MU-NLPC/Calc-aqua_rat huggingface dataset:
Ms. Feldman invested $10,000 for 1 year, part at 7% and part at 6.25%.
If she earned a total interest of $656.50, how much was invested at each rate?  Choices:
A) 4200 & 5800  B) 4600 & 5400  C) 9000 & 1000  D) 7000 & 3000  E) 6000 & 4000

Solution: Interest rate of 4200/- =294   Interest rate of 5800/- =362.50   4200 & 5800nswer is 4200 & 5800
Answer: A
A boat can travel with a speed of 24 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 196 km downstream  Choose the correct choice from the following choices.
A) 3 hours	B) 4 hours	C) 5 hours	D) 6 hours	E) 7 hours

Solution: 7 hoursxplanation:   Speed of the boat in still water = 24 km/hr   speed of the stream = 4 km/hr   Speed downstream = (22+5) = 28 km/hr   Distance travelled downstream = 196 km   Time taken = distance/speed = 196/28= 
196/28 = 7
7 hours   Answer: Option 7 hours
Answer: E
If x > y^4 > z^7, which of the following statements could be true? I.x>y>z II.z=x III.x<z	Choose the correct choice from the following answers:
A) I,III only	B) I only	C) II only	D) III only	E) I,II only

Solution: Answer : I only
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 red ball is selected?  Choose the correct choice from the following options:
A) x/(x + 4)  B) y/(x + 5)  C) (x + 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   x+5 is the number of red balls   so (x + 5)/(x + y + 9)   the answer is (x + 5)/(x + y + 9)
Answer: C
A train 275 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
Choose the most appropriate option.
A) 8
B) 6
C) 5
D) 15
E) 1

Solution: Speed of train relative to man = 60 + 6= 
60 + 6 = 66
66 km/hr.= 66 * 5/18 = 55/3 m/sec.   Time taken to pass the men = 275 * 3/55= 
275 * 3/55 = 15
15 sec.   Answer: 15
Answer: D
Two pipes A and B can fill a cistern in 37.5 minutes and 45 minutes respectively. This cistern will be filled in half an hour if both the pipes are opened together initially and pipe B is then turned off after X minutes. What is X?	Choose the correct choice
A) 10 minutes
B) 15 minutes
C) 12 minutes
D) 9 minutes
E) 8 minutes

Solution: Explanation:   Let B be turned off after X minutes.   Part of water will be filled by A + B in x minutes + After tap B is closed rest filled by A in (30-x) minutes = 1   => x/(time taken to fill the container by each separately) + 30 - x/(time taken to fill the container by A alone) = 1   => x(2/75 + 1/45) + (30-x)2/75 = 1   => 11x + 180 – 6x = 225   Therefore, x = 9 minutes   ANSWER: 9 minutes
Answer: D
Mira is making telescopes, each consisting of 2 lenses, 1 tube, and 1 eyepiece. Lenses can be purchased only in packs of 50, tubes only in packs of 10, and eyepieces only in packs of 30. However, half of the lenses in each pack are not usable for telescopes. If all parts are used only for the telescopes, what is the minimum number of lenses Mira must purchase to make a set of telescopes with no leftover components other than the unusable lenses?  Choose the correct choice from the following answers.
A) 75 B) 150 C) 300 D) 1200 E) 7,500

Solution: I'd use backsolving for this question. Check option C first:   300 lenses = 150 usable lenses = 75 tubes = 75 eyepieces. We cannot buy 75 tubes or 75 eyepieces, so that not to have leftovers.   A and B are automatically out. Check D:   1200 lenses = 600 usable lenses = 300 tubes = 300 eyepieces. We CAN buy 300 tubes and 300 eyepieces, so that not to have leftovers.   Answer: 1200.
Answer: D
Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
Select the correct option.
A) 26 km/hr  B) 17 km/hr  C) 60 km/hr  D) 77 km/hr  E) 46 km/hr

Solution: Let the speed of the slower train be x m/sec.   Then, speed of the train = 2x m/sec.   Relative speed = ( x + 2x) = 3x m/sec.   (100 + 100)/8 = 3x => x = 25/3.   So, speed of the faster train = 50/3 = 50/3 * 18/5= 
50/3 * 18/5 = 60
60 km/hr.   Answer:60 km/hr
Answer: C
J is 25% less than P and 20% less than T. T is x% less than P. What is the value of x?
Choose the correct choice:
A) 93.5 B) 90 C) 6.75 D) 6.25 E) 2

