MU-NLPC/Calc-aqua_rat huggingface dataset:
The average salary per month of 55 employees in a company is Rs 8500. If the managers salary is added, the average salary increases to Rs 8800, what is the salary of the manager ?  Choose the correct choice from the following answers: A) 10000 B) 12000 C) 23000 D) 25300 E) 45000

Solution: Explanation :   Salary of the manager = (56*8800 - 55*8500)= 
(56*8800 - 55*8500) = 25_300
25300   Answer : 25300
Answer: D
The contents of a certain box consist of 24 plums and 30 kiwis. How many kiwis must be added to the box so that exactly 30% of the pieces of fruit in the box will be plums? Answers.
A) 24 B) 26 C) 30 D) 46 E) 50

Solution: plums = (plums + kiwi + x)*0.3   24 = (30 + 24 + x)*0.3   x = 26.   Answer: 26.
Answer: B
A sum of money at simple interest amounts to Rs. 815 in 4 years and to Rs. 854 in 5 years. The sum is:	Pick
A) 659 B) 698 C) 780 D) 910 E) None

Solution: Sol.   S.I. for 1 year = Rs. (854 - 815) = Rs. 39.   S.I. for 4 years = Rs. (39 * 4) = Rs. 156.   âˆ´ Principal = Rs. (815 - 156) = Rs. 659   659nswer 659
Answer: A
9 engines consume 24 metric tonnes of coal, when each is working 8 hours day. How much coal is required for 8 engines, each running 13 hours a day, if 3 engines of former type consume as much as 4 engines of latter type?	Choose the correct choice from the following choices.
A) 20 metric tonnes
B) 22 metric tonnes
C) 24 metric tonnes
D) 26 metric tonnes
E) 28 metric tonnes

Solution: Explanation:   Let required amount of coal be x metric tones   More engines, more amount of coal (direct proportion)   If 3 engines of first type consume 1 unit, then 1 engine will consume 13 unit which is it’s the rate of consumption.   If 4 engines of second type consume 1 unit, then 1 engine will consume 14 unit which is it’s the rate of consumption   More rate of consumption, more amount of coal (direct proportion)   More hours, more amount of coal(direct proportion)   Hence we can write as   (engines) 9:8   (consumption rate )13:14   (hours) 8:13::24}::x   ⇒9×1/3×8×x=8×1/4×13×24   ⇒3×8×x=8×6×13   ⇒3×x=6×13   ⇒x=2×13=26   Answer: Option 26 metric tonnes
Answer: D
Operation#is defined as adding a randomly selected two digit multiple of 8 to a randomly selected two digit prime number and reducing the result by half. If operation#is repeated 10 times, what is the probability that it will yield at least two integers?	Choose the correct choice from the following:
A) 0%	B) 10%	C) 20%	D) 30%	E) 40%

Solution: Any multiple of 8 is even.   Any two-digit prime number is odd.   (even+odd)/2 is not an integer. Thus # does not yield an integer at all.   Therefore P=0.   0%nswer: 0%.
Answer: A
16 men can complete a piece of work in 25 days. In how many days can 20 men complete that piece of work?	Choose the correct choice from the following options.
A) 23 days  B) 26 days  C) 22 days  D) 29 days  E) 20 days

Solution: 20 days   20 days   16 * 25 = 20 * x => x = 20 days
Answer: E
Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled ? Options.
A) 2.5 hours
B) 2 hours
C) 3.5 hours
D) 3 hours
E) None of these

Solution: Explanation:   Part filled by A in 1 hour = 1/5   Part filled by B in 1 hour = 1/10   Part filled by C in 1 hour = 1/30   Part filled by (A+B+C) in 1 hour =1/5 +1/10 +1/30   =1/3   So all pipes will fill the tank in 3 hours.   Answer is 3 hours
Answer: D
A certain club has exactly 5 new members at the end of its first week. Every subsequent week, each of the previous week's new members (and only these members) brings exactly M new members into the club. If y is the number of new members brought into the club during the twelfth week, which of the following could be y? Choose the correct choice from the following choices:
A) 5^1/12 B) 3^11 * 5^11 C) 3^12 * 5^12 D) 3^11 * 5^12 E) 60^12

