MU-NLPC/Calc-aqua_rat huggingface dataset:
When the positive integer A is divided by 4 and 7, the remainder is 3 and 4, respectively. When the positive integer B is divided by 4 and 7, the remainder is 3 and 4, respectively. Which of the following must be a factor of A-B?  Choose the correct choice.
A) 12
B) 24
C) 28
D) 16
E) 30

Solution: A = 4k+3 = 7j+4   B 4 +3= 
4 +3 = 7
7j+4   B= 4m+3 = 7n+4   A-B 4 +3= 
4 +3 = 7
7n+4   A-B= 4(k-m) = 7(j-n)   Thus A-B is a multiple of 4 and 7, so it is multiple of 28.   The answer is 28.
Answer: C
Prizes totaling $75,000 were awarded unequally between 3 contestants. Which of the following choices could be the highest prize?  Choose the correct choice from the following options:  A) (a) $5,000  B) (b) $10,000  C) (c) $15,000  D) (d) $24,000  E) (e) $65,000

Solution: The highest prize cannot possibly be less than 1/3rd of 75,000 (because in this case the sum of 3 prizes would be less than 75,000) and cannot be more than 75,000.   Answer: (e) $65,000.
Answer: E
If the sum of a set of 5 different positive prime numbers is 94, what is the difference between larger 2 prime numbers between them?	Choices:
A) 11  B) 12  C) 23  D) 17  E) 13

Solution: All prime numbers apart from 2 are odd.   Even + Even = Even   Odd + Even = Odd   Odd + Odd = Even   We are given 5 different prime numbers, whose sum is 94 i.e even   If we include 2, we will have 4 odd prime numbers and one even.   This sum would be odd   If we exclude 2, we will have 5 odd numbers.   This sum would be even   Hence 2 is included.   The possible 5 no. are = 11+7+2+43+31= 
11+7+2+43+31 = 94
94   difference between larger 2 prime numbers between them= 43 - 31= 
43 - 31 = 12
12   Ans - 12
Answer: B
If the height of an equilateral triangle RBC is equal in length to the hypotenuse of an isosceles right triangle DEF, a side of ΔRBC is how many times as long as a leg of the right triangle DEF? Select the correct option
A) (√2)/(√3)
B) (√3)/(√2)
C) √2
D) (2√2)/(√3)
E) 2/(√3)

Solution: Side of the equilateral triangle RBC = 2m ----> height = m * sqtr(2)   Hipotenuse of the right triangle RBC = m * sqrt(3) ----> side = m * sqtr(3) / sqtr(2)   Question is 2m/m * sqtr(3) / sqtr(2) = 2*sqrt(2)/sqrt(3)=(2√2)/(√3)
Answer: D
There are two numbers. If 40% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
Choose the correct option:	A) 3/7	B) 5/8	C) 6	D) 6/7	E) 7

Solution: Let the two numbers be x and y.   40/100 * x + y = 5/4y   => 2/5 x = 1/4 y => x/y = 5/8   5/8)
Answer: B
A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A.	Choose the correct answer:	A) Rs.240	B) Rs.350	C) Rs.340	D) Rs.390	E) Rs.370

Solution: Explanation:   (3*8 + 2*4):(4*8 + 5*4)   8:13   8/21 * 630= 
8/21 * 630 = 240
240   Rs.240NSWER IS Rs.240
Answer: A
Two cubes of their volumes in the ratio 64 : 1331. The ratio of their surface area is:  Select the correct option:
A) 1.5:5
B) 2:5
C) 3:5
D) 4:11
E) 4:5

Solution: The ratio of their surface area is   64 : 1331   4 : 11   Answer is 4:11.
Answer: D
56 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780. The bigger part is :	Choose the correct choice:
A) 33.0
B) 37.66
C) 32.1
D) 31.23
E) 19

Solution: Explanation:   Let the two parts be (56 - x) and x.   Then, 10 (56 - x) + 22x = 780   => 12x = 220   => x = 20.   Bigger part = (56 - x) = 37.66.   Answer: 37.66) 37.66
Answer: B
A man purchases the milk at Rs. x/litre and sells it at Rs. 2x/liter stillhe mixes 2liters water with every 6liters of pure milk. What is the profit %?	Pick one:
A) 100.12%	B) 123.16%	C) 154.66%	D) 166.66%	E) None