Solution: Let, P = 400   then J = (75/100)*400= 
(75/100)*400 = 300
300   also J= (80/100)*T   i.e. T = 300*100/80= 
300*100/80 = 375
375   and T= [1-(x/100)]*P   i.e. 100-x = 100*T/P = 100*375/400= 
100*375/400 = 375/4 = around 93.75
93.75   i.e. x= 6.25   Answer: Option 6.25
Answer: D
The monthly rent of a shop of dimension 10feet × 8feet is Rs.2400. What is the annual rent per square foot of the shop?
Choose the most appropriate option.
A) 43  B) 56  C) 68  D) 360  E) 92

Solution: Sol. Monthly rent per square feet = 2400/(10*8)= 
2400/(10*8) = 30
30   & Annual rent per square feet=12*30= 
12*30 = 360
360   Answer : 360
Answer: D
Tomy's age 18 years hence will be thrice his age four years ago. Find Tomy's present age?	Choose the correct choice from the following
A) 12 years	B) 13 years	C) 15 years	D) 17 years	E) 18 years

Solution: Let MTomy's present age be 'x' years.   x+ 18 = 3(x- 4)   => 2x = 30 => x = 15 years.   15 years
Answer: C
Sum of 42 odd numbers is? Choose the correct answer:
A) 1764  B) 1774  C) 1784  D) 1794  E) 1754

Solution: sum of 1st n odd no.s = 1+3+5+7+... = n^2   so, Sum of 1st 42 odd numbers = 42^2 = 1764   1764NSWER:1764
Answer: A
A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.196 where as B does not. In what ratio should they divide the second year's profit? Select the correct option:
A) 39:40	B) 39:49	C) 24:25	D) 39:47	E) 39:41

Solution: Explanation:   3: 4   A = 3/7*196= 
3/7*196 = 84
84   384: 400   24:25   Answer:24:25
Answer: C
A certain no. when divided by 35leaves a remainder 25, what is the remainder if the same no.be divided by 15?
Choose the correct choice from the following
A) 2  B) 4  C) 7  D) 8  E) 9

Solution: Explanation:   35 + 25= 
35 + 25 = 60
60/15= 
60/15 = 4
4 (Remainder)   4
Answer: B
The probability that event A occurs is 0.4, and the probability that events A and B both occur is 0.25. If the probability that either event A or event B occurs is 0.6, what is the probability that event B will occur?	Select.
A) 0.05
B) 0.15
C) 0.45
D) 0.5
E) 0.55

Solution: P(A or B) = P (A) + P(B) - p(a n b)   0.6= 0.4 + P(B) - 0.25   P(B) = 0.45   ANSWER:0.45
Answer: C
A right triangle ARC has to be constructed in the xy-plane so that the right angle is at A and AR is parallel to x axis. The coordinates of A, R and C are integers and satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. How many different triangles can be constructed with these properties? Choose the correct choice from the following options
A) 63	B) 336	C) 567	D) 3024	E) 5040

Solution: All the cordinates are integer hence,   possible AR values are   {-1,0}, {-1,1} ....{-1,7}: 8 ways   ....   {7,-1}, {7,0} ......{7,6}: 8 ways     9*8= 
  9*8 = 72
72   for AC values can be   {1,2}, {1,3} .... {1,7} : 6ways   ......   {7,1}, {7,2} ..... {7,6} : 6 ways     7*6= 
  7*6 = 42
42   Total= 72 * 42= 
72 * 42 = 3_024
3024 hence 3024
Answer: D
In how many different number of ways a Committee of 3 person of can be selected from 5 men and 3 women such that atleast 1 women is included in the committee  Choose the correct option:
A) 36	B) 46	C) 50	D) 52	E) 56

Solution: 1W 2M 2W 1M 3W   = 3C1 × 5C2 + 3C2 × 5C1 + 3C3s   = 3 × (5 × 4)/2 + 3 × 5 + 1   = 30 + 15 + 1= 
30 + 15 + 1 = 46
46   Total 5M 3W   8C3= 56   5C3 = 10   At least one women = total - with out women   At least one women = 56 - 10= 
56 - 10 = 46
46   46)
Answer: B
An error 2% in excess is made while measuring the side ofa square. The % of error in the calculated area of the square is?  Choose the correct choice from the following.
A) 4% B) 4.04% C) 4.23% D) 4.56% E) 5%

