MU-NLPC/Calc-aqua_rat huggingface dataset:
How many Books each of Volume 150 meter cube can be packed into a crate of volume 3000 meter cube? Choose the correct choice from the following options: A) cannot be determined B) 20 C) 25 D) 30 E) 35

Solution: Gud question with a simple concept.   In geo if we want to insert one shape into another we need to know the dimensions of the two shapes.   In above with volume given , we can come up with different shapes, so we cant know the answer   For ex :3000 m3 can be 300*10 or 30*100 or just 3000*1 we don't know , so we cant calculate   cannot be determinednswer : cannot be determined
Answer: A
If the average (arithmetic mean) of the four numbers 23, 15, 32, and (N + 1) is 50, then N =  Pick:
A) 19 B) 20 C) 121 D) 122 E) 129

Solution: 23+15+32+N+1= 50 x 4 = 200   =>N +71 = 200   =>N=129   Answer 129
Answer: E
At an upscale fast-food restaurant, Shin can buy 3 burgers, 7 shakes, and one cola for $130. At the same place it would cost $164.50 for 4 burgers, 10 shakes, and one cola. How much would it cost for a meal of one burger, one shake, and one cola?  Select the correct option.
A) $21
B) $27
C) $31
D) $61
E) It cannot be determined

Solution: let's suppose that the price of a burger is BB, of a shake - SS and that of a cola is CC. We can then construct these equations:   3B+7S+C=130   4B+10S+C=164.5   Subtracting the first equation from the second gives us B+3S=34.5   Now if we subtract the new equation two times from first or 3 times from second we will get B+S+C=61. In any case, there is no necessity to know each item's price, just the sum.   Answer: $61
Answer: D
A sum of money lent out at S.I. amounts to a total of $480 after 2 years and to $680 after a further period of 5 years. What was the initial sum of money that was invested?	Options:
A) $360	B) $380	C) $400	D) $420	E) $440

Solution: S.I for 5 years = $680 - $480 = $200   The S.I. is $40/year   S.I. for 2 years 680 -  480= 
680 -  480 = 200
$200   The S.I. is $40/year   S.I. for 2 years= $80   Principal = $480 - $80 = $400   The answer is $400.480 -  80= 
480 -  80 = 400
$400   The answer is $400.
Answer: C
The HCF of two numbers is 52 and the other two factors of their LCM are 11 and 12. What is the largest number.
Choose the correct option:
A) 624  B) 450  C) 480  D) 504  E) 555

Solution: Explanation:   HCF of the two numbers = 52   HCF will be always a factor of LCM   52 is factor of LCM   other two factors are 11 & 12   Then the numbers are (52 *11) and (52 x 12)   = 572 and 624   624nswer: Option 624
Answer: A
A man invests some money partly in 12% stock at 105 and partly in 8% stock at 88. To obtain equal dividends from both, he must invest the money in the ratio:	Answers: A) 31 : 44 B) 31 : 27 C) 16 : 15 D) 35 : 44 E) 35 :27

Solution: n case of stock1, if he invest Rs.105, he will get a dividend of Rs.12 (assume face value = 100)   In case of stock2, if he invest Rs.88, he will get a dividend of Rs.8 (assume face value = 100)   ie, if he invest Rs.(88*12)/8, he will get a dividend of Rs.12   Required ratio = 105 : (88 × 12)/8 = 105 : (11 × 12) = 35 : (11 × 4) = 35 : 44   Answer : Option 35 : 44
Answer: D
A train covered a certain distance at a uniform speed. If the train had been 6 km/hr faster, it would have taken 4 hour less than the scheduled time. And, if the train were slower by 6 km/hr, the train would have taken 6 hr more than the scheduled time. The length of the journey is:
Choose the most appropriate option.
A) 720 km	B) 700 km	C) 740 km	D) 600 km	E) None of these

Solution: Explanation :   Let the length of the journey be d km and the speed of train be S km/hr.   Then,   =>d/(S+6)=t−4. ---------------(i)   =>d/(S−6)=t+6. ---------------(ii)   Subtracting the (i) equation from(ii), we get :-   =>d/(S−6)−d/(S+6)=10 --------------(iii)   Since, Time=Distance/Speed.   From (i) , (ii) and (iii), w get :-   S=30 and d = 720 km.   720 kmnswer : 720 km
Answer: A
Of the five numbers in a sequence, the first term is 15,000, and each of the following terms is 20% of the previous term. What is the value range of the five numbers?
Choose the correct choice from the following options:
A) 9,375	B) 9,750	C) 9,975	D) 9,984	E) 14,976

