MU-NLPC/Calc-aqua_rat huggingface dataset:
What number has a 5:1 ratio to the number 10?	Pick one:
A) 74
B) 50
C) 94
D) 59
E) 48

Solution: Answer: Option 50   Explanation:   5:1 = x: 10   x = 50   Answer: Option 50
Answer: B
In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 4 out of 10 consecutive days in Rwanda?
Choose the most appropriate option
A) 4/7	B) 3/7	C) 105/512	D) 4/28	E) 28/135

Solution: using Binomial. theorem   n105/512r (p)^r (q)^n-r   10105/5124 (1/2)^4 (1/2)^r   which is 105/512   Answer is 105/512.
Answer: C
A walks at 10 kmph and 10 hours after his start, B cycles after him at 20 kmph. How far from the start does B catch up with A? Choose the correct choice from the following options:
A) 100km
B) 150km
C) 50km
D) 120km
E) 200km

Solution: Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 10 hours.   x/10 - x/20 = 10   x = 200 km   Answer is 200km
Answer: E
20% of a 6 liter solution and 60% of 4 liter solution are mixed. What percentage of the mixture of solution Choices
A) 36%	B) 18%	C) 35%	D) 34%	E) 30%

Solution: 20% of 6 lit =6/5   60% of 4 lit =12/5   (6/5) + (12/5) =18/5   percentage of 10 lit = (18/5)*(1/10)*100= 
(18/5)*(1/10)*100 = 36
36% 36%NSWER:36%
Answer: A
Ravi purchased a car and a mobile phone for Rs. 150000 and Rs. 10000 respectively. He sold the refrigerator at a loss of 2 percent and the mobile phone at a profit of 10 percent. Overall he make a.
Choose the correct choice from the following.
A) loss of Rs. 200  B) loss of Rs. 2000  C) profit of Rs. 100  D) profit of Rs. 200  E) None of these

Solution: Total C.P. = 150000+10000= 
150000+10000 = 160_000
160000   S.P. of car= 150000/100*98= 
150000/100*98 = 147_000
147000   S.P. of Mobile= 10000/100*110= 
10000/100*110 = 11_000
11000   Total S.P.= 147000 + 11000= 
147000 + 11000 = 158_000
158000   Tota. S.P. - Total C.P.= 158000 - 160000 = -2000   Answer : loss of Rs. 2000
Answer: B
If a positive integer n is divisible by both 2 and 7, then n must also be divisible by which of the following?
I. 14
II. 9
III. 42	Choose the most appropriate option:
A) None
B) I only
C) II only
D) I and II
E) II and III

Solution: A multiple of 2 and 7 is also a multiple of 14, but not necessarily a multiple of 9 or 42.   The answer is I only.
Answer: B
A student chose a number, multiplied it by 4, then subtracted 138 from the result and got 102. What was the number he chose?  Pick
A) 60 B) 120 C) 130 D) 140 E) 150

Solution: Solution:   Let xx be the number he chose, then   4⋅x−138=102   4x=240   x=60   60nswer 60
Answer: A
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? Choose the correct choice
A) 289 m B) 676 m C) 240 m D) 239 m E) 186 m

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.   Answer:240 m
Answer: C
If a is a positive integer then 6^(2a) + (144^a)/(2^(2a)) = Choices
A) 2 × 36^a B) 2 / 36^a C) 3 × 36^a D) 2 × 64^a E) 2 × 18^a

Solution: 6^(2a) + 144^a/ 2^(2a) = 36^a + 144^a/4^a = 36^a + (144/4)^a + 144  /4= 
+ 144  /4 = 36
36^a + (144/4)= 
+ (144/4) = 36
36^a + 36^a= 2 × 36^a   2 × 36^answer : 2 × 36^a
Answer: A
A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?	Pick:	A) 30/16	B) 30/10	C) 30/14	D) 30/13	E) 30/11

Solution: Speed downstream = 20 + 6= 
20 + 6 = 26
26 kmph.   Time required to cover 60 km downstream= d/s = 60/26 = 30/13 hours. Answer:30/13
Answer: D
The profit earned by selling on article for 900 is double the loss incurred when the same article is sold for 450. At what price should the article be sold to make 25% profit?  Choose the correct choice from the following answers.
A) 750
B) 800
C) 850
D) 860
E) 890