Solution: 100 cm is read as 102 cm.   A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.   (A2 - A1) = [(102)2 - (100)2]   = (102 + 100) x (102 - 100)   = 404 cm2.   Percentage error = 404 x 100 % = 4.04%   100 x 100   4.04%
Answer: B
A train passes a station platform in 36 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?
Select:
A) 240  B) 377  C) 2908  D) 287  E) 201

Solution: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.240nswer: 240
Answer: A
he speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?	Select the correct option
A) 25 kmph
B) 15 kmph
C) 17 kmph
D) 95 kmph
E) 14 kmph

Solution: 90 * 10/60= 
90 * 10/60 = 15
15 kmph   Answer:15 kmph
Answer: B
In 2010, Arman’s birthday was on a Thursday. What day of the week was it 66 days after his birthday?  Choose the correct choice from the following answers.
A) Thursday	B) Friday	C) Saturday	D) Sunday	E) Monday

Solution: Day of week after 66 days after Arman's birthday = 7*9 + 3   Saturday as the period will have 9 weeks and 3 days .   The 3 days in the end will be Friday - Saturday and Sunday   Answer Sunday
Answer: D
Find the fraction which has the same ratio to 1/2 that 2/5 has to 3/7 Pick one
A) 1/2 B) 2/12 C) 14/30 D) 3/8 E) 7/9

Solution: A : 1/2 = 2/5 : 3/7   As the product of the means is equal to the product of the extremes.   A*3/7 = 1/2 * 2/5   A*3/7 = 2/10   A = 14/30 => A = 14/30   ANSWER:14/30
Answer: C
The ratio of the ages of Maala and Kala is 3 : 5. The total of their ages is 3.2 decades. The proportion of their ages after 0.8 decades will be
[1 Decade = 10 years] Choose the correct choice
A) 6:5
B) 5:7
C) 4:5
D) 7:9
E) 3:6

Solution: Let, Maala’s age = 3A and Kala’s age = 5A   Then 3A + 5A = 32   A = 4   Maala’s age = 12 years   and Kala’s age = 20 years   Proportion of their ages after 8 is = (12 + 8) : (20 + 8)   = 20 : 28   = 5 : 7   Answer : 5:7
Answer: B
The smallest 3 digit prime number is Select.
A) A)103 B) B)101 C) C)109 D) D)113 E) E)None

Solution: The smallest 3-digit number is 100, which is divisible by 2.   100 is not a prime number.   101 < 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11.   101 is a prime number.   Hence 101 is the smallest 3-digit prime number.   101)
Answer: B
John can complete a given task in 20 days. Jane will take only 12 days to complete the same task. John and Jane set out to complete the task by beginning to work together. However, Jane was indisposed 5 days before the work got over. In how many days did the work get over from the time John and Jane started to work on it together? Choose the correct choice from the following answers.
A) 95/8	B) 93/8	C) 90/8	D) 12	E) 10

Solution: In such questions, you need to start from the end. Last 4 days John works alone and completes 5 * (1/20) = 1/4 of the work.   So 3/4 of the work should have been completed by the two of them together before Jane left.   Their combined rate of work is 1/20 + 1/12 = 8/60   Time taken to complete 3/4 of the work = (3/4)/(8/60) = 45/8 days.   So total number of days taken to complete the work = 45/8 + 5 = 95/8 days.   95/8
Answer: A
What is the next number of the following sequence
4, 16, 12, 48, 44, 176 (...)	Choose one
A) 142
B) 146
C) 154
D) 168
E) 172

Solution: The series is   4*4= 
4*4 = 16
16   16-4= 
16-4 = 12
12   12*4= 
12*4 = 48
48   48-4= 
48-4 = 44
44   44*4= 
44*4 = 176
176   176-4= 
176-4 = 172
172   ANSW172R: 172
Answer: E
A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 200 per month. What is his monthly salary? Choices:
A) Rs.5000
B) Rs.25000
C) Rs.7500
D) Rs.8500
E) Rs.9500