Solution: Let the cost price of 1 litre pure milk be Re.1, then   \inline \begin{Bmatrix} 6 & litres(milk) & \rightarrow & CP=Rs.6\\ 2 & litres(water) & \rightarrow & CP=Rs.0 \end{Bmatrix}\rightarrow CP=Rs.6 only   and 8 litre mixture \rightarrow SP \rightarrow 8 x 2 = Rs.16   Profit %= 166.66%   166.66%
Answer: D
With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. If the second valve emits 50 cubic meters of water more than the first every minute, then what is the capacity E of the pool?  Pick one.
A) 9000 cubic meters B) 10500 cubic meters C) 11750 cubic meters D) 12000 cubic meters E) 12500 cubic meters

Solution: D. 12000 cubic meters.   If both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in   (48*120)/(120-48)= 
  (48*120)/(120-48) = 80
80 minutes.   Now, if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120x and also 80 (x+50).   or, 120x= 80 (x + 50).   or x = 100.   Hence, the capacity of pool = 120x = 12000 cubic meters.
Answer: D
The probability of pulling a black ball out o f 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?	Options
A) 1/(XY).
B) Y/X
C) X by 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 by Y.
Answer: C
Krista, a personal trainer, is buying energy drinks for her clients. If she has $20 on hand, which of the following options could Krista NOT buy if:
Rock Star = $2.00
Red Bull = $3.25
Monster = $2.50
NOs = 1.25 Choose the correct choice from the following choices: A) 5 Rock Stars, 2 Red Bulls, 1 Monster & 1 NO's (20.25) B) 8 Monster's (17.50) C) 1 Rockstar, 4 Red Bulls & 4 No's (20) D) 10 Rock Stars (20) E) 8 No's (20)

Solution: The Correct Answer would exceed the $20 Krista had on hand.   5 Rock Stars, 2 Red Bulls, 1 Monster & 1 NO's (20.25)= $20.25 (exceeds budget by 25 cents)   B= $20   C= $20   D= $20   E= $20   The Correct answer is 5 Rock Stars, 2 Red Bulls, 1 Monster & 1 NO's (20.25)
Answer: A
two friends deepak and rajeev have agreed to meet at a definite spot on a particular day between 9pm and 10pm. the first person to come waits for some time and leaves.If the other one does not turn up by that time.If Deepak comes first,he waits for 45minutes and if Rajeev comes first,he waits for 15minutes.What is the probability of meeting between Deepak and rajeev if their arrival times are independent of eachother and each person arrives during the indicated period at random?
Answers:
A) 3/4 B) 11/16 C) 7/8 D) 3/16 E) 3/15

Solution: deepak : 45/60 = 3/4   rajeev : 15/60= 1/4   as these are independent events   total probability = (3/4)*(1/4)   = 3/16   ANSWER:3/16
Answer: D
The difference in compound interest earned on a deposit (compounded annually) in year 1 and year 2 is $ 40. Had the interest rate been three times its present value, the difference q would have been how much?  Options:  A) 40/3  B) 40  C) 120  D) 360  E) 420

Solution: CASE 1:   Deposit = $x;   Rate of increase = r.   Interest yearned in 1 year = xr. Deposit in 1 year = x + xr.   Interest yearned in 2 year = (x + xr)r.   The difference q= (x + xr)r - xr = xr^2 = 40.   CASE 2:   Deposit = $x;   Rate of increase = 3r.   Interest yearned in 1 year = x(3r). Deposit in 1 year = x + 3xr.   Interest yearned in 2 year = (x + 3xr)3r.   The difference = (x + 3xr)3r - 3xr = 9xr^2. Since from CASE 1 we know that xr^2 = 40, then 9xr^2 = 9*40= 
9*40 = 360
360.   Answer: 360.
Answer: D
Look at this series: 21, 9, 21, 11, 21, 13, 21, ... What number should come next?
Select.
A) 14
B) 15
C) 21
D) 23
E) 24

Solution: Explanation: In this alternating repetition series, the random number 21 is interpolated every other number into an otherwise simple addition series that increases by 2, beginning with the number 9.   Answer: Option 15
Answer: B
From a container having pure milk, 10% is replaced by water and the process is repeated twice. At the end of the second operation, the milk is?  Choose the correct choice from the following options.
A) 50%
B) 60%
C) 55%
D) 75%
E) 81%