Solution: 1st number= 15,000   2nd number = 20% of 15,000= 3000   3rd number= 20% of 3000= 600   4th number = 20% of 600= 120   5th number= 20% of 120= 24   Range = 15,000-24= 14976   14,976 is the answer
Answer: E
How many seconds will a 550 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? Choose the correct choice from the following answers:
A) 12 sec
B) 30 sec
C) 33 sec
D) 16 sec
E) 18 sec

Solution: Speed of train relative to man = 63 - 3= 
63 - 3 = 60
60 km/hr.= 60 * 5/18 = 50/3 m/sec.   Time taken to pass the man = 550 * 3/50= 
550 * 3/50 = 33
33 sec.   Answer: 33 sec
Answer: C
A survey was sent to 80 customers, 12 of whom responded. Then the survey was redesigned and sent to another 63 customers, 10 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey?
Choose the correct answer:
A) 2%  B) 5%  C) 14%  D) 28%  E) 63%

Solution: Rate of first survey = 12/80   Rate of second survey = 10/63   % Response rate increase (10/63-12/80)/(12/80) = 5%   Answer is 5% = 5%
Answer: B
A train 120 m long is running at a speed of 68 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train?	Choose the correct choice from the following options:
A) 7.2 sec B) 9.3 sec C) 12 sec D) 15.2 sec E) 18 sec

Solution: Speed of the train relative to man = (68 - 8) kmph   = (60* 5/18) m/sec = (50/3)m/sec   Time taken by the train to cross the man   = Time taken by It to cover 120 m at 50/3 m / sec = 120 *3/ 50= 
120 *3/ 50 = 36/5 = around 7.2
7.2 sec   7.2 secnswer : 7.2 sec.
Answer: A
A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?
Choose the correct choice from the following options: A) 3 B) 4 C) 7 D) 8 E) 9

Solution: M = 4   S = 2   US = 4 - 2= 
4 - 2 = 2
2   D= 6   T = 6/2= 
6/2 = 3
3   3nswer:3
Answer: A
A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 4 inches wide on each side, the total area would have been (M + 90) square inches. What is the perimeter of the photograph, in inches? Choose the correct choice from the following
A) 10  B) 20  C) 30  D) 40  E) 50

Solution: Let x and y be the width and length of the photograph.   (x+2)(y+2)=M and so (1) xy + 2x + 2y + 4 = M   (x+8)(y+8)=M and so (2) xy + 8x + 8y + 64 = M+90   Let's subtract equation (1) from equation (2).   6x + 6y + 60 = 90   2x + 2y = 10, which is the perimeter of the photograph.   The answer is 10.
Answer: A
Mandrake has to choose 4 from 20 people. There are 3 girls, 5 boys , 12 children. What is total probability that he will choose 1G , 2B , 1C? Options:
A) 1/27  B) 2/27  C) 3/7  D) 4/7  E) 5/7

Solution: (3C1 * 5C2 * 12C1)/ 20C4 = 3*10*12/4845= 360/4845=2/27   ANSWER:2/27
Answer: B
Compute the perimeter of a square with area 36.  Choose the most appropriate option.
A) 24  B) 27  C) 25  D) 26  E) 29

Solution: If the length of the square is s, then s2 = 36 so s = 6. The perimeter is therefore   4s = 24 .   correct answer 24
Answer: A
A teacher gave the same test to three history classes: U, B, and C. The average (arithmetic mean) scores for the three classes were 65, 80, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined?  Answers
A) 74 B) 75 C) 76 D) 77 E) 78

Solution: Ans : B (75)   lets say class U indeed has 4 children, B has 6 children and C has 5 children.   now, if the average of class U is 65, hence total marks awarded in the class = 65*4= 
65*4 = 260
260   Similarly,   class B= 80*6= 
80*6 = 480
480   class C= 77*5= 
77*5 = 385
385   total marks provided= U+B+C = 260+480+385= 
260+480+385 = 1_125
1125   avg. marks= 1125 / 15 (total no. of students) = 75=75
Answer: B
If a tire rotates at 400 revolutions per minute when the car is traveling 120km/h, what is the circumference of the tire?  Choose the most appropriate option.
A) 7 meters	B) 9 meters	C) 8 meters	D) 5 meters	E) 3 meters