Solution: At the end of the first week, there are 5 new members;   At the end of the second week, there are 5M new members (since each 5 new members from the previous week brings M new members);   At the end of the third week, there are 5M^2 new members (since each 5M new members from the previous week brings M new members);   ...   At the end of the twelfth week, there are 5M^11 new members (since each 5M^10 new members from the previous week brings M new members).   We are given that 5M^11=y. Out of the answers only D yields integer value for M: 5M^11=3^11 * 5^12 --> M=3*5= 
3*5 = 15
15.   Answer: 3^11 * 5^12.
Answer: D
The average age of a family of 6 members is 24 years.If the age of the youngest member is 8 years,what was the average age of the family at the birth of the youngest member?	Select.
A) 15  B) 16  C) 21  D) 12  E) 19

Solution: Present age of total members = 6 X 24 = 144   8 yrs back their ages were = 6 x 8 = 48   Ages at the birth of youngest member = 144 - 48= 
144 - 48 = 96
96   Therefore, avg age at the birth of youngest member= 96/6= 
96/6 = 16
16.   ANSWER:16
Answer: B
in a certain flower shop, which stocks four types of flowers, there are 1/4 as many violets as carnations, and 1/4 as many tulips as violets. If there are equal numbers of roses and tulips, what percent of the flowers in the shop are carnations? Choose the correct choice from the following options: A) 31 B) 30 C) 29 D) 28 E) 27.27

Solution: Given :-   Violets - C/4   Carnations - C   Tulip - C/16   Rose - C/16   Total flowers in terms of C = C/4+C+C/16+C/16 = 22C/6   Percentage of Carnations = C/22C/6 *100 =27.27   Answer 27.27
Answer: E
The length of a rectangular floor is more than its breadth by 100%. If Rs. 600 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?  Choose the correct choice from the following answers:	A) 15.0m.	B) 14.4m.	C) 12.0m.	D) 16.2m.	E) 16.5m.

Solution: Let the length and the breadth of the floor be l m and b m respectively.   l = b + 100% of b = l + 1b = 2b   Area of the floor = 600/3= 
600/3 = 200
200 sq m   l b= 200i.e., l * l/2 = 108   l2 = 216 => l = 14.4m.   ANSWER:14.4m.
Answer: B
A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is:	Choose the correct choice from the following answers:  A) 4.14 kmph  B) 5.10 kmph  C) 4.50 kmph  D) 4.4 kmph  E) 5.00 kmph

Solution: 4.14 kmph speed = (5*5/18) = 25/18   time taken by 4.14 kmph to cover 100 m = (100*18/25)= 
(100*18/25) = 72
72   time taken by B to cover 92 m= (72+8)= 
(72+8) = 80
80 sec   B's speed= (92/80 * 18/5)= 
(92/80 * 18/5) = 207/50 = around 4.14
4.14   4.14 kmphNSWER 4.14 kmph
Answer: A
The length of a rectangular plot is thrice its width. If the area of the rectangular plot is 588 sq meters, then what is the width (in meters) of the rectangular plot?
Choose the correct choice
A) 14 B) 16 C) 18 D) 20 E) 22

Solution: 14rea = L*W = 3W^2 = 588   W^2 = 196   W = 14   The answer is 14.
Answer: A
When Alice entered the Forest of Forgetfulness, she forgot the day of
the week. She met the Lion and the Unicorn resting under a tree. The
Lion lies on Mondays, Tuesdays and Wednesdays and tells the truth
on the other days of the week. The Unicorn, on the other hand, lies
on Thursdays, Fridays, and Saturdays, but tells the truth on the other
days of the week. They made the following statements:
Lion: \Yesterday was one of my lying days."
Unicorn: \Yesterday was one of my lying days."
From these two statements, Alice was able to deduce the day of the
week. What day was it? Choose the correct choice from the following answers.
A) Monday	B) Wednesday	C) Thursday	D) Friday	E) Sunday

Solution: If the Lion is telling the truth, the day of the week must be Thursday. If he   is lying, then the day of the week must be Monday. So the day of the week must be   either Thursday or Monday. If the Unicorn is telling the truth, the day of the week must   be Sunday. If he is lying, then the day of the week must be Thursday. The day of the   week cannot be Sunday (since we have already said that it must be Thursday or Monday).   Therefore, it must be Thursday   correct answer Thursday
Answer: C
A furniture manufacturer has two machines, but only one can be used at a time. Machine Q is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine Q can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule?
Choose the most appropriate option.
A) 14  B) 13  C) 11  D) 9  E) 7