Solution: Let ‘x’ be the CP of the article;   Then 900 – x = 2(x – 450); :. x= 600.   25% of 600 = 150   :. New SP = 600 + 150= 
600 + 150 = 750
750   Option '750'
Answer: A
There are some pigeons and hares in a zoo. If heads are counted, there are 200. If legs are counted, there are 480. The number of hares in the zoo is?
Choose one
A) 40
B) 99
C) 77
D) 66
E) 221

Solution: 200*2= 
200*2 = 400
400   480   -----   80   1----2   ?----80= 40   40nswer:40
Answer: A
A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?  Choose the correct choice from the following answers.
A) Rs. 4991  B) Rs. 5991  C) Rs. 6001  D) Rs. 6991  E) Rs. 6976

Solution: Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.   Required sale = Rs. [ (6500 x 6) - 34009 ]   = Rs. (39000 - 34009)   = Rs. 4991.   Rs. 4991nswer:Rs. 4991
Answer: A
The probability of pulling a black ball out of a glass is 1/X. The probability of pulling a black ball out of a glass and breaking the glass is 1/Y. What is the probability of breaking the glass?	Select the correct option
A) 1/(XY).
B) Y/X
C) X/Y
D) 1/(X+Y).
E) 1/(X-Y).

Solution: pulling a black ball out of a glass and breaking the jar both are independent events.   For 2 independent events, we know, P(a) * P(b) = P(a∩b)   If Prob of pulling a black ball out of a glass = P(a) and Prob of breaking the glass= P(b)   1/x * P(b) = 1/y ---> P(b) = x/y   Hence, answer should be X/Y.
Answer: C
A statue is being carved by a sculptor. The original piece of marble weighed 200 kg. In the first week 20 percent is cut away. In the second week 25 percent of the remainder is cut away. In the third week the statue is completed when 35 percent of the remainder is cut away. What is the weight of the final statue?
Pick.
A) 97.5 kg	B) 103 kg	C) 108 kg	D) 125 kg	E) 117 kg

Solution: 97.5 kg   97.5 kg   250 Ã— 0.8 Ã— 0.75 Ã— 0.65 = 97.5 kg.
Answer: A
A collection of books went on sale, and 2/3 of them were sold for $1.50 each. If none of the 36 remaining books were sold, what was the total amount received for the books that were sold? Select:	A) $180	B) $135	C) $108	D) $60	E) $54

Solution: Since 2/3 of the books in the collection were sold, 1/3 were not sold. The 36 unsold books represent 1/3 of the total number of books in the collection, and 2/3 of the total number of books equals 2(36) or 72. The total proceeds of the sale was 72($1.50) or $108. The best answer is therefore $108.
Answer: C
If the perimeter of a rectangular garden is 500 m, its length when its breadth is 100 m is?
Select
A) 299 m	B) 777 m	C) 200 m	D) 167 m	E) 150 m

Solution: 2(l + 100) = 500 => l   = 150 m   Answer:150 m
Answer: E
At what rate percent on simple interest will Rs.1800 amount to Rs.2000 in 5 years? Choose the correct choice from the following choices:
A) 4 %  B) 3 6/7 %  C) 2 6/7 %  D) 3.47%  E) 6 %

Solution: Explanation:   250 = (1800x5xR)/100   R = 3.47%   Answer: Option 3.47%
Answer: D
we have 5 weights one of 2 kg one of 3 kg one of 5 kg one of 1 kg one of 10 kg by using only four weight how many wight u can weight
Choose one:
A) 1	B) 2	C) 3	D) 4	E) 5

Solution: select 4 weight out of 5, 5C4=5   ANSW5R:5
Answer: E
In a Lake, there is a patch of lily pads. Every day, the patch doubles in size. It takes 25 days for the patch to cover the entire lake, how many days would it take the patch to cover half of the lake? Choose the correct choice from the following options:  A) 36  B) 2^4*3  C) 24  D) 38  E) 47

Solution: So 24 days   Answer 24=24
Answer: C
Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 14 days. If B starts, they take a day more. How long does it take to complete the task if they both work together?	Answers.
A) 12	B) 14	C) 10	D) 11	E) 13

Solution: Work done by AB in a day = xy respectively.   When A starts:   No. of days when A works = 8No. of days when B works = 6 → 8x + 6y = 1   When B starts:   No. of days when A works = 7No. of days when A works = 7 → 7x + 7y = 1   Solving the above two equations for xy   x = 1/14 y = 1/14   → Total work done by AB in a day = 1/14 + 1/14 = 2/28= 1/14   → No. of days to complete the work when both work together =14   Answer: 14
Answer: B
A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount was offered? Options.
A) 70%	B) 60%	C) 30%	D) 10%	E) 20%