Solution: Income = Rs. 100   Expenditure = Rs. 80   Savings = Rs. 20   Present Expenditure 80*(20/100) = Rs. 96   Present Savings = 100 – 96 =Rs. 4   100 ------ 4   ? --------- 200 => 5000   Rs.5000NSWER:Rs.5000
Answer: A
There is a 20% chance that Lions will not win at all during the whole season. There is a 30% chance that Tigers will not play at all in the whole season. What is the greatest possible probability that the Lions will win and Tigers will play during the season?  Choose the correct choice:
A) 55% B) 60% C) 70% D) 72% E) 80%

Solution: There is a 20% chance that Lions will not win at all during the whole season   We can infer that there is 80% chance Lions will win .   Similarly There is a 30% chance that Tigers will not play at all in the whole season   We can also infer that there is 70% chance that Tigers will play.   Answer 70%
Answer: C
If A and B are two events such that P (A) = 1/2, P (B) = 3/4 and P (A n B) = 3/8,
find P (not A and not B).  Choose the correct choice from the following answers.
A) A)1/7
B) B)1/8
C) C)1/9
D) D)1/10
E) E)2/11

Solution: P(not A and not B) = 1 - (P(A) + P(B) - P(AB))   which you might find somewhere in your text.   Substituting in our probabilities we get:   P(not A and not B) = 1 - (1/2 + 3/4 - 3/8)   P(not A and not B) = 1 - (7/8)   P(not A and not B) = 1/8.   1/8
Answer: B
If b= (a-1)(a+2), then what is the least possible value of b?
Choices.
A) -9/4  B) 3  C) 2  D) 1  E) 0

Solution: -9/4nswer : -9/4
Answer: A
The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 140 runs and his average excluding these two innings is 58 runs, find his highest score.
Choose the correct choice from the following answers:
A) 179	B) 367	C) 269	D) 177	E) 174

Solution: Explanation:   Total runs scored by the batsman = 60*46= 
60*46 = 2_760
2760 runs   Now excluding the two innings the runs scored= 58*44= 
58*44 = 2_552
2552 runs   Hence the runs scored in the two innings= 2760 â€“ 2552 = 208 runs.   Let the highest score be x, hence the lowest score = x â€“ 140   x + (x - 140) = 208   2x = 348   x = 174 runs   ANSW174R: 174
Answer: E
There are 8 books in a shelf that consist of 2 paperback books and 6 hardback books. If 3 books are selected at random without replacement, how many different combinations are there that at least one paperback book is selected? Choose the correct choice from the following choices
A) 36
B) 45
C) 50
D) 55
E) 60

Solution: 8C3 [Select any four] - 6C3 [Select all hard backs] = 36.   36
Answer: A
If a and y are integers and (15^a + 15^(a+1))/4^y = 15^y what is the value of a?	Choose the correct choice:	A) 2	B) 3	C) 4	D) 5	E) Cannot be determined

Solution: \frac{15^a( 1+ 15)}{4^y} = 15^y   (15^a . 4^2 ) / 4^y = 15^y. 4^0   15^a . 4^(2-y) = 15^y. 4^0   Equating the powers, a = y; 2-y = 0; So a = y = 2=2
Answer: A
6 points are marked on a straight line and another 7 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points?	Choose the most appropriate option:
A) 9	B) 105	C) 196	D) 21	E) 14

Solution: assuming that the top line can have either 2 points or 1 point...   6! / 1!5! - 6! / 2! 4! yields 9.   9
Answer: A
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:  Select
A) 200m B) 225m C) 245m D) 250m E) 260m

Solution: Speed = 45/18 x	5	m/sec	= 25/2	m/sec.   Time = 30 sec.   Let the length of bridge be x metres.   Then,	130 + x/ 30	=	25/2   2(130 + x) = 750   x = 245 m.   ANSWER IS 245m
Answer: C
Jim rides the bus to and from school each day. A one-way trip is 8.12 kilometers. How many kilometers does he travel in 3 days? Select:
A) 77km
B) 56km
C) 25.9km
D) 48.72km
E) 50km

Solution: 1 day=2 trips,   3 days=2*3= 
2*3 = 6
6 trips   6*8.12= 
6*8.12 = 48.72
48.72km.   Answer is 48.72km.
Answer: D
If the number of 53,n87, where n represents the hundreds digit, is a multiple of 3, then the value of n could be which of the following?
Choose one:	A) 0	B) 1	C) 2	D) 3	E) 4

Solution: Then for any number to be a multiple of 3,The sum of its digits should be the multiple of 3.   i.e 5+3+n+8+7 = multiple of three   or, 23 + n = multiple of 3.   If n=1, 23 + n =24,which is a multiple of 3.   Hence answer is 1.
Answer: B
A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is
Choose the correct answer:	A) 7/19	B) 6/19	C) 5/19	D) 4/19	E) None of these

