MU-NLPC/Calc-aqua_rat huggingface dataset:
What is the absolute value of twice the difference of the roots of the equation F=5y^2 − 20y + 15 = 0 ?
Choose the correct choice from the following answers:
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: F=5y^2 − 20y + 15 = 0 --> y^2 − 4y + 3 = 0 --> y=1 or y=3. The difference is 2, twice the difference is 4.   Answer: 4.
Answer: E
Five bells begin to toll together at 12:00 noon and toll respectively at intervals of 4, 5, 6, 7, and 8 seconds. Not including the toll at 12:00 noon, how many more times will all five bells toll together before 2:00 pm (i.e. two hours later)?  Options:
A) 6 B) 7 C) 8 D) 9 E) 10

Solution: The least common multiple is 2*2*2*3*5*7= 
2*2*2*3*5*7 = 840
840.   7200 seconds / 840= 8 + remainder.   The answer is 8.
Answer: C
Before a salary increase, the weekly salary of a worker for 45 hours in a week was as much as the worker is paid now for 40 hours of work in a week. What is the percent increase in the worker's salary per hour?
Choose the correct choice:  A) 5  B) 7.5  C) 8  D) 10  E) 12.5

Solution: Let x be the original salary per hour.   Let y be the salary per hour after the increase.   40y=45x   y=(45/40)= 
(45/40) = 9/8 = around 1.125
1.125x   The salary increased 12.5%.   The answer is 12.5.
Answer: E
If the domain of function f given by f(x) = -x 2 + 6x is given by the interval [0 , 6], then the range of f is given by the interval	Choose the correct choice from the following.
A) [0 , 9]
B) [0 , 6]
C) [0 , 3]
D) [3 , 6]
E) None

Solution: If the domain of function f given by f(x) = -x 2 + 6x is given by the interval [0 , 6], then the range of f is given by the interval   Answer [0 , 6]
Answer: B
In a contest, there are 9 identical boxes: in 7 boxes there are a $50 bill into each box, and in 2 boxes there are a $100 bill into each one. To win and get the money picked, you have to choose two boxes that contain different bills. What is the probability to win?  Choose the correct choice
A) 2/9  B) 1/9  C) 49/1296  D) 7/36  E) 7/18

Solution: We are told that we have 9 identical boxes, 7 of $50 and 2 of $100. The bills are picked simultaneous and randomly, B1 and B2, in different flavors. There are two acceptable outcomes: 1) B1 is $50 and B2 is $100; 2) B1 is $100 and B2 is $50. Let's go: 1) B1 = (7/9)(2/8)= 7/36 chance of this happening. 2) B2 = (2/9)(7/8) = 7/36 chance of this happening. Then: (7/36)+(7/36)= 7/18, chance of getting the result that you wanted. Answer 7/18.
Answer: E
A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
Pick one:
A) 76 seconds B) 17 seconds C) 40 seconds D) 16 seconds E) 14 seconds

Solution: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec   Total distance = 360+140= 
360+140 = 500
500 meter   Time= Distance/speed   = 500 * (2/25)= 
500 * (2/25) = 40
40 seconds   Answer:40 seconds
Answer: C
A train 160 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform? Choose the correct choice from the following answers
A) 443 m  B) 354 m  C) 340 m  D) 350 m  E) 250 m

Solution: 340 m   340   340 m = (72 * 5/18)*25-160= 
(72 * 5/18)*25-160 = 340
340
Answer: C
If p and q are prime numbers, how many divisors does the product p^3 * q^6 have?
Choose the correct choice from the following answers:
A) 9	B) 12	C) 18	D) 28	E) 36

Solution: Lets take an example: find the number of factors of 100   try to represent 100 in least possible prime numbers   100= 2^2 * 5^2=p^a*q^b   no of factors is given by the formula (a+1)* (b+1)=(2+1)(2+1)=9   similarly find the number of factors of p^3 * q^6--->a=3,b=6   (3+1)(6+1)=28 Ans 28.
Answer: D
in a certain flower shop, which stocks four types of flowers, there are 1/2 as many violets as carnations, and 1/2 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 most appropriate option.
A) 50
B) 55
C) 60
D) 45
E) 40