Solution: Let the total quantity of original milk = 1000gm   Milk after 1st operation = 90% of 1000 = 900gm   Milk after second operation = 90% of 900 = 810gm   Strength of final mixture = 81%   Answer is 81%
Answer: E
If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many V such committees are possible?
Choose the correct choice from the following answers:
A) 20  B) 40  C) V=50  D) V=80  E) V=120

Solution: Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) each to send onerepresentativeto the committee: 5C3=10.   But these 3 chosen couples can send two persons (either husband or wife): 2*2*2=2^3=8.   Total # of ways: 5C3*2^3=80.   Answer: V=80.
Answer: D
A train running at the speed of 100 km/hr crosses a pole in 18 seconds. What is the length of the train?	Choose the correct choice from the following.
A) 300 B) 400 C) 500 D) 600 E) 700

Solution: Speed=(100 * 5/18) m/sec = (250/9) m/sec Length of the train = (Speed x Time) = (250/9 * 18)= 
(250/9 * 18) = 500
500 m.   Answer: 500
Answer: C
Of the diplomats attending a summit conference, 30 speak French, 32 do not speak Russian, and 20% of the diplomats speak neither French nor Russian. If 10% of the diplomats speak both languages, then how many diplomats attended the conference?	Pick one
A) 20 B) 96 C) 108 D) 120 E) 150

Solution: {Total} = {French} + {Russian} - {Both} + {Neither}   {Total} = 30 + ({Total} - 32) - (0.1*{Total}) + 0.2*{Total}   Solving gives {Total} = 20.   20nswer: 20.
Answer: A
A boat traveled upstream 90 miles at an average speed of (v-3) miles per hour and then traveled the same distance downstream at an average speed of (v+3) miles per hour. If the trip upstream took a half hour longer than the trip downstream, then how many hours did it take the boat to travel downstream? Select
A) 2.5 B) 2.4 C) 2.3 D) 2.2 E) 2.1

Solution: 90/(V-3) = 90/(V+3) + 0.5 hours   => 90(V+3) = (V-3) [90 + 0.5 V + 1.5]   90V + 270 = (V-3)(183/2 + V/2)   180V + 540 = (V-3)(183+V)= 183V- 549+ V^2 -3V   V^2 - 1089= 0 => V= 33 miles/hr   => Time downstream = 90/36 = 30/12= 5/2= 
5/2 = 5/2 = around 2.5
2.5 hrs   2.5NSWER 2.5 2.5
Answer: A
A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color? Choose the correct choice from the following.
A) 1/9	B) 5/9	C) 7/9	D) 7/11	E) None

Solution: Explanation:   Two balls can be picked from nine balls in ⁹C₂ ways.   We select one white ball and one red ball from five white balls and four red balls. This can be done ⁵C₁ . ⁴C₁ ways.   The required probability = (5 * 4)/⁹C₂ = 20/36 = 5/9   5/9)
Answer: B
A certain taxi company charges $2.10 for the first 1/5 of a mile plus $0.40 for each additional 1/5 of a mile. What would this company charge for a taxi ride that was 8 miles long?  Choose the correct option:
A) 15.6
B) 16.0
C) 17.7
D) 18.7
E) 19.1

Solution: A certain taxi company charges $2.10 for the first 1/5= 
1/5 = 1/5 = around 0.2
0.2 miles.   The cost of 8 miles long ride would be $2.10 for the first 0.2 miles plus (8-0.2)/0.2*0.4= $2.1 + $15.6 = $17.7.   Answer: 17.7.
Answer: C
P and Q together can complete a piece of work in 4 days. If P alone can complete the same work in 20 days, in how many days can Q alone complete that work?
Pick one:
A) 2	B) 7	C) 5	D) 9	E) 1

Solution: Explanation:   (P + Q)'s 1 day's work = 1/4, P's 1 day's work = 1/20   Q's 1 day's work = (1/4 – 1/20) = (4/20) = (1/5)   Hence, Q alone can complete the work in 5 days.   ANSWER: 5
Answer: C
The cost price of a radio is Rs.1500 and it was sold for Rs.1275, find the loss %? Choose the correct choice from the following choices
A) 15%
B) 16%
C) 17%
D) 78%
E) 28%