Solution: machine Q finish the job in 2*12= 
2*12 = 24
24 shifts   machine B finish the job in   2*15= 
  2*15 = 30
30 shifts   Lets assume total work require 120 shifts   Therefore,   rate of Q= 5 shifts/day   rate of B = 4 shifts/day   rate of (Q+B) = 9 shifts/day   According to current schedule work complete in a day = 5+4+(9/2)= 
5+4+(9/2) = 27/2 = around 13.5
13.5 shifts/day   Therefore, Time required to finish 120 shifts= (120/13.5) = 8.88.. days ~ 9 days=9
Answer: D
A circular metal plate of even thickness has 12 holes of radius 1 cm drilled into it. As a result the plate lost 1/6th its original weight. The radius of the circular plate is
Options
A) 16sqrt2	B) 8sqrt2	C) 32sqrt2	D) sqrt72	E) sqrt82

Solution: Area of 12 holes=12*Pi*1^2=12*Pi   As 12*Pi=(1/6)th weight,so total Area of Plate=12*Pi/(1/6)=72*Pi   If r=radius of the plate,then its Area=Pi*r^2=72*Pi, So r=Sqrt72   ANSWER:sqrt72
Answer: D
Find the amount on Rs.5000 in 2 years, the rate of interest being 4% per first year and 5% for the second year?	Options
A) 2328	B) 2798	C) 5460	D) 2799	E) 2771

Solution: 5000 * 104/100 * 105/100= 
5000 * 104/100 * 105/100 = 5_460
> 5460.Answer: 5460
Answer: C
By selling 100 pens, a trader gains the cost of 30 pens. Find his gain percentage?
Select:  A) 30%  B) 33%  C) 31%  D) 32%  E) 34%

Solution: Let the CP of each pen be Rs. 1.   CP of 100 pens = Rs. 100   Profit = Cost of 30 pens   = Rs. 30   Profit% = 30/100* 100= 
30/100* 100 = 30
30%   30%nswer: 30%
Answer: A
How many integers are between 7 and 57/4, inclusive? Pick:	A) 4	B) 5	C) 7	D) 8	E) 10

Solution: 57/4 = 14.xx   We are not concerned about the exact value of 57/4 as we just need the integers.   Since the values are small, we can write down the integers.   The different integers between 7 and 57/4 would be 7, 8, 9, 10, 11, 12,13,14   Total number of integers = 8   Option 8
Answer: D
If the sum of 6 consecutive integers is y, which of the following must be true?
I. y is an even number
II. y is an odd number
III. y is a multiple of 6  Choose the correct choice:
A) I only
B) II only
C) III and I only
D) I onlyII
E) II and III

Solution: I. If you start off with an even number, the sum (y) is even, and if you start off with an odd number the sum (y) is odd. Therefore this is not always true.   II. Same as above. This need not be always true.   III. Say, the first number is p. Then the sum of the five numbers = p + (p+1) + (p+2)...... + (p+4)   = 6p + 12 = 6 (p+2) => divisible by 6. There this must be true in all cases.   Therefore I onlyII is the answer.
Answer: D
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 126 km/hr, what is the length of the platform?
Select the correct option:
A) 338	B) 240	C) 560	D) 267	E) 191

Solution: Speed = (126 * 5/18) m/sec = 35 m/sec. Length of the train = (35 x 20)m = 700 m. Let the length of the platform be x meters. Then, (x + 700)/36 = 35 ==> x + 700 = 1260 ==>   x = 560 m.   Answer: 560
Answer: C
If f(x) = 12 - x^2/2 and f(2k) = 6k, what is one possible value for k? Choose the correct choice:	A) 2	B) 3	C) 4	D) 6	E) 8