Solution: Given :-   Violets - C/2   Carnations - C   Tulip - C/4   Rose - C/4   Total flowers in terms of C = C/2+C+C/4+C/4 = 2C   Percentage of Carnations = C/2C *100 =50%   50nswer 50
Answer: A
The ratio of males and females in a city is 7 : 8 and the percentage of children among males and females is 25% and 20% respectively. If the number of adult females in the city is 156800 what is the total population?
Choose the correct choice from the following answers:
A) 245000  B) 367500  C) 196000  D) 171500  E) None of these

Solution: Number of females = 156800 × 100⁄80 = 196000   \ Number of males = 7⁄8 × 196000 = 171500   \ Total population = 196000 + 171500= 
196000 + 171500 = 367_500
367500   Answer 367500
Answer: B
Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?  Choose the correct answer:
A) 3.5	B) 4.5	C) 5.6	D) 6.5	E) 7.5

Solution: C.P. of 1 toy = 375/12 = Rs. 31.25   S.P of 1 toy = Rs. 33   Profit = 1.75/31.25 * 100 = 28/5= 
28/5 = 28/5 = around 5.6
5.6%   ANSWER:5.6
Answer: C
Find large number from below question The difference of two numbers is 1395. 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 answers
A) 1234	B) 1265	C) 1350	D) 1467	E) 1671

Solution: Let the smaller number be x. Then larger number = (x + 1395).   x + 1395 = 6x + 15   5x = 1380   x = 276   Large number = 276+1395= 
276+1395 = 1_671
1671   1671
Answer: E
A container has a capacity of 20 gallons and is full of spirit. 5 gallons of spirit is drawn out and the container is again filled with water. This process is repeated 5 times. Find how much spirit is left in the resulting mixture finally? Choose one:  A) (257/525) gallons  B) 1.5552 gallons  C) 1.5 gallons  D) 1.25 gallons  E) None of these

Solution: There is a direct formula to calculate such repetition:   Left QTY / Orig QTY = ( (Orig QTY - Rep QTY) / Orig QTY )^n   where n is number of times mixing done:   Left QTY / 20 = (20 -5)^5 / 20^5   Left QTY = 20 (15/20)^5   Left QTY = 20 ( 3/5 )^5   Left QTY = 1.5552   Answer is 1.5552 gallons
Answer: B
A 6% stock yields 8%. The market value of the stock is:
Options.
A) Rs. 48  B) Rs. 75  C) Rs. 96  D) Rs. 133.33  E) none

Solution: For an income of Rs. 8, investment = Rs. 100.   For an income of Rs. 6, investment = Rs. (100/8 * 6) = Rs. 75.   Market value of Rs. 100 stock = Rs. 75.   Answer = Rs. 75
Answer: B
W, X, Y, Z are integers. The expression X - Y - Z is even and the expression Y - Z - W is odd. If X is even what must be true?
Answers.
A) U
B) W
C) E
D) H
E) R

Solution: Sol: X is even so Y, Z both are even or both are odd.   Now Y - Z in both cases even. So (Y - Z ) - W = odd happens only when w is odd   Ans: W is odd   Answer:W
Answer: B
A train 130 meters long completely crosses a 320-meter long bridge in 30 seconds. What is the speed of the train in km/h?
Select:
A) 42 km/h  B) 46 km/h  C) 50 km/h  D) 54 km/h  E) 58 km/h

Solution: speed = distance / time = (130 + 320)/30 = 450/30 (m/s) * 3600/1000 = 54 km/h   The answer is 54 km/h.
Answer: D
The simple form of the ratio 7/6:3/2 is?  Choose the correct choice from the following:
A) 5:8 B) 7:9 C) 5:9 D) 5:3 E) 5:1

Solution: 7/6 : 3/2 = 7:9   Answer: 7:9
Answer: B
To be eligible for retirement benefits at the Norman Corporation, the sum of an employee's age, in years, and the number of years employment must be at least 68. If x, where x <68, is a certain employee's age when hired and y is the minimum number of years of employment required for the employee to be eligible for retirement benefits, which of the following equations represents the relationship between x and y? Choose one:
A) xy=68
B) x+y=68
C) 2x+y=68
D) 2x+2y=68
E) x+2y=68