Solution: 400 rev / minute = 400 * 60 rev / 60 minutes   = 24,000 rev / hour   24,000 * C = 12,0000 m : C is the circumference   C = 5 meters   correct answer 5 meters
Answer: D
How many of the following numbers are divisible by 132?
264, 396, 462, 792, 968, 2178, 5676, 6336
Choose the correct answer:
A) 4
B) 5
C) 6
D) 7
E) 8

Solution: A number is divisible by 132, if it is divisible by each one of 11, 3 and 4.   Clearly, 968 is not divisible by 3. None of 462 and 2178 is divisible by 4.   Each one of remaining 5 is divisible by each one of 11, 3 and 4 and therefore, by 132.   ANSWER:5
Answer: B
15 tennis players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played?	Pick:
A) 190	B) 200	C) 210	D) 220	E) 225

Solution: 15 th player can play with remaining 14 members two times = 2*14= 
2*14 = 28
28   14 th " remaining 13= 2*13= 
2*13 = 26
26   2*(1+2+3+4+......+14)=2(14)(14+1)/2=210   ANSWER:210
Answer: C
If f(x) = 4x − √x and g(x) = x^2, what is f(g(5))?	Options: A) -4 B) 8 C) 16 D) 32 E) 95

Solution: g(x) = x²   g(5) = 5² = 25   So, f(g(5)) = f(25)   f(x) = 4x − √x   So, f(25) = 4(25) − √25   = 100 - 5= 
100 - 5 = 95
95= 95
Answer: E
The public library has exactly 2 floors. It has 1/2 as many shelves on its 2nd floor as it does on its 1st. If the second floor has 5/6 as many books per shelf as the first floor, what fraction of the library's books are on the first floor?
Pick one
A) 1/4
B) 5/14
C) 12/17
D) 9/14
E) 5/6

Solution: Lẹt x bé thế nó of shelves and ý bé thế nó of books per shelf on first floor.   Now no of shelves on 2nd floor = (1/2)*x   no of books per shelf on 2nd floor = (5/6) * y   Số total no books on first floor = xy and total no of books on 2nd floor = (1/2)*x*(5/6)*y = (5/12)*xý   fraction of library books on first floor = (xý)/(xý + (5/12)*xý)   =1 / (1+(5/12))   =12/17   Số 12/17
Answer: C
A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?  Choose the correct choice from the following options.
A) 78 sec B) 89 sec C) 27 sec D) 24 sec E) 12 sec

Solution: Speed = 240/24= 
240/24 = 10
10 m/sec.   Required time= (240 + 650)/10= 
(240 + 650)/10 = 89
89 sec.   Answer:89 sec
Answer: B
Two-third of a positive number and 49/216 of its reciprocal are equal. The number is:	Choices:	A) 5/12	B) 7/12	C) 25/144	D) 144/25	E) 146/25

Solution: Let the number be x. Then,   2/3 x = 49/216 * 1/x   x2 = 49/216 * 3/2 = 49/144   x = 7/12   ANSWER:7/12
Answer: B
Scott's average (arithmetic mean) golf score on his first four rounds was 28.What score does he need on his fifth round to drop his average score by 2 points?	Choose the correct choice.
A) 18 B) 72 C) 78 D) 88 E) 312

Solution: 18verage score for first 4 rounds = 28   18verage score after 5 rounds = 26   Score Scott needs on his 5th round to drop average score by 2 points = 28 - (2*5)= 
28 - (2*5) = 18
18   18nswer 18
Answer: A
If 2^4, 2^3, and 11^3 are factors of the product of 1,452 and w, where w is a positive integer, what is the smallest possible value of w? Choose the correct choice.
A) 176  B) 288  C) 363  D) 396  E) 484

Solution: I will go with 176 (pending elements to match is 2^2*2^2*11^1 = 176
Answer: A
If in a certain code, If NEPOLEAN is written as OBFMPQFO, how can IMPOSING be written?  Choose the correct answer
A) HOJTPQNI	B) HOJTPQNK	C) HOJTPQNL	D) HOJTPQNJ	E) HOJTPQND