Solution: 1500 ---- 225   100 ---- ? => 15%   15%nswer:15%
Answer: A
A circular swimming pool is surrounded by a concrete wall 4 feet wide.if the area of the wall is 11/25 of the area of the pool, then the radius of the pool in feet is? Choose the correct choice from the following answers.
A) 22	B) 88	C) 37	D) 20	E) 289

Solution: Let the radius of the pool be r. Then area of the wall and pool = π(r+4)2π(r+4)2   Area of the pool = π(r)2π(r)2   Area of the wall = π(r+4)2−π(r)2π(r+4)2−π(r)2   Given π(r+4)2−π(r)2π(r+4)2−π(r)2 = 1125(πr2)1125(πr2)   r2+8r+16−r2=1125r2r2+8r+16−r2=1125r2   11r2−200r−400=011r2−200r−400=0   Solving r = 20   Answer:20
Answer: D
In a corporation, 50 percent of the male employees and 40 percent of the female employees are at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fraction of the employees in the corporation are females?  Pick one:
A) 3/5  B) 2/3  C) 3/4  D) 4/5  E) 5/6

Solution: You can use the weighted averages formula for a 10 sec solution.   No of females/No of males = (50 - 42)/(42 - 40 )= 
(50 - 42)/(42 - 40 ) = 4
4/1= 
4/1 = 4
4/(4+1)= 4/5;   ANSWER:4/5
Answer: D
The weight of a glass of jar is 30% of the weight of the jar filled with coffee beans. After some of the beans have been removed, the weight of the jar and the remaining beans is 60% of the original total weight. What fraction part of the beans remain in the jar? Choose the correct option
A) 1/5
B) 1/3
C) 2/5
D) 1/2
E) 3/7

Solution: Let weight of jar filled with beans = 100 g   Weight of jar = 30 g   Weight of coffee beans = 70 g   Weight of jar and remaining beans = 60 g   Weight of remaining beans = 30 g   Fraction remaining = 30/70 = 3/7   Answer is 3/7.
Answer: E
How many ways can 840 be written as the product of two numbers ? Choose the correct answer:
A) 32  B) 16  C) 6  D) 18  E) 8

Solution: factor of 840 = 2*2*2*3*5*7;   Total number of method to select the combination = (3+1)*(1+1)*(1+1)*(1+1)/2= 
(3+1)*(1+1)*(1+1)*(1+1)/2 = 16
16   (here we should make attention in one step that a*b and b*a will be considered as 1 case)   ANSWER:16
Answer: B
A man sells a horse for Rs. 700 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse? Choose the most appropriate option:
A) 27  B) 98  C) 93.3  D) 96.2  E) 90.1

Solution: 93.3P = SP + 193.3P = SP - g   700 + x = 980 - 2x   3x = 280 => x = 93.3   Answer:93.3
Answer: C
Bookman purchased 40 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for $10 each. If 14 copies were sold and the total value of the remaining books was 300, how many paperback copies were sold?	Pick one
A) 6  B) 4  C) 8  D) 10  E) 12

Solution: The bookman had 10 hardback ad  40-10= 
 40-10 = 30
30 paperback copies;   14 copies were sold, hence  40-14= 
 40-14 = 26
26 copies were left. Let # of paperback copies left be p then 10p+20(26-p)=300 --> 10 p=220 --> p=22   # of paperback copies sold is 30-22= 
30-22 = 8
8   Answer: 8
Answer: C
A metallic sheet is of rectangular shape with dimensions 20 m x 25 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 2 m, the volume of the box (in m cube) is:
Select the correct option:
A) 4120 m cube
B) 4140 m cube
C) 5140 m cube
D) 1344 m cube
E) None of these

Solution: Explanation:   l = (20- 4)= 
(20- 4) = 16
16 m, [because  2+2= 
 2+2 = 4
4]   b= (25 -4)= 
(25 -4) = 21
21 m,   h= 2 m.   Volume of the box = (16 X 21 X 4) m cube   = 1344 m cube.   Option 1344 m cube
Answer: D
How many integers are there between 15 and 97, inclusive?
Select.
A) 51
B) 55
C) 56
D) 57
E) 83