Solution: We are told that when a certain employee was hired he was x years old and that the he needed minimum y years to be eligible for benefits.   Now,after y years of employment, when the employee will be be eligible for benefits, the employee will be x+y years old and will have y years of employment, thus{age after y years}+{employment years}=(x+y)+y=x+2y=68.   Answer: x+2y=68
Answer: E
A pupil's marks were wrongly entered as 35 instead of 23. Due to that the average marks for the class got increased by half. The number of pupils in the class is :	Pick:
A) 30	B) 80	C) 20	D) 25	E) 24

Solution: Let there be x pupils in the class.   Total increase in marks = (X*1/2) = X/2.   X/2 = (35 - 23)   => X/2 = 12   => X = 24.   ANSW24R:24
Answer: E
In how many ways 6 Indians and 1 Englishmen can be seated in a row so that they are alternate?
Answers
A) 120
B) 265
C) 144
D) 720
E) 256

Solution: number of ways = 6!*1! = 720   Answer is 720
Answer: D
A family has two children. find the probability that both the children are girls given that at least
one of them is a girl? Answers:
A) 1/3
B) 4/7
C) 4/9
D) 4/11
E) 5/7

Solution: Let b stand for boy and g for girl. The sample space of the experiment is   S = {(g, g), (g, b), (b, g), (b, b)}   Let E and F denote the following events :   E : ‘both the children are girls’   F : ‘at least one of the child is a girl’   Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}   Now E n F = {(g,g)}   Thus P(F) = 3/4   and P (E n F )= 1/4   Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3   1/3)
Answer: A
A man buys two cycles for 1200 each, he sells first cycle at a loss of 20% ,if he desires to get a profit of 15% on whole for how much should he sell his 2nd cycle?	Choose the correct choice:
A) 1600  B) 1700  C) 1800  D) 1900  E) 1950

Solution: 1st cycle sold at a loss of 20%, so the Sp of 1st cycle= 1200*(1-20/100)= 
1200*(1-20/100) = 960
960   Total 1800P for 2 cycles= 1200*2= 
1200*2 = 2_400
2400   Desired SP for 2 cycles= 2400*(1+15/100)= 
2400*(1+15/100) = 2_760
2760   so, SP of 2nd cycle= 2760-960= 
2760-960 = 1_800
1800   ANSWER:1800
Answer: C
7^1+7^2+7^3+...........+7^2015 find out how many numbers present which unit place contain 3 ?	Select the correct option
A) 502  B) 503  C) 504  D) 505  E) 506

Solution: 7^3,7^7,7^11,7^15,7^19.........7^2015 contains last digit=3.   Now,we see   3,7,11,15....2015 are in AP   tn=a+(n-1)d   2015=3+(n-1)4   2015=3+4n-4   4n=2016   n=504   ANSWER:504
Answer: C
There is enough provisions for 600 men in an army camp for 25 days. If there were 300 men less, how long will the provision last?	Pick.
A) 35 days  B) 40 days  C) 45 days  D) 50 days  E) 55 days

Solution: Exp: We have, M1D1 = M2D2   600*25= 300* D2   D2 = 600*25/300= 
600*25/300 = 50
50 days.   Answer: 50 days
Answer: D
In three years, Janice will be three times as old as her daughter. Six years ago, her age was her daughter’s age squared. What would be the age of Janice Daughter after 3 years
Choose one:
A) 18
B) 36
C) 40
D) 42
E) 45

Solution: Let Jane's age be J and daughters' age be D...   Given J   + 3= 
  + 3 = 3
3(D + 3 )=> J - 6 = 3D -> Eq1.   Given J-6 = (D-6)^2 --> Eq 2..   sub J-6 value in eq 2... 3D = D^2 - 12D + 36.   0 = D^2 - 15D + 36 => D = 12 or D = 3.   When D = 12 we get from eq 1... J+3 = 45 => J =42..   When D = 3 ..we get from eq 1.. J+3 = 18 => J = 15...   IMO option 18 is correct answer..
Answer: A
Given that x and y are nonnegative integers, compute the number of pairs (x; y) such that
5x + y = 20. Select the correct option:
A) 1  B) 5  C) 10  D) 15  E) 20

Solution: For x = 0,1,2,3,4, there is a valid y, giving the answer 5 .   correct answer 5
Answer: B
If the speed of the boat in still water is 12km/hr and the speed of the stream is 5km/hr. Find the time taken to travel 34kms down stream.  Choose the correct option
A) 4 hrs.	B) 1 hrs.	C) 3 hrs.	D) 2 hrs.	E) 5 hrs.