Solution: NEPOLEAN - OBFMPQFO   N+1 = O   E+1 = F   P+1 = Q   O+1 = P   L+1 = M   E+1 = F   A+1 = B   N+1 = O   Now write in reverse order... You ll get OBFMPQFO   Similarly for IMPOSING   I+1 = J   M+1 = N   P+1 = Q   O+1 = P   S+1 = T   I+1 = J   N+1 = O   G+1 = H   Now write in reverse order... HOJTPQNJ   ANSWER:HOJTPQNJ
Answer: D
In a City, 35% of the population is composed of migrants, 20% of whom are from rural areas. Of the local population, 48% is female while this figure for rural and urban migrants is 30% and 40% respectively. If the total population of the city is 728400, what is its female population ?	Select the correct option.
A) 324138  B) 248888  C) 378908  D) 277880  E) 379010

Solution: Explanation:   Total Population = 728400   Migrants = 35 % of 728400 = 254940   local population = (728400 - 254940)= 
(728400 - 254940) = 473_460
473460.   Rural migrants= 20% of 254940 = 50988   Urban migrants = (254940 - 50988)= 
(254940 - 50988) = 203_952
203952   Female population= 48% of 473460 + 30% of 50988 + 40% of 203952 = 324138   324138nswer: 324138
Answer: A
Rick deposited $800 to his bank account using $5 and $15 dollar bills only. If Rick came to the bank with 70 bills and left with 10 bills only, how many $15 dollar billsმ did he deposit?
Choose the correct choice from the following answers
A) 5. B) 25. C) 50. D) 55. E) 65.

Solution: 5x+15y=800 --1   x+y=60 ---2   multiply eq 2 with 5 and subtract from eq 1   5x+15y=800   5x+5y=300   10y= 500   y=50 and x = 10   therefore $15 bills = 50   Answer 50.
Answer: C
Barbata invests $3000 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment?
Choose the correct choice from the following:
A) 1200 B) 3000 C) 1000 D) 3600 E) 1500

Solution: Let the additional invested amount for 8% interest be x;   1500quation will be;   3000+0.05*3000+x+0.08x = 3000+x+0.06(3000+x)   0.05*3000+0.08x = 0.06x+0.06*3000   0.02x = 3000(0.06-0.05)   x = 3000*0.01/0.02= 
3000*0.01/0.02 = 1_500
1500   Ans: "1500"
Answer: E
M is 30% of Q, Q is 20% of P and N is 50% of P. What is M / N  Pick:
A) 3/28
B) 3/27
C) 3/21
D) 3/22
E) 3/25

Solution: Take P = 100, then N = 50, Q = 20, M = 6. So M/N = 3/25   3/25
Answer: E
An outgoing batch of students wants to gift a PA system worth Rs 4,200 to their school. If the teachers, offer to pay 50 more than the students and an external benefactor gives three times the teacher's contribution, then how much should the teachers donate?  Choose the correct choice from the following answers:
A) Rs 600
B) Rs 900
C) Rs 700
D) Rs 1200
E) None of these

Solution: Explanation :   The ratio of the share students : teacher: benefactor=1:1.5:4.5.   So the proportion to teacher's share = 1.5/7.   Hence, the teachers would donate (1.5/7)×4200=Rs 900.   Answer : Rs 900
Answer: B
In a race of length L metres, Johnson beats Lewis by M metres and Greene by N metres, By how many metres does Lewis beat Greene in the same race ? (M<N)  Select:
A) L(L-N) /L-M	B) L(N-M) / L-M	C) L-N	D) M-N	E) M+

Solution: the ans is quite simple N-M but since the ans is not given, the best way to 'find' the correct option is to plug in the numbers. For my work, i took the following numbers:   L = 200   M = 10   N =20.   So basically, L beat G by 20 meters. Now whatever options comes close to the figure 10 is the right ans..   looking the the opion C to E, one can make out that they are incorrect, A.   Out of which, i choose L(L-N) /L-M.
Answer: A
A local bank that has 12 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 12 codes? Choose the correct answer:
A) 3  B) 4  C) 12 ( 2 integers 4 codes)  D) 6  E) 7