Solution: Explanation:   Let C.P. be Rs. 100.   Then, S.P. = Rs. 123.50   Let marked price be Rs. x. Then, 95/100 x = 123.50   x = 12350/95 = Rs. 130   Now, S.P. = Rs. 130, C.P. = Rs. 100   Profit % = 30%.   Answer 30%
Answer: C
How much is 40% of 60 is greater than 4/5 of 25? Options.
A) 2
B) 5
C) 12
D) 8
E) 4

Solution: (40/100) * 60 â€“ (4/5) * 25   24 - 20= 
24 - 20 = 4
4   Answer: 4
Answer: E
A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work done?
Choose the correct answer
A) 14 days	B) 21 days	C) 22 days	D) 11 days	E) 43 days

Solution: 11 days   11 days   x/24 + x/30 + x/40 = 1   x = 11 days
Answer: D
From 2008 to 2009, the number of Easter eggs in a certain egg hunt rose 20%, then fell 17% from 2009 to 2010. From 2008 to 2009, the ratio of Easter eggs to Easter bunnies in the same hunt fell 20%, then rose 22% from 2009 to 2010. By what approximate percent did the number of bunnies change over the full period from 2008 to 2010?	Choose the correct choice from the following answers:
A) 5% increase  B) 2% increase  C) 1% decrease  D) 3% decrease  E) 6% decrease

Solution: Let the number of Easter eggs be x1 in 2008 and x2 in 2010   Given that it rose 20% in 2009 and then fell 17% in 2010   =>x2 = (0.83)(1.2)x1 ---(1)   Let the number of Easter bunnies be y1 in 2008 and y2 in 2010   Given that the ratio of x to y fell 20% in 2009 and then rose 22% in 2010   => x2/y2 = (0.8)(1.22)(x1/y1)   => y1/y2 = (0.8)(1.22)(x1/x2) ----(2)   substituting (1) in (2),   y1/y2 = (0.8)(1.22)/(0.83)(1.2)   => y2/y1 = (0.83)(1.2)/(0.8)(1.22) = 249/244   % change in y2 from y1 = (y2-y1)*100/y1   = (y2/y1 - 1)*100 = (249/244 - 1)*100   = (5/244)*100 = +2%   It's a 2% increase   Answer option "2% increase"
Answer: B
If Juan takes 12 seconds to run y yards, how many seconds will it take him to run x yards at the same rate? Choose the most appropriate option
A) 12x/y B) 12y/x C) x/(12y) D) 13/(xy) E) xy/12

Solution: This problem is testing us on the Rate x Time = Distance relationship. This relationship also tells us that Rate = Distance/Time and Time = Distance/Rate.   Ultimately, we are looking for how many seconds it will take Juan to run x yards. Thus, the equation we’ll use is: Time = Distance/Rate. We know the distance is x yards, and we need to find Juan’s rate.   We can find Juan’s rate as follows: Rate = Distance/Time = y yards/12 seconds   Using that rate, we need to determine how long it takes him to run x yards at the same rate. So we have:   Time = Distance/Rate   Time = x yards/(y yards/12 seconds)   Time = (x yards) x (12 seconds/y yards)   Time = 12x/y seconds   12x/ynswer 12x/y.
Answer: A
The area of a rectangular field is equal to 500 square meters. Its perimeter is equal to 90 meters. Find the width of this rectangle.	Select.
A) 5	B) 10	C) 15	D) 20	E) 25

Solution: L * W = 500 : area , L is the length and W is the width.   2 L + 2 W = 90 : perimeter   L = 45 - w : solve for L   (45 - W) * W = 500 : substitute in the area equation   W = 20 and L = 25   correct answer 20
Answer: D
The sum of two numbers is 30 and their product is 1050. What will be the sum of their reciprocals?  Options.
A) (1/35)  B) (11/210)  C) (35/4)  D) (75/8)  E) None

Solution: Solution   x+y=30 xy=1050 1/x+1/y=x+y/xy 30/1050 = (1/35).   (1/35)nswer (1/35)
Answer: A
Tough and Tricky questions: Remainders.
1^1 + 2^2 + 3^3 + ... + 10^10+11^11 is divided by 5. What is the remainder?  Choose the correct option
A) 0	B) 1	C) 2	D) 3	E) 4