Solution: DS =speed of the boat + speed of the stream 5+12= 
5+12 = 17
17km/hr. Time taken to cover 34km down stream=34/17= 
34/17 = 2
2hrs. Answer : 2 hrs.
Answer: D
The sum of 5 hours 45 minutes and 55 minutes is approximately what percent of a day?
Choose the correct choice from the following choices:
A) approx 27% B) 16% C) 24% D) approx 18% E) approx 72%

Solution: Since the question is asking for an approximate percentage   5:45 + 0:45 ~ 6:30 hours   % of day = 6.5*100/24 = 7*100/24 ~ 27%   Answer is A.   If you had 27 and 29 as options you would probably need to do more accurate calculations. In this particular case while approximating values we increase both numerator and denominator so our calculations should be close
Answer: A
Before being simplified, the instructions for computing income tax in country R were to add 5 percent of one's annual income to the average(arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in country R's currency, for a person in that country whose annual income is I? Choices
A) 50 + I/200 B) 50 + 3I/100 C) 50+ 11I/200 D) 100+ I/50 E) 100+ 3I/100

Solution: Income of a person is I   5 percent of ones annual income = 5I/100   100 units of 50+ 11I/200ountry R's currency = 100   1 percent of one's annual income = I/100   Average of 100 units and 1 percent annual income = 50 + I/200   Sum of average and 5 percent = 5I/100 + 50 + I/200   = 50 + 11I/200   So answer is 50+ 11I/200.
Answer: C
sale of Rs 6835, Rs. 9927, 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 ?  Pick:	A) 4966	B) 2477	C) 2877	D) 2676	E) 1881

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. 4966   4966nswer: 4966
Answer: A
The area of a rectangle is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the rectangular field ? Pick:
A) 18 meter
B) 20 meter
C) 22 meter
D) 25 meter
E) 30 meter

Solution: Explanation:   Let breadth =x metres.   Then length =(115x/100)metres.   =x∗115x/100=460   x2=(460x100/115)x2=400x=20   ANSWER IS 20 meter
Answer: B
A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 30 hrs and a machine of type S does the same job in 15 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?	Choose the correct choice from the following:
A) A)3
B) B)4
C) C)5
D) D)9
E) E)12

Solution: Rate of machine R =1/30   Rate of machine S =1/15   since same no of machines used for R and S to do the same work in 2 hrs   So collective rate needed to finish the work in 2 hrs= 1/2   Let the no of machine be x   So, x/30 +x/15 =1/2   x3/30=1/2   x=30/6= 
30/6 = 5
5   So no of machine R is 5   Answer 5
Answer: C
x percent of y percent of z is decreased by y percent What is the result?  Select:
A) (100xyz - xy^z2) / 1,000,000 B) (xz - y) / 100 C) (xz - y) / 10,000 D) (xyz - 2y) / 100 E) (xyz - 2y) / 10,000

Solution: We're told that X percent of Y percent of Z is DECREASED by Y percent. We're asked for the result of all of this math.   IF....   X = 10   Y = 50   Z = 100   First, 50% of 100 = 50   Next, 10% of 50 = 5   Finally, 5 decreased by 50% of itself is 2.5   So we're looking for an answer that equals 2.5 when X=10, Y=50 and Z=100.   Answer A. (100xyz - xy^2z) / 1,000,000 = (5,000,000 - 2,500,000)/1,000,000 = 2,500,000/1,000,000 = 2.5 This is a M(100xyz - xy^z2) / 1,000,000TCH   (100xyz - xy^z2) / 1,000,000
Answer: A
How much time will take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
Choose the correct choice from the following
A) 7
B) 4
C) 5
D) 3
E) 2