Solution: First of all, see thisGMAT blog postand check the related lesson linked below for some background on function notation.   We can plug anything in for x and get a result. You can find f(1), for example, by plugging in 1 where x is, and you would get 12 - 1/2 = 11.5. Or we could find f(2), which would be  12 - 4/2= 
 12 - 4/2 = 10
10.   So the notation f(2k) means that we are going to plug a 2k in for x everywhere in the formula for f(x). That would be:   f(2k)= 12 - (2k)^2/2 = 12 - 2k^2.   Remember that we have to square both the 2 and the k, to get 4k2. Now, this expression, the output, we will set equal to 2k.   12 - 2k^2 = 2k --> k = -3 or k = 6.   All the answers are positive, so we choose k = 2.   Answer = 6
Answer: D
Two sides of triangle are ln(50) and ln(8), third side is ln(n). Find out the number of possible values of n?	Select the correct option:
A) 392 B) 398 C) 393 D) 395 E) 399

Solution: Explanation :   Sum of two sides of a triange is always greater than the third side   case 1:   So, ln(50) + ln(8) > ln(n)   => ln(50x8) > ln(n) ( ∵ log (a) + log(b) = log(ab) )   => 400 > n   i.e. n < 400   logax is defined for x > 0. So, n will be greater than 0   So, 0 < n < 400   case 2:   So, ln(50) + ln(n) > ln(8)   => ln(50n) > ln(8) ( ∵ log (a) + log(b) = log(ab) )   => 50n > 8   i.e. n > 4/25   case 3:   So, ln(8) + ln(n) > ln(50)   => ln(8n) > ln(50) ( ∵ log (a) + log(b) = log(ab) )   => 8n > 50   i.e. n > 25/4   393ombining results from case 1, case 2 and case 3 we get:   25/4 < n < 400   So, range of integral values of n satisfying the above condition is: 7 ≦ n ≦ 400   Hence no of integral values of n are: 393   Answer : 393
Answer: C
If two different numbers are randomly selected from set { 1, 2, 3, 4, 5} what is the probability that the sum of the two numbers is greater than 4?  Pick one:
A) 2/5 B) 3/5 C) 4/5 D) 6/5 E) 7/5

Solution: First problem is 5C2 = 10 .. Not 20..   Point 2, you sum should be greater than 4, so these are the following possibilities you have   ({1,4},{1,5},{2,3},{2,4},{2,5},{3,4},{3,5},{4,5}) which leads to 8 pairs   So the probability is 8 on 10 or 4/5..   ANSWER:4/5
Answer: C
The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling alongthe oundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is?  Choose the correct option:  A) 143600 m  B) 144600 m  C) 153600 m  D) 162600 m  E) 165600 m

Solution: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.   60   Let length = 3x metres and breadth = 2x metres.   Then, 2(3x + 2x) = 1600 or x = 160.   Length = 480 m and Breadth = 320 m.   Area = (480 x 320) m2 = 153600 m   153600 m
Answer: C
If Jane takes 12 seconds to run y yards, how many minutes will it take her to run x yards at the same rate? Choose one.
A) xy/12 B) 12x/(60y) C) 60xy/12 D) xy/720 E) 720x/y

Solution: The answer is B.   She runs x yards in 12x/y seconds =12x/60y minutes.
Answer: B
List K consists of 10 consecutive integers. If -4 is the least integer in list K, what is the range of the positive integers in list K?
Pick one
A) 5 B) 6 C) 7 D) 11 E) 4

Solution: Answer = 4 = 4   If least = -4, then largest = 5   Range = 5 - 1= 
5 - 1 = 4
4
Answer: E
The cash realised on selling a 14% stock is Rs.101.25, brokerage being 1/4% is  Choices.
A) 123 B) 106 C) 100 D) 101 E) 240

Solution: Explanation:   Cash realised= Rs. (101.25 - 0.25)   = Rs. 101.   Answer: 101
Answer: D
A boat can travel with a speed of 5km/hr in still water. If the speed of the stream is 5km/hr, find the time taken by the boat to go 100km downstream. Options.
A) 1 hr B) 2 hrs C) 3 hrs D) 4 hrs E) 10 hrs

Solution: Speed downstream = (5 + 5) km/hr = 10 km/hr.   Time taken to travel 100 km downstream = 100/10= 
100/10 = 10
10 hrs.   Answer : 10 hrs
Answer: E
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?	Choose the correct choice from the following answers:
A) 126  B) 217  C) 150  D) 277  E) 212