Solution: a number is divisible by 5, if its last digit is divisible by 5   let's look into the sum of last digits of each term of the given expression   1^1=1   2^2=4   3^3=7   4^4=6   5^5=5   6^6=6   7^7=3   8^8=6   9^9=9   10^10=0   11^11=1   adding all these numbers we get 48 which gives a remainder of 3 when divided by 5. so answer must be 3.   bunuel, can you please confirm the answer of this question.   Yes, the OA is D. Clicked the wrong button when posting. Edited. Thank you.   3
Answer: D
What is 35% of 4/13 of 780?
Choose one:
A) 62	B) 73	C) 84	D) 95	E) 106

Solution: This problem can be solved easily if we just use approximation: 35% is a little over 1/3, while 4/13 is a little less than 4/12, which is 1/3. Thus, the answer is about 1/3 of 1/3 of 780, or 1/9 of 780. Since the first 1/3 is a slight underestimate and the second 1/3 is a slight overestimate, the errors will partially cancel each other out. Our estimate will be relatively accurate.   The number 780 is between 720 and 810, so (1/9)*780 will be between 80 and 90.   Keeping track not only of your current estimate, but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently.   The closest answer is 84, so this is the answer to choose.   The answer is 84.
Answer: C
If a + b - c = 2d, and if a - b + c =-2e, then a = Choose the correct choice from the following choices.
A) 2(d + e)  B) d – e  C) (d + e)/2  D) d-2e  E) e-d

Solution: Add both equations:   a + b - c = 2d   a - b + c =-2e   a+b-c+a-b+c=2d-2e   2a=2d-2e   a=(d-e)   Ans:d – e
Answer: B
Three partners A , B , C start a business . B's Capital is four times C's capital and twice A's capital is equal to thrice B's capital . If the total profit is Rs 16500 at the end of a year ,Find out B's share in it.	Select the correct option
A) 4000
B) 5000
C) 6000
D) 7000
E) None of these

Solution: Explanation :   Suppose C's capital = x then   B's capital = 4x (Since B's Capital is four times C's capital)   A's capital = 6x ( Since twice A's capital is equal to thrice B's capital)   A:B:C =6 x : 4x : x   = 6 : 4 : 1   B's share = 16500 * (4/11) = 1500*4= 
1500*4 = 6_000
6000. Answer : Option 6000
Answer: C
A typist uses a sheet measuring 20cm by 30 cm lenghtwise. If a margin of 2 cm is left on each side and a 3 cm margin on the top and bottom, then what is the percentage of page used by the typist?	Select the correct option.
A) 62 %  B) 63 %  C) 64 %  D) 65 %  E) 66 %

Solution: Area of the sheet=(20*30)cm2= 600 cm2   Area used for typing=([20-4]*[30-6]) cm2 = 384 cm2   Therefore Required Percentage =(384/600)*100= 
(384/600)*100 = 64
64%   Answer 64 %
Answer: C
A rectangular grassy plot 110 m. by 65 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 80 paise per sq. metre
Choose the correct choice from the following options:
A) Rs680
B) Rs780
C) Rs880
D) Rs480
E) Rs980

Solution: area of the plot=110m*65m=7150sq.m   area of plot excluding gravel110 *65= 
110 *65 = 7_150
7150sq.m   area of plot excluding gravel=105m*60m=6300sq.m   area of gravel 105 *60= 
105 *60 = 6_300
6300sq.m   area of gravel=7150sq.m-6300sq.m =850sq.m   cost of building it = 850sq.m*80   = 68000p   in Rs =68000/100= 
68000/100 = 680
Rs680   Rs680NSWER:Rs680
Answer: A
A semicircle has a radius of 12. What is the approximate perimeter of the semicircle?	Choices:  A) 58  B) 62  C) 66  D) 70  E) 74

Solution: The perimeter of a circle is 2*pi*r.   The perimeter of a semicircle is 2*pi*r/2 + 2r = pi*r + 2r   The perimeter is pi*12 + 2*12 which is about 62.   The answer is 62.
Answer: B
Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.54000 after completion of one year. What will be Jose's share of profit?	Choose the correct choice.
A) 20000  B) 24000  C) 34000  D) 35000  E) 30000