Solution: Time = (100 * 81) / (450 * 4.5)= 
(100 * 81) / (450 * 4.5) = 4
4 years'   Answer:4
Answer: B
Working individually, Jane can bake cakes for 4 hours and Roy can bake cakes in 5 hours. If Jane and Roy work together but independently at the task for 2 hours, at which point Roy leaves, how many remaining hours will it take Jane to complete the task alone? Answers.
A) 1/2  B) 2/5  C) 3/4  D) 1/4  E) 1/5

Solution: In first 2 hrs Roy will finish 2/5 = 2/5 of work and Jane will finish 2/4 work so total 2/5 + 1/2 = 9/10 work is finished and 1-9/10 = 1/10 work remaining. Now Jane will take (1/10)*4 = 2/5 hrs to finish it.   So answer is 2/5.
Answer: B
Two bus stations are 600 km apart. if two separate buses depart from both stations and travel towards each other, at what time will they meet each other, given that the first bus left at 12 p.m. and travels at a speed of 60 kmph while the second bus left at 1 p.m. and travels at a speed of 40 kmph.
Choose the correct option.
A) 2.40 p.m.
B) 8.40 p.m.
C) 5.40 p.m.
D) 7.40 p.m.
E) 6.40 p.m.

Solution: Suppose they meet x hours after 12 p.m.   Distance moved by first bus in x hours + distance moved by 2nd bus in x-1 hrs = 600   60x+40(x-1) =600   60x+40x-40= 600   100x= 640   x = 6.4   So they meet 6.4 hr after 12 p.m. which is at 6.40 p.m.   Answer is 6.40 p.m.
Answer: E
A Caterpillar crawls a distance with speed of 21inches/min in the one direction and after feeding moves back in the same direction with 7inches/min and what is the average speed of it?	Choose the correct choice from the following answers:
A) 11.5 inch/ min B) 10.5 inch/ min C) 12.5 inch/ min D) 13.5 inch/ min E) 14.5 inch/ min

Solution: average speed = 2*21*7/(21+7) = 2*21*7/28 = 21/2= 
21/2 = 21/2 = around 10.5
10.5 inch/ min   ANSWER:10.5 inch/ min
Answer: B
The remainder obtained when a prime number greater than 8 is divided by 8 is  Choose the correct choice:
A) a) 1 or 3	B) b) 1 or 5	C) c) 3 or 5	D) d) 4 or 5	E) e) 5

Solution: The easiest way to answer this question is probably to pick numbers. Use the next two prime numbers greater than 8, i.e. 13 and 11:   13/8 = 1 + remainder of 5   11 / 8 = 1 + remainder of 3   This is already sufficient to see that answer choice b) is correct.   c) 3 or 5
Answer: C
After working for 6 days, Ashok finds that only 1/3 rd of the work has been done. He employs Ravi who is 60% as efficient as Ashok. How many days more would Ravi take to complete the work?  Choose the correct choice from the following:
A) 20 days  B) 24 days  C) 27 days  D) 21 days  E) 26 days

Solution: 20 days   20 days   1/3 ---- 6   1 -------? 20 days = 18   R = 1/18 * 60/100 = 1/30   1 ----- 1/30   2/3 ----? => 20 days
Answer: A
70,76, 74,85,90,105,105,130,130,130
The list consists of the times in seconds that it took each of the 10 school children to run a distance of 400 mts . If the standard deviation of the 10 running times is 22.4, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times.  Choose the correct choice.
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: How many of the 10 running times are more than one SD below the meanmeans how many data points from given 10 are less thanmean-1SD.   We are given that SD=22.4, so we should find mean --> mean=100 --> there are only 3 data points below  100-22.4= 
 100-22.4 = 77.6
77.6, namely 70 75, and 74.   Answer: 3.
Answer: C
A student is ranked 6th from right and 5th from left. How many students are there in totality ?	Choose one
A) 10  B) 19  C) 20  D) 21  E) 22

Solution: From right 6 , From left 5   Total = 6+5-1= 
6+5-1 = 10
10   10NSWER:10
Answer: A
The diagonals of a rhombus are 17 cm and 20 cm. Find its area?
Options
A) 176	B) 186	C) 150	D) 170	E) 172

Solution: 1/2 * 17 * 20= 
1/2 * 17 * 20 = 170
170   Answer:170
Answer: D
Caleb spends $68.50 on 50 hamburgers for the marching band. If single burgers cost $1.00 each and double burgers cost $1.50 each, how many double burgers did he buy?  Choose one:
A) 5
B) 10
C) 37
D) 40
E) 45