Solution: Pick any two integer.   Integers: 12   Code: 11, 12, 21, 22 = 4 Codes   Add one more integer: 3   13, 31, 33, 23, 32 = 5 Codes   Add one more integer: 4   44, 14, 41, 24, 42, 34, 43 = 7 Codes   Total = 16 Codes. Enough. Answer: 12 ( 2 integers 4 codes)   4 integers create 12 codes.
Answer: C
For any numbers a and b, a#b = ab(2 − b). If a and a#b both represent positive numbers, which of the following could be a value of b? Choose the correct choice from the following answers:
A) 2 B) 1 C) 3 D) 4 E) 5

Solution: a#b positive then b may be positive or negative. if positive then b< 2 may be 1 and if negative then it is more than or equal to - 1negative . ab will be -ve which is not possible as a and a#b should be positive   ans 1
Answer: B
In how many ways a committee of 10 men and 8 women can be made out of total of 15 men and 12 women?	Choose the correct option:  A) 336/987  B) 1001/165  C) 1245/789  D) 3256/789  E) 256/85

Solution: Required number of ways = 15C10 * 12C8 = 15C5 * 12C4 = 3003/495 = 1001/165   Answer is 1001/165
Answer: B
Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts water. The painter has by mistake added water so that he has 6 litres of paint which is half water and half paint. What must he add to make the proportions of the mixture correct?  Select:
A) 1 litre paint
B) 1 litre water
C) ½ litre water and one litre paint
D) ½ litre paint and one litre water
E) ½ litre paint

Solution: Reqd. ratio = 2 : 1.5 i.e. 4 : 3 between paint and water respectively.   6 litres of paint which is half water(3 litres) and half paint (3 litres)   Right now the ratio is 1:1   Looking at the options,   A. Paint : Water = 4 : 3 which is the reqd. ratio . Correct Answer   B. Paint : Water = 3 : 4   C. Paint : Water = 4 : 3.5   D. Paint : Water = 3.5 : 4   E. Paint : Water = 3.5 : 3   1 litre paintnswer : 1 litre paint
Answer: A
Today Joelle opened an interest-bearing savings account and deposited $6,000. If the annual interest rate is 4 percent compounded interest, and she neither deposits nor withdraws money for exactly 2 years, how much money will she have in the account?	Choose the correct choice from the following.
A) $6,048.00 B) $6,240.00 C) $6,450.00 D) $6,480.00 E) $6,489.60

Solution: To calculate the interest earned on the account over two years, we use the following formula:   Interest = Deposit × Interest Rate × Number of Years   Interest = $6,000 × 0.04 = $240.   So, the amount of money in the account after 2 years is:   Total Amount = Initial Deposit + Interest Earned   Total Amount = $6,240(1.04) = 6,489.60.   The correct answer is choice ($6,489.60).
Answer: E
Three pipes of same capacity can fill a tank in 8 hours. If there are only two pipes of same capacity, the tank can be filled in?	Choose the correct choice.
A) 08 hours  B) 12 hours  C) 03 hours  D) 04 hours  E) 21 hours

Solution: The part of the tank filled by three pipes in one hour = 1/8   => The part of the tank filled by two pipes in 1 hour = 2/3 * 1/8 = 1/12.   The tank can be filled in 12 hours.   Answer:12 hours
Answer: B
Train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. The length of train P is three-fourths the length of train Q. What is the ratio of the speed of train P to that of train Q?  Choose the most appropriate option: A) 5:8 B) 5:6 C) 5:1 D) 5:3 E) 5:2

Solution: Given that train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds.   Let the length of train P be LP and that of train Q be LQ   given that LP = 3/4 LQ   5:8s the train P and Q crosses the pole in 30 seconds and 75 seconds respectively,   => Speed of train P = VP = LP/30   Speed of train Q = VQ = LQ/75   LP = 3/4 LQ   => VP = 3/4 LQ/(30) = LQ/40   Ratio of their speeds = VP : VQ   = LQ/40 : LQ/75 => 1/40 : 1/75 = 1   5:8   5:8nswer:5:8
Answer: A
If N = 23×34 , M = 22×3×5, then find the number of factors of N that are common with the factors of M. Pick.
A) 3 B) 9 C) 8 D) 6 E) 2