Solution: Explanation:   Please remember that Maximum portability is 1.   So we can get total probability of non defective bulbs and subtract it form 1 to get total probability of defective bulbs.   So here we go,   Total cases of non defective bulbs   16C2=16∗15/2∗1=120   total cases = 20C2=20∗19/2∗1=190   probability = 120/190=12/19   P of at least one defective = 1−12/19=7/19   Option 7/19
Answer: A
The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is?
Choose the correct answer:
A) Rs. 3000
B) Rs. 4000
C) Rs. 5000
D) Rs. 6000
E) Rs. 7000

Solution: Let P, Q and R represent their respective monthly incomes. Then, we have:   P + Q = (5050 x 2) = 10100 .... (i)   Q + R = (6250 x 2) = 12500 .... (ii)   P + R = (5200 x 2) = 10400 .... (iii)   Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 or P + Q + R = 16500 .... (iv)   Subtracting (ii) from (iv), we get P = 4000.   P's monthly income = Rs. 4000.   Rs. 4000)
Answer: B
The mean of 50 observations is 200. But later he found that there is decrements of 34 from each observations. what is the the updated mean is ?
Choose the correct choice:
A) 165 B) 166 C) 190 D) 198 E) 199

Solution: 166   Answer is 166
Answer: B
X and Y run a 50 m race,where X beats Y by 5 m. To do a favor to Y, X starts 5 m behind the starting line in a second 50 m race. Both run at the same previous speed. Which of the following is true?
Choose the correct choice from the following answers:	A) X Beats Y by 2m	B) X Beats Y by 0.5 m	C) Y Beats X by 10m	D) Y Beats X by 11m	E) Y Beats X by 11m

Solution: Let's suppose that the speed of X is 5m/s and that the speed of Y is 4.5m/s.   So, in the first race, the results are the following:   X crosses the finish line in 10s. In other words, X has run 50 m in 10 s.   In 10s, Y has run 45 meters.   Therefore, there is the difference of 5 meters mentioned in the question.   Now, let's review the second race.   In 11 seconds, X can complete the 50 meters race. We have to remember that X is 5 meters behind the starting line.   But in 11 seconds, Y has covered (45+4.5 )= 
(45+4.5 ) = 49.5
49.5 meters. Also, it is important to notice that in 11 seconds Y cannot arrive to the finish line.   So, 50- 49.5= 0.5 meter   Answer: X Beats Y by 0.5 m
Answer: B
What is the perimeter of a regular polygon with sides of length 15 cm and internal angles measuring 144° each?
Choose the correct choice from the following answers.
A) 96 cm B) 108 cm C) 120 cm D) 132 cm E) 150 cm

Solution: Sum of all interior angles is given by:   180(n-2) = n is number of sides   180(n-2) = 144*n   from here   n = 10   So perimeter becomes 15*10= 
15*10 = 150
150   answer 150 cm
Answer: E
Working together, John and Jack can type 10 pages in one hour. If they would be able to type 12 pages in one hour if Jack increases his typing speed by 25%, what is the ratio of Jack's normal typing speed to that of John? Choose the correct choice
A) 3/1 B) 1/3 C) 4/1 D) 1/4 E) 5/4

Solution: Lets say John types x pages an hour and Jack types y pages an hour.   We know that x+y=10   Jack increase speed by 25% means he will type 1.25y pages an hour.   So we get x+1.25y=12   We need to know the ratio of Jack's speed to John's speed. This is going to be proportional to the number of pages each can type in an hour, hence (y/x).   Subtracting both : 0.25y=2 so y=8 ... so x=2   (y/x)=8/2= 
8/2 = 4
4/1   Answer is (4/1)
Answer: C
3^x + 9*3^-x = 6 What is the value of x?
Select the correct option
A) -1 B) 1 C) 0 D) 1/2 E) -1/2

Solution: let 3^x = t   t+9/t =6   t^2 -6t +9 =0   (t-3)^2=0   t-3=0   t=3   3^x=3   x=1   Ans: 1
Answer: B
A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Euro 1000 more than D, what is B's share?	Answers
A) Euro 1000	B) Euro 3000	C) Euro 5000	D) Euro 4000	E) Euro 2000