Solution: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9)= 
(50/3 * 9) = 150
150 m. Answer:277
Answer: D
A can have a piece of work done in 15 days, B can work three times faster than the A, C can work two times faster than A. How many days will they take to do the work together ? Choose the correct answer.
A) 3 days
B) 8/9 days
C) 10/3 days
D) can't say
E) none

Solution: A's 1 day work is 1/20   B's 1 day work is 3/20   10/3 days's 1 day work is 2/20   (A+B+10/3 days)'s 1 day work(1/20+3/20+2/20) is 3/10   so, they can finish the work in 10/3 days   ANSWER:10/3 days
Answer: C
The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?  Pick one.
A) 887 B) 267 C) 342 D) 276 E) 277

Solution: 400*(90/100)*(95/100)= 
400*(90/100)*(95/100) = 342
342   Answer: 342
Answer: C
A certain company consists of 8 managers and 8 non-managers. How many different teams of 3 employees can be formed in which at least one member of the team is a manager and at least one member of the team is not a manager? (Two groups are considered different if at least one group member is different)	Options
A) 84	B) 108	C) 135	D) 270	E) 448

Solution: Total # of teams of 3 possible is 16C3=560   # of teams with only managers or only non-managers is: 8C3+8C3=56+56= 
56+56 = 112
112;   # of teams of 3 with at least one manager or at least one non-manager is: 560-112= 
560-112 = 448
448.   ANSW448R:448
Answer: E
The length of a rectangle is four times its width. If the area is 100 m2 what is the length of the rectangle?  Choices:
A) 60 m B) 50 m C) 40 m D) 30 m E) 20 m

Solution: Let L be the length and W be the width of the rectangle. Hence   L = 4 W   We now use the area to write   100 = L * W   Substitute L by 4 W in the equation above   100 = 4 W * W = 4 W2   Solve for W and find L   4 W2 = 100   W2 = 25 , W = 5 and L = 4 W = 20 m   correct answer 20 m
Answer: E
The average weight of A, B and C is 46 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
Choose the correct choice:
A) 28 kg B) 32 kg C) 33 kg D) 34 kg E) None of these

Solution: Explanation:   Let A, B, C represent their respective weights. Then, we have:   A + B + C = (46 x 3) = 138 …. (i)   A + B = (40 x 2) = 80 …. (ii)   B + C = (43 x 2) = 86 ….(iii)   Adding (ii) and (iii), we get: A + 2B + C = 166 …. (iv)   Subtracting (i) from (iv), we get : B = 28.   B’s weight = 28 kg.   28 kgnswer: 28 kg
Answer: A
A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2415?	Choose one:  A) s.800  B) s.810  C) s.805  D) s.900  E) s.920

Solution: 2415 * 1/3= 
2415 * 1/3 = 805
805   Option s.805
Answer: C
A sum of money at simple interest amounts to $ 980 in 3 years and to $1024 in 4 years. The sum is:  Answers:
A) $153	B) $848	C) $398	D) $549	E) $675

Solution: B   $848   S.I. for 1 year = $(1024 - 980)= 
(1024 - 980) = 44
$44.   S.I. for 3 years= $(44 x 3) = $132.   Principal = $(980 - 132)= 
(980 - 132) = 848
$848.
Answer: B
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) 299 m	B) 982 m	C) 399 m	D) 150 m	E) 354 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: D
A train running at the speed of 60 km/hr crosses a pole in 15 seconds. Find the length of the train?	Choose the correct option.
A) 150
B) 872
C) 250
D) 288
E) 212

Solution: Speed = 60*(5/18) m/sec = 50/3 m/sec   Length of Train (Distance) = Speed * Time     (50/3) * 15= 
  (50/3) * 15 = 250
250 meter   Answer:250
Answer: C
(469 + 174)2 - (469 - 174)2	/(469 x 174)=? Choose the most appropriate option:
A) 2	B) 4	C) 295	D) 643	E) 123

Solution: Explanation:   Given exp. =	(a + b)2 - (a - b)2/ab   =	4ab/ab   = 4 (where a = 469, b = 174.)   ANSWER IS 4
Answer: B
What is the sum of all the composite numbers up to 20?  Select the correct option
A) 228
B) 277
C) 198
D) 132
E) 281

Solution: Explanation:   4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 = 132   Answer: 132
Answer: D
Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?  Choose the correct choice.
A) 10/7 sec  B) 12/7 sec  C) 20/7 sec  D) 17/7 sec  E) 19/7 sec