Solution: Solution -   Lets say, Single hamburgersxand Double hamburgersy   Given that,   x+y=50 and 1x+1.5y=68.50. By solving the equations y=37. ANS 37.
Answer: C
A train passes a station platform in 30 sec and a man standing on the platform in 12 sec. If the speed of the train is 54 km/hr. What is the length of the platform?  Choices.
A) 227 B) 240 C) 200 D) 178 E) 270

Solution: Speed = 54 * 5/18= 
54 * 5/18 = 15
15 m/sec.   Length of the train= 15 * 12= 
15 * 12 = 180
180 m.   Let the length of the platform be x m . Then,   (x + 180)/30= 15 => x = 270 m.   Answer:270
Answer: E
A certain list of 100 data has an average (arithmetic mean) of 5 and a standard deviation of d, where d is positive. Which of the following pairs of data, when added to the list, must result in a list of 100 data with standard deviation less than d?  Choices:
A) -5 and 0 B) 0 and 0 C) 0 and 5 D) 0 and 10 E) 5 and 5

Solution: Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.   So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller.   According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount.   Closest to the mean are 5 and 5 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD.   Answer: 5 and 5.
Answer: E
how many five digit numbers are there such that two left most digits are even and remaining are odd and 4 digit should not be repeated.  Select:
A) 950
B) 960
C) 970
D) 980
E) 990

Solution: even numbers are 2,4,6,8 and odd 1,3,5,7,9   so choice for first 2 digit 4 and 4   and for last 3 digit 5 ,4 ,3 coz not repeated   so ans 4*4*5*4*3= 
4*4*5*4*3 = 960
960   ANSWER:960
Answer: B
In a chess competition involving some men and women, every player needs to play exactly one game with every other player. It was found that in 45 games, both the players were women and in 190 games, both players were men. What is the number of games in which one person was a man and other person was a woman?	Choices.
A) 40	B) 120	C) 180	D) 200	E) 220

Solution: This is similar to handshake problem, If there are NN people, then number of handshakes = 1+2+...N=N∗(N−1)/2   No. of Women be xx and given x∗(x−1)/2=45 This gives x=10   |||y No. of Men : solve y∗(y−1)/2=190. This gives y=20   so total Men vs. Women = 10*20= 
10*20 = 200
200. Answer is 200
Answer: D
How many numbers between 200 and 700 begin or end with 5?  Select the correct option:
A) 20
B) 60
C) 140
D) 110
E) 120

Solution: How many numbers between 200 and 700 begin or end with 5?   Just think that those numbers are:   i) The ones ending in 5: 205, 215, 225, ... , 695 --> 50 numbers   ii) The ones beginning in 3: 300, 301, 302, 303, ... , 393, ... , 399 --> 100 numbers   BUT 10 out of the first 50 numbers are repeated in the second set.   THEREFORE, the solution is 140 numbers.   Answer: 140
Answer: C
If a(a - 5) = 6 and b(b -5) = 6 where a ≠ b, then a + b = Answers:  A) −48  B) −2  C) 2  D) 9  E) 5

Solution: i.e. if a = -1 then b = 6   or if a = 6 then b = -1   But in each case a+b = -1+6= 
-1+6 = 5
5   Answer: option 5
Answer: E
A new home buyer pays 4% annual interest on her first mortgage and 9% annual interest on her second mortgage. If she borrowed a total of $340,000, 80% of which was in the first mortgage, what is her approximate monthly interest payment?	Choose the correct choice from the following options:  A) $1,416  B) $1,733  C) $3,466  D) $13,333  E) $20,796

Solution: 0.04x + 0.09y = 340000 [1]   0.04x = 0.80 * 340000= 
0.80 * 340000 = 272_000
272000 [2]   272000 + 0.09y= 340000 --> 0.09y = 64000 [3]   272000 / 12 = 22666.67 [4]   64000 / 12 = 5666.67 [5]   $1,416dding [4,5] we get: 28333.33 [6]   Dividing [6] / 2 to get an average we get 1.416,$1,416NS $1,416
Answer: A