Solution: E   Euro 2000   Let the shares of A, B, C and D be Euro 5x, Euro 2x, Euro 4x and Euro 3x respectively.   Then, 4x - 3x = 1000   x = 1000.   B's share = Euro 2000uro 2x = Euro 2000uro (2 x 1000) = Euro 2000uro 2000.
Answer: E
The average age of a husband and his wife was 23 years at the time of their marriage. After five years they have a one-year old child. The average age of the family now is : Choose the most appropriate option:
A) 25	B) 23	C) 19	D) 18	E) 17

Solution: Explanation:   Sum of the present ages of husband, wife and child = (23 * 2 + 5 * 2) + 1= 
(23 * 2 + 5 * 2) + 1 = 57
57 years.   Required average= (57/3)= 
(57/3) = 19
19 years. Answer: 19
Answer: C
The sum of money will be double itself in 10years and simple interest find rate of interest?	Select the correct option:	A) 10%	B) 15%	C) 20%	D) 25%	E) 30%

Solution: T = 10 years   P= principle amount = x   10% = total amount = 2x   SI = simple interest = 10%-P = 2x-x = x   R = 100SI/PT = 100x/10x =10%   10%nswer is 10%100 /10= 
100 /10 = 10
10%   10%nswer is 10%
Answer: A
Chocolate bars are sold in packages of four or nine only. If Mark bought 97 chocolate bars exactly, what could be the number of large packs Mark bought?
Pick one
A) 3	B) 4	C) 8	D) 9	E) 13

Solution: Let number of packs of four = f   let number of packs of nine = n   4f + 9n = 97   Now , we need to test for values of n.   Since sum 97 is odd and 4f will always be even , n can't be even .   Now , we can test for values e = 2 , 4 and 6   4*4 + 9*9 = 16 + 81= 
16 + 81 = 97
97   Answer 9
Answer: D
For the FIFA world cup, Paul the octopus has been predicting the winner of each match with amazing success. It is rumored that in a match between 2 teams A and B, Paul picks A with the same probability as A's chances of winning. Let's assume such rumors to be true and that in a match between Ghana and Bolivia, Ghana the stronger team has a probability of 2/3 of winning the game. What is the probability that Paul will correctly pick the winner of the Ghana-Bolivia game?
Options
A) 1/9  B) 4/9  C) 5/9  D) 2/3  E) 1/3

Solution: Paul picks A with the same probability as A’schances of winning   So probability of picking a winner = prob picking of ghana * ghana winning + prob picking of bolivia * bollivia winning   = 2/3 * 2/3 + 1/3 * 1/3   = 5/9   ANSWER:5/9
Answer: C
If Susan takes 8 seconds to run y yards, how many minutes will it take her to run x yards at the same rate?	Choices.
A) xy/8
B) 8x/(60y)
C) 60xy/8
D) xy/480
E) 480x/y

Solution: The answer is B.   She runs x yards in 8x/y seconds =8x/60y minutes.
Answer: B
A, B, C enter into a partnership investing Rs. 35,000, Rs. 45,000 and Rs. 55,000 respectively. The respective shares of A, B, C in annual profit of Rs. 40,500 are?  Choose the correct choice from the following answers:
A) Rs. 10,500, Rs. 13,500, Rs. 16,500
B) Rs. 10,600, Rs. 13,500, Rs. 96,500
C) Rs. 10,500, Rs. 73,500, Rs. 16,500
D) Rs. 10,500, Rs. 18,500, Rs. 16,500
E) Rs. 40,500, Rs. 13,500, Rs. 16,500

Solution: A:B:C = 35000 : 45000 : 55000 = 7:9:11   A's share = 40500 * 7/27 = Rs. 10500   B's share = 40500 * 9/27 = Rs. 13500   C's share = 40500 * 11/27 = Rs. 16500   Rs. 10,500, Rs. 13,500, Rs. 16,500nswer:Rs. 10,500, Rs. 13,500, Rs. 16,500
Answer: A
In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?  Choose one:
A) 44	B) 73	C) 53	D) 32	E) 62

Solution: A   44   Let the capacity of the can be T litres.   Quantity of milk in the mixture before adding milk = 4/9 (T - 8)   After adding milk, quantity of milk in the mixture = 6/11 T.   6T/11 - 8 = 4/9(T - 8)   10T = 792 - 352 => T = 44.
Answer: A