Solution: I guess the easiest way to answer this is -   Say you have two positive integers, x and y where y > x   Then the number of integers between x and y is given by - (y - x) + 1   In this case, it's (97 - 15) + 1= 
(97 - 15) + 1 = 83
83. Option 83
Answer: E
A bullock cart has to cover a distance of 80km in 10hrs. If it covers half of the journey in 3/5th time. what should be its speed to cover the remaining distance in the time left.	Choose the correct choice from the following.
A) 10 kmph speed	B) 20 kmph	C) 30 kmph	D) 40 kmph	E) 50 kmph

Solution: 10 kmph speed   10 kmph   Time left = 10 - 3/5*10= 
10 - 3/5*10 = 4
4 hr 10 km/h   speed=40 km /4 hr   =10 kmph
Answer: A
An empty fuel tank is filled with brand Z gasoline. When the tank is half empty, it is filled with brand x gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand x gasoline. At this time, what percent of the gasoline in the tank is brand Z?
Options
A) 50%	B) 37.5%	C) 40%	D) 33%	E) 25%

Solution: Work with fraction of brand Z in the tank.   1st step: brand Z is 1   2nd step: brand Z is 1/2   3rd step: brand Z is (1/2)*(1/2) + 1/2 = 3/4   4th step: brand Z is (1/2)*(3/4) = 3/8 = 37.5%   Answer (37.5%)
Answer: B
By using the numbers 7, 2, 3, 4 and 6 only once, how many five digit numbers can be made that are divisible by 14?  Choose one:
A) 12
B) 48
C) 42
D) 6
E) 24

Solution: A number to be divisible by 14 must end with 14, 28, 42,56,70,84   So, there are the following cases possible:   736-42 --> the first three digits can be arranged in 3=6 ways.   Total = 6 = 6.   Answer: 6.
Answer: D
A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit? Choose the correct choice from the following.
A) Rs. 18.20	B) Rs. 70	C) Rs. 72	D) Rs. 88.25	E) None

Solution: C.P. = Rs. 100	x 392 = Rs. 1000	x 392 = Rs. 320   122.5	1225   Profit = Rs. (392 - 320) = Rs. 72.   Rs. 72)
Answer: C
Points A, B, C, and D, in that order, lie on a line. If AB = 2 cm, AC = 4 cm, and BD = 6 cm, what is CD, in centimeters?
Choices:	A) 1	B) 2	C) 3	D) 4	E) 5

Solution: Putting a value to each point, lets use the following:   A - 0   B - 2 (AB = 2)   C - 4 (AC = 4)   D - 8 (BD = 6)   CD is 8-4= 
8-4 = 4
4.   Ans 4
Answer: D
The ratio of ages of Aman, Bren, and Charlie are in the ratio 5:8:7 respectively. If 8 years ago, the sum of their ages was 76, what will be the age of Charlie 10 years from now? Select the correct option
A) 17
B) 25
C) 45
D) 47
E) 50

Solution: Let the present ages of Aman, Bren, and Charlie be 5x, 8x and 7x respectively.   5x-8 + 8x-8 + 7x-8 = 76   x = 5   Present age of 45harlie = 7*5= 
7*5 = 35
35   45harlie's age 10 years hence= 35+10= 
35+10 = 45
45   Answer= 45
Answer: C
If M is the set of all consecutive multiples of 9 between 100 and 500, what is the median of M?  Pick one:
A) 300	B) 301	C) 301.5	D) 302.5	E) 306

Solution: Since 100/9 =11.11, 500/9=55.55, M can be written as {9*12, 9*13, ...., 9*54, 9*55}. The number of elements of M is, therefore, 44(=55-12+1). Since the number of elements is even number the median is the average of the 22nd element(=9*33) and 23rd element(=9*34). So the median is (9*33 + 9*34)/2 = 301.5. The answer is 301.5.
Answer: C
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?	Choose the correct option:	A) 9/20	B) 1/20	C) 5/20	D) 8/15	E) 6/9

Solution: Here, S = {1, 2, 3, 4, ...., 19, 20}.   Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.   p(E)=n(E)/n(S)   =9/20   The answer should be 9/20
Answer: A
Anthony and Michael sit on the six-member board of directors for company A. If the board is to be split up into 2 three-person subcommittees, what percent of all the possible subcommittees that include Michael also include Anthony?
Options.
A) 20%	B) 30%	C) 40%	D) 50%	E) 60%

