expenditure = 140-2x..   Now 140-2x+100-x = 2(100-x)...   240-3x = 200-2x ................x = 40...   saving % = 40/100 * 100= 
40/100 * 100 = 40
40%   ANSWER:40%
Answer: B
If x is the median of the set {8/2, 11/3, 27/9, 21/5, x}, x could be
Answers:
A) 4 B) 17/5 C) 16/5 D) 30/7 E) 31/7

Solution: The median is the middle number once all the numbers are arranged in increasing/decreasing order.   We see that   11/3 = 3.something,   28/9 = 3.something   21/5 = 4.something   9/2 = 4.something   So x should greater than the smallest two numbers and smaller than the greatest two numbers. We can see that x = 4 is possible. (First look at the simplest option or the middle option since options are usually arranged in increasing/decreasing order)   4nswer (4)
Answer: A
If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll?
Choose one:  A) 25/36  B) 125/216  C) 91/216  D) 11/36  E) 36/216

Solution: Thus, the probability of at least 1 roll = 1- Probability of NO 3s = 1- (5/6)(5/6)(5/6) = 1-125/216 = 91/216.   5/6 is the probability of NOT getting a 3 in any 1 roll with 5 allowed numbers (=1,2,4,5,6) out of a total of 6 possibilities.   answer:91/216
Answer: C
Murali travelled from city A to city B at a speed of 60 kmph and from city B to city C at 40 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?	Select
A) kmph	B) kmph	C) kmph	D) kmph	E) kmph

Solution: Let the distances between city A to B and B to C be 2x km and 3x km respectively.   Total time taken to cover from A to C   = (2x)/60 + (3x)/40   = (4x + 9x)/120 = 13x/120   = (2x + 3x)/(13x/120) = 46.2 kmph.   Answer: kmph
Answer: B
Evaluate permutation
3P3  Pick
A) 6 B) 7 C) 8 D) 9 E) 10

Solution: Explanation:   nPn=n!   3P3=3∗2∗1=6   Option 6
Answer: A
1000 men have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now?  Choose the most appropriate option:  A) 12.9  B) 18.9  C) 12.5  D) 12.2  E) 12.1

Solution: :   1000*15 = 1200*x   x = 12.5   Answer: 12.5
Answer: C
A certain auto manufacturer sold 6% fewer vehicles in 2007 than in 2006. If the manufacturer sold 2.1 million vehicles in 2006, how many vehicles, to the nearest 10,000, did the manufacturer sell in 2007? Pick one
A) 63,000 B) 1,980,000 C) 2,030,000 D) 2,040,000 E) 2,300,000

Solution: Let's assume in 2006 the manufacturer sold X.   In 2007 he sold X-6/100(X)   If sales in 2006,X= 2.1 million find X-6/100(X)   (2.1 x 10^6)-6/100(2.1 x 10^6)   2100000-126000=1,974,000-----> 1,980,000(approx)   ANSWER:1,980,000
Answer: B
If r is a positive integer and r^2 is divisible by 12, then the largest positive integer that must divide r ^3 is Choose the correct choice from the following choices
A) 2^3 B) 2^6 C) 3^3 D) 6^3 E) 12^2

Solution: Since r is an integer so r cannot have a 2 and sqrt 3 (because squaring this will give us a 2^2 and 3 (making the product as 12, and making r^2 as a multiple of 12))   r^2 is divisible by 12 (12 = 2*2*3), So, r should have at least one 2 and one 3 so that r^2 has a 2^2 and two 3   So, r will have a 2 and a 3. Or r will be a multiple of 6   So, largest possible integer than should divide r^3 is 6^3   So, Answer will be 6^3
Answer: D
If z is the smallest positive integer that is not prime and not a factor of 50!, what is the sum of the factors of z?
Choices:  A) 51  B) 162  C) 72  D) 54  E) 50!+2

Solution: In fact 51=3*17 IS a factor of 50!.   The smallest positive integer that is NOT prime and NOT a factor of 50! is 106=2*53. The sum of the factors of 106 is 162.   Answer: 162.
Answer: B
A certain quantity of 70% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?
Choose one:
A) 1/4	B) 1/3	C) 1/2	D) 2/3	E) 7/9

Solution: Let's say that the total original mixture A is 100 ml   The original mixture A thus has 70 ml of alcohol out of 100 ml of solution   You want to replace some of that original mixture A with another mixture B that contains 25 ml of alcohol per 100 ml. Thus, the difference between 70 ml and 25 ml is 45 ml per 100 ml of mixture. This means that every time you replace 100 ml of the original mixture A by 100 ml of mixture B, the original alcohol concentration will decrease by 45%. The question says that the new mixture, let's call it C, must be 35% alcohol, a decrease of only 35%. Therefore, 35 out of 45 is 7/9 and 7/9 is the answer.
Answer: E
If 10 litres of an oil of Rs.54 per litres be mixed with 5 litres of another oil of Rs.66 per litre then what is the rate of mixed oil per litre?	Choose the correct option:
A) Rs.49.17 B) Rs.58 C) Rs.54.17 D) Rs.55.33 E) None of the above

Solution: 54*10= 
54*10 = 540
540   66*5= 
66*5 = 330
330   870/15= 
870/15 = 58
58   ANSWER:Rs.58
Answer: B
If 6x^2 + x - 12 = (ax + w)(cx + d), then |a| + |w| + |c| + |d| =
For a complete solution and more practice problems, see this blog:
http://magoosh.com/gmat/2012/algebra-on ... to-factor/  Choose the correct answer
A) 10 B) 12 C) 15 D) 18 E) 20

Solution: 6x^2+x-12 = 6x^2 + 9x -8x -12   => 3x(2x+3) -4(2x+3)   => (2x+3)(3x-4) = (ax+w)(cx+d)   Hence a=2, w=c=3, d=-4   So, 2+3+3+ |-4| = 2+3+3+4= 
2+3+3+4 = 12
12   Answer 12.
Answer: B
The average age 20 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
Select
A) 18 B) 99 C) 77 D) 40 E) 12

Solution: 20 * 2= 
20 * 2 = 40
40 years   Answer: 40
Answer: D