Solution: Answer: c   Explanation:   N = 23×34   M = 22×3×5   By taking common powers we get 22×3   So common factors = (2 + 1)(1 + 1) = 6.   (formula for number of factors of a number)   Answer:6
Answer: D
The average age of 36 students in a group is 13 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ?  Options:  A) 35 years  B) 45 years  C) 51 years  D) 54 years  E) 50 years

Solution: Explanation:   Age of the teacher = (37 * 14 - 36 * 13)= 
(37 * 14 - 36 * 13) = 50
50 years. Answer: 50 years
Answer: E
The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A? Pick:
A) 12	B) 31	C) 16	D) 18	E) 10

Solution: (12 + B) - (B + C) = 12   12 - C = 12   12nswer: 12
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 46 kg, then the weight of B is:
Choose the correct answer:
A) 31 kg	B) 32 kg	C) 37 kg	D) 34 kg	E) None of these

Solution: Explanation:   Let A, B, C represent their respective weights. Then, we have:   A + B + C = (45 x 3) = 135 …. (i)   A + B = (40 x 2) = 80 …. (ii)   B + C = (46 x 2) = 92 ….(iii)   Adding (ii) and (iii), we get: A + 2B + C = 172 …. (iv)   Subtracting (i) from (iv), we get : B = 37.   B’s weight = 37 kg.   Answer: 37 kg
Answer: C
Let a be a positive integer. If r is divisible by 2^a and r is also divisible by 3^(2a), then it is possible that r is NOT divisible by
Options
A) 6	B) 3 × 2^a	C) 2 × 3^(2a)	D) 6^a	E) 6^(2a)

Solution: Since, r is divisible by 2^a and 3^(2a), it must be divisible by 6. As least value of a = 1   Only for 6^(2a), 6^(2a) doesn't satisfy, if a = 1 and r=18, it is not divisible by 6^2 (i.e 36)   Hence answer is 6^(2a)
Answer: E
The speed at which a man can row a boat in still water is 6 km/hr. If he rows downstream, where the speed of current is 3 km/hr, how many seconds will he take to cover 110 meters?
Choose the correct choice from the following answers.
A) 40 B) 44 C) 48 D) 52 E) 56

Solution: The speed of the boat downstream = 6 + 3= 
6 + 3 = 9
9 km/hr   9 km/hr * 5/18= 2.5 m/s   The time taken to cover 110 meters = 110/2.5= 
110/2.5 = 44
44 seconds.   The answer is 44.
Answer: B
A focus group is currently made up of x red balls and y green balls. If 5 red balls and 4 green balls are added to the group, and if one ball is selected at random from the larger focus group, then what is the probability that a green ball is selected?	Choose the correct choice:
A) y/x+5
B) y/x+4
C) (y+5)/(x+y+9)
D) (y+4)/(x+y+9)
E) (x+4)/(x+y+9)

Solution: x red balls   y green balls   x+4+y+5 is the total   =x+y+9   y+4 is the number of green balls   so (y + 4)/(x + y + 9)   the answer is (y+4)/(x+y+9)
Answer: D
10^9 - 10^2 is approximation of which of the following? Options:
A) 9^7
B) 9^8
C) 9^9
D) 9^11
E) 10^9

Solution: => Since 9^2 is a small number compared to 10^9, it can be disregarded. Thus, 10^9-10^2=10^9 is derived and the answer is 10^9.
Answer: E
If x, y, and f are positive numbers such that 10*x/(x+y)+ 20*y/(x+y)=f and if x is less than y, which of the following could be the value of f?
Choose the correct choice from the following answers
A) 10	B) 12	C) 15	D) 18	E) 30

Solution: Answer choice C: f= 15   (10x + 20y)/(x+y) = 15   10x + 20y = 15x + 15y   5y = 5x   y = x   Doesn't work because the problem states that x<y.   We need y to be larger, so let's try answer choice D: f=18   10x + 20y = 18x + 18y   2y = 8x   y/x = 8/2   Success! x<y.   The correct answer is 18.
Answer: D
Find the average of first 8 multiples of 5? Choose the correct option
A) 10  B) 15  C) 12.5  D) 22.5  E) 21

Solution: average = (5+10+15+20+25+30+35+40)/8= 
(5+10+15+20+25+30+35+40)/8 = 45/2 = around 22.5
22.5   Answer is 22.5
Answer: D