Solution: Soln: Let the commitees be I and II   Assuming that Anthony and Michael from A go into commitee I, there is just one more place left to be filled in that commitee and it can be taken by any of the 4 remaining people. Thus 4 ways.   Since the Anthony and Michael can also go into commitee II, we get 4 ways for that commitee also.   So in total = 8 ways   Now total number of ways of choosing 3 from 6 people is   = 640%3   = 6 * 5 * 4/3!   = 20 ways   Therefore Probability is = (8 /20) * 100= 
(8 /20) * 100 = 40
40%
Answer: C
A and B together can plough a field in 10 hours but by himself A requires 15 hours. How long would B take to plough the same field? Pick:  A) 10 hours  B) 20 hours  C) 30 hours  D) 40 hours  E) 50 hours

Solution: If A and B together can do a piece of work in x days and A alone can do the same work in y days,   then B alone can do the same work in x y/ y – x days.   Therefore, the No. of hours required by B = 10 × 15/ 15 – 10 = 150/5= 
150/5 = 30
30 hours.   Answer : 30 hours
Answer: C
The product of two numbers is 220 and the sum of their squares is 289. The sum of the number is?	Answers.
A) A)23  B) B)25  C) C)27  D) D)31  E) E)35

Solution: Let the numbers be x and y.   Then, xy = 220 and x2 + y2 = 289.   (x + y)2 = x2 + y2 + 2xy = 289 + (2 x 220) = 729   x + y = 27.   Option 27
Answer: C
find the average of first 20 multiples of 7? Pick one.
A) 73.5 B) 56.4 C) 25.8 D) 12.4 E) 56.9

Solution: Required average =7(1+2+3+…….+20)/20   =(7*20*21)/(20*2)   =(147/2)=73.5.   73.5ns: 73.5
Answer: A
A certain board game has a row of squares numbered 1 to 100. If a game piece is placed on a random square and then moved 9 consecutive spaces in a random direction, what is the probability the piece ends no more than 9 spaces from the square numbered 49? Select the correct option
A) 19%
B) 29%
C) 25%
D) 20%
E) 15%

Solution: No more than 9 spaces from 49 means in the rangefrom 49-9= 
49-9 = 40
40 to  49+9= 
 49+9 = 58
58, inclusive. Total numbers in this range   58-40+1= 
  58-40+1 = 19
19, the probability favorable/total=19/100   19%nswer: 19%
Answer: A
The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:	Choose one
A) 153601	B) 153600	C) 153602	D) 153603	E) 153604

Solution: Perimeter = Distance covered in 8 min. =(12000/60) x 8m = 1600 m.   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 m2.   Answer: 153600
Answer: B
The perimeter of a triangle is 48 cm and the in radius of the triangle is 2.5 cm. What is the area of the triangle? Pick: A) 76 B) 88 C) 60 D) 55 E) 35

Solution: Area of a triangle = r * s   Where r is the in radius and s is the semi perimeter of the triangle.   Area of triangle = 2.5 * 48/2= 
2.5 * 48/2 = 60
60 cm2   Answer:60
Answer: C
Of the employees in a company, 40 % are female who have a master degree. If 20 % of the female employees do not have a master degree, what percent of the employees in the company are female?  Choose the correct choice from the following choices.
A) 54% B) 52% C) 50% D) 51% E) 55%

Solution: Let E be total no. of employees and F be total no of female employees.   Question asked what is F/E X 100%?   No. of female employees with Masters = 0.4 x E (From the question)   No. of female employees without masters = 0.2 x F (From the question)   Therefore No. of female employees with masters = F - 0.2 F = 0.8 F   The 2 expressions equal each other therefore 0.8F = 0.4E; F/E = 0.4/0.8 = 50%   Ans: 50%
Answer: C
Two numbers are 30% and 37% are less than a third number .How much percent is the second number less than the first?  Choose the correct choice from the following options
A) 15%	B) 12%	C) 10%	D) 5%	E) 18%

Solution: I II III   70 63 100   70 -------- 7   100 ------ ? => 10%   ANSWER:10%
Answer: C