Solution: Explanation:   They are moving in opposite directions, relative speed is equal to the sum of their speeds.   Relative speed = (54 + 72)*5/18 = 7*5= 
7*5 = 35
35 mps.   The time required= d/s = 100/35 = 20/7 sec.   ANSWER IS 20/7 sec
Answer: C
A boy has five trousers and 14 shirts. In how many different ways can he select a trouser and a shirt? Options:  A) 60  B) 278  C) 70  D) 108  E) 271

Solution: The boy can select one trouser in five ways.   The boy can select one shirt in 14 ways.   The number of ways in which he can select one trouser and one shirt is   5 * 14= 
  5 * 14 = 70
70 ways.   Answer: 70
Answer: C
If the cost of 8 erasers and 5 sharpeners is Rs.31/-, what will be the cost of 24 erasers and 10 sharpeners?  Choose the most appropriate option:  A) Rs.62/-  B) Rs.84/-  C) Rs.78/-  D) Rs.150  E) None of these

Solution: Explanation:   By analysis, we get 8x2 = 16 (erasers)   5x3 = 15 (sharpeners)   :.1 Eraser costs Rs.2/- and 1 sharpener costs Rs.3/-   Hence, the cost of 24 erasers + 10 sharpeners = 24x2 + 10x3 = 48+30 = Rs.78/-   Answer: Option Rs.78/-
Answer: C
In how many ways can the letters of word DEVELOP be arranged such that all the vowels as well as all the Consonants always appear together?  Choose the correct choice from the following choices.
A) 9!	B) 3!*4!*2!	C) 5!*5!	D) 5!*4!*2!	E) 6!*4!

Solution: Since all the vowels and consonants have to be together there can only be there are 3! way to order the vowels and 4! to order the consonants. But they must be together either vowels come first or consonants so you multiply by 2.   So 3!4!2! (3!*4!*2!)
Answer: B
Cole drove from home to work at an average speed of 75 kmh. He then returned home at an average speed of 105 kmh. If the round trip took a total of 6 hours, how many minutes did it take Cole to drive to work? Choose the correct choice from the following answers:	A) 84	B) 136	C) 172	D) 210	E) 478

Solution: First round distance travelled (say) = d   Speed = 75 k/h   Time taken, T2 = d/75 hr   Second round distance traveled = d (same distance)   Speed = 105 k/h   Time taken, T2 = d/105 hr   Total time taken = 6 hrs   Therefore , 6 = d/75 + d/105   LCM of 75 and 105 = 525   6= d/75 + d/105   => 6 = 7d/525 + 5d/525   => d = 525 / 2 Km   Therefore, T1= d/75   => T1 = 525 / (2 x 75)   => T1 = (7 x 60) / 2 -- in minutes   => T1 = 210 minutes.   210
Answer: D
A dice has one of the first 4 prime number on each its six sides ,with no two sides having the same number .the dice is rolled 10 times and the results added.the addition is most likely to be closet to Choose the correct option.
A) 41	B) 43	C) 60	D) 68	E) 70

Solution: if die is rolled then avg score = (2+3+5+7 )/4 = 41/4   so, most likely sum for 10 times = 41/4 * 10 = 43   ANSWER:43
Answer: B
Sarah operated her lemonade stand Monday through Friday over a two week period and made a total profit of 350 dollars. On hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days. Each cup she sold had a total cost of 75 cents and Sarah did not incur any other costs. If every day she sold exactly 32 cups and 3 of the days were hot, then what was the price of 1 cup on a hot day?
Answers:  A) $ 1.50  B) $ 1.88  C) $ 2.14  D) $ 2.50  E) $ 3.25

Solution: 7 regular days --> sales = 7*32*x = 224x;   3 hot days --> sales = 3*32*(1.25x) = 120x;   Total sales 3*32*(1.25 )= 
3*32*(1.25 ) = 120
120x;   Total sales= 224x+120x = 344x.   Total cost 224 +120= 
224 +120 = 344
344x.   Total cost= 10*32*0.75= 
10*32*0.75 = 240
240.   Profit= 344x - 240 = 350 --> x=1.715.   1.25x=~2.14.   Answer:$ 2.14.
Answer: C