Solution: SoL = ~s- So Anju’s share = [5/9] x 54000 = 30000   30000
Answer: E
The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 600 resolutions.  Choose the correct choice from the following answers:  A) 843.03 m  B) 844.03 m  C) 845.03 m  D) 846.03 m  E) 847.03 m

Solution: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 600 resolutions.   = 600 * 2 * 22/7 * 22.4   = 84403 cm   = 844.03 m   Answer: 844.03 m
Answer: B
The probability of two events A and B are 0.15 and 0.40 respectively. The probability that both A and B occur is 0.15. The probability that neither A nor B occur is _________	Choose one
A) 0.45  B) 0.4  C) 0.5  D) 0.05  E) 0.6

Solution: we are apply that formula..............   P(AorB)=P(A)+P(B)-P(A AND B)   =.15+.40-.15= 
.15+.40-.15 = 0.4
.40   but the probability of neither A nor B=1-.40= 
1-.40 = 0.6
0.60   ANSW0.6R:0.6
Answer: E
The area of a square is 144 m². Find its perimeter.	Choose one.
A) 18 m B) 28 m C) 38 m D) 42 m E) 48 m

Solution: Area of square = side × side   Given; area of square = 144 m²   Therefore, side² = 144 m²   Therefore, side = √(144 m²) = √(2 × 2 × 2 × 2 × 3 × 3) m² = 2 × 2 × 3 m = 12 m   Now, the perimeter of the square = 4 x side = 4 × 12 m = 48 m   ANSW48 mR : 48 m
Answer: E
In a room filled with 7 people, 1 people have exactly 1 sibling in the room and 6 people have exactly 2 siblings in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings?  Select.
A) 5/21 B) 3/7 C) 4/21 D) 5/7 E) 16/21

Solution: There are suppose A B 4/21 D E F G members in the room 4 people who have exactly one sibling....A B 4/21 D....(A is Bs∘SSsibl∈g∘SSand∘SSviceversa)∘SS(4/21∘SSis∘SSDs∘SSsibl∈g∘SSand∘SSviceversa)∘SS(4/21∘SSis∘SSDssibl∈gandviceversa)(4/21isDs sibling and viceversa) (4/21 is Ds sibling and viceversa)...now remaning EFG are 6 people who have exactly 2 siblings....(E has F and G as his/her sibling and so on..)   there are now 3 different set of siblings (A and B)   (4/21 and D);(EFG)   Now first selecting 2 people out of 7 is 74/212=21   first sibling pair----(A and B)--selecting 2 people --24/212=1   second sibling pair (4/21 and D)--selecting 2 people--24/212=1   third sibling pair (E F G)--selecting 2 out of 6 --64/212=15   total= 1+1+15= 
1+1+15 = 17
17   but,a/c to formula P(success)-1-p(fail)   here,p(failure)is selecting 2 people who are siblings=17/21(21 is 74/212)   =1-17/21   =4/21   ANS 4/21
Answer: C
A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
Choose the correct choice from the following answers:
A) 158 m	B) 150 m	C) 110 m	D) 130 m	E) 157 m

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 15 => y = x/15   (x + 100)/25 = x/15 => x = 150 m.   Answer: 150 m
Answer: B
Two pipes can fill a tank in 12 minutes and 15 minutes. An outlet pipe can empty the tank in 10 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?  Pick one:
A) 20	B) 22	C) 24	D) 26	E) 28

Solution: Let V be the volume of the tank.   The rate per minute at which the tank is filled is:   V/12 + V/15 - V/10 = 3V/60 = V/20 per minute   The tank will be filled in 20 minutes.   The answer is 20.
Answer: A
If x% of y is the same as 4/5 of 80, then the value of xy is?  Select:
A) 4250  B) 6205  C) 5260  D) 4852  E) 6400

Solution: x/100 * y = 4/5 * 80= 
4/5 * 80 = 64
64*100= 
64*100 = 6_400
6400   Answer is 6400
Answer: E
A bag holds 5 red marbles and 5 green marbles. If you removed two randomly selected marbles from the bag, without replacement, what is the probability that both would be red? Choose the correct answer
A) 1/6 B) 2/5 C) 3/10 D) 2/9 E) 1/2

Solution: probability of selecting first red marble = 5/10   probability of selecting second red marble without replacement = 4/9   final probability = 5/10 * 4/9 = 2/9   The correct answer is 2/9.
Answer: D
If you drove at average speed of 66 miles per hour, what distance, in miles, did you drive in 99 minutes?	Choose the correct choice from the following:
A) 100.2 miles	B) 112.7 miles	C) 120.5 miles	D) 108.9 miles	E) 105.6 miles

Solution: We first convert the speed into miles per minute.   66 / 60 = 1.2 miles per minute   We now use the speed and the time to find the distance.   1.2 (miles/minute) * 99 minutes = 108.9 miles   correct answer 108.9 miles
Answer: D
How many pieces of 85 cm length can be cut from a rod of 17 meters long?
Choices:
A) 50  B) 40  C) 30  D) 20  E) 10

Solution: Number of pieces = 1700/85= 
1700/85 = 20
20   The answer is 20.
Answer: D
The midpoints of three of the edges of a cube are
labelled A, B, and C as shown in the diagram. What
is the measure of L ABC ?  Select the correct option
A) 90o	B) 105o	C) 120o	D) 135o	E) 150o

Solution: Let D be the point on the base of the cube such that CD is perpendicular to   the base. Let s be the length of the sides of the cube. Then AB = BC = AD =   p   2s/2.   Using the Pythagorean Theorem in 4ADC, we get AC =   p   3s/   p2. By the Law of   Cosines AC2 = AB2 +BC2 −2AB · BC · cos(\ABC). We get cos(\ABC) = −1/2, so   L ABC = 120o.   correct answer 120o
Answer: C
If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 6?
Select: A) 2/3 B) 3/8 C) 1/2 D) 5/8 E) 3/4

Solution: I get 5/8 as well   1 to 96 inclusive means we have 48 odd and 48 even integers   E O E / 6 = Integer, therefore we have 48 / 96 numbers divisible by 6   O E O / 6 = Not Integer   We cannot forget multiples of 6 from 1 to 96   We have 16 numbers that are multiple of 8   Therefore, 48/96 + 16/96 = 64/96 = 2/3   answer : 2/3
Answer: A
In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together.  Options.
A) 720	B) 740	C) 770	D) 780	E) 790

Solution: 720   Option '720'
Answer: A
A person purchases 90 clocks and sells 40 clocks at a gain of 10% and 50 clocks at a gain of 20%. If he sold all of them at a uniform profit of 15%, then he would have got Rs. 40 less. The cost price of each clock is:  Choose the correct choice from the following
A) 50	B) 90	C) 80	D) 28	E) 93

Solution: Let C.P. of clock be Rs. x.   Then, C.P. of 90 clocks = Rs. 90x.   [(110% of 40x) + (120% of 50x)] - (115% of 90x) = 40   44x + 60x - 103.5x = 40   0.5x = 40 => x = 80   Answer: Option 80
Answer: C
Find large number from below question The difference of two numbers is 1385. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder	Choose the correct choice from the following:  A) 1235  B) 1345  C) 1678  D) 1767  E) 1659

Solution: Let the smaller number be x. Then larger number = (x + 1385).   x + 1385 = 6x + 15   5x = 1370   x = 274   Large number = 274+1385= 
274+1385 = 1_659
1659   1659
Answer: E
There are 6 girls and 6 boys. If they are to be seated in a row, what is the probability that boys and girls sit alternately?	Pick
A) 1/12! B) 12C6/12! C) 6!6!/12! D) 2∗6!6!/12! E) 6!7!/12!

Solution: Total number of ways in which 6 boys and 6 girls can sit in a row = 12!/6!∗6!   Number of ways in which 6 boys and 6 girls can sit alternately = 2 (BGBG..... or GBGB.....)   Probability = 2∗6!∗6!/12!   Answer: 2∗6!6!/12!
Answer: D
A car is traveling 85 kilometers per hour. How many meters does the car travel in one minute?
Choices
A) 1250m/min B) 1360m/min C) 2560m/min D) 1670m/min E) 1416.67m/min

Solution: Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify   85 kilometers per hour = 85 km/hr   = (85 × 1000 meters) / (60 minutes) = 1,416.67 meters / minute   correct answer is 1416.67m/min)1416.67m/min
Answer: E
A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it? Choose the correct choice from the following:  A) 87 days  B) 20 days  C) 16 days  D) 19 days  E) 36 days

Solution: C = 1/2 - 1/4 - 1/5 = 1/20   => 20 days   Answer:20 days
Answer: B