MU-NLPC/Calc-aqua_rat huggingface dataset:
For all positive integers n and m, the function A(n) equals the following product:
(1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/9 + 9^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number, while B(m) equals the sum of the reciprocals of all the positive integers from 1 through m, inclusive. The largest reciprocal of an integer in the sum that B(25) represents that is NOT present in the distributed expansion of A(5) is Choices.
A) 1/4  B) 1/5  C) 1/6  D) 1/7  E) 1/2

Solution: For all positive integers n and m,   A(n) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number,   note:i think there's a typo in the above function, A(n) could be (1 + 1/2 + 1/2^2)(1 + 1/3 +1/3^2)(1 + 1/5 +1/5^2)…(1 + 1/p_n + 1/p_n^2)   B(m) = sum of the reciprocals of all the positive integers from 1 through m, inclusive.   A(5), here 5 represents the 5th smallest prime number; the 5th smallest prime number is 11 {2, 3, 5, 7, 11, ...}   A(5) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)(1 + 1/7 + 1/7^2)(1 + 1/11 + 11^2)   The distributed expansion of A(5) = 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 +1/7 + 1/9+ 1/10 + 1/11 +1/12 + 1/14+ ...   missing numbers are 1/8, 1/13, 1/16, ....   B(25) = (1 + 1/2 + 1/3 + 1/4 + ... + 1/16 + 1/17 + ... + 1/25)   here the largest reciprocal is 1 and the reciprocals are arranged in descending order based on their values   The largest reciprocal that present in B(25) but not in A(5) is 1/2   Answer 1/2
Answer: E
If s and t are positive integers such that s/t = 64.15, which of the following could be the remainder when s is divided by t ?
Choose the correct choice from the following answers
A) 2
B) 4
C) 8
D) 20
E) 45

Solution: The remainder is 0.15 or 15/100. You can go one step further and say that X/Y=12/100, where X and Y are whole numbers. Plug in all the answer choices for X and see which one makes Y a whole number.   One thing that jumps out at me is that A, B, C, and D are all even. E on the other hand is odd. Why? Maybe I'll start plugging in here first.   45/Y=15/100   15Y=4500   Y=300   Answer: 45.
Answer: E
In Town X, 96 percent of the population are employed, and 24 percent of the population are employed males. What percent of the employed people in Town X are females?
Choose the correct choice from the following answers:	A) 16%	B) 25%	C) 32%	D) 75%	E) 52%

Solution: Total employed people 96%, out of which 24 are employed males, hence 72% are employed females.   (employed females)/(total employed people)=72/96=3/4=75%   Answer: 75%.
Answer: D
On Charlie's cell phone plan, he signed up for 8GB of data per 4 week period. If he went over the 8GB per month, it would cost him an extra $10.00 per GB.
In the first week, he used 2 GB; in the 2nd week, he used 3 GB; in the 3rd week, he used 5 GB; and in the 4th week, he used a whopping 10GB.
How much extra did Charlie need to pay on his cell phone bill?	Choose the correct answer:
A) $120
B) $40
C) $80
D) $100
E) $140

Solution: To determine how much extra he would need to pay, you have to add all 4 weeks of GB usage (2+3+5+10 = 20).   To determine the extra amount of GB usage, you have to subtract the the original amount of GB (8) allowed on his plan. 20-8 = 12   To determine the extra cost on his cell phone plan, you have to multiply $10.00 per extra usage (12) for a total of $120.00.   The correct answer is $120
Answer: A
The ratio between the speeds of two trains is 3: 4. If the second train runs 400 kms in 6 hours, then the speed of the first train is ?
Select:	A) 50.01 km/hr	B) 51.01 km/hr	C) 40.01 km/hr	D) 52.01 km/hr	E) None of these

Solution: Explanation:   Let the speeds of two trains be 3X and 4X km/hr.   4/X=400/6=>X=16.67 Km/hr   So speed of first train is   16.67*3= 
  16.67*3 = 50.01
50.01 km/hr   Option 50.01 km/hr
Answer: A
In how many different number of ways 6 men and 2 women can sit on a shopa which can accommodate persons?  Choose the most appropriate option.
A) A)160
B) B)170
C) C)190
D) D)1680
E) E)230

Solution: 8p4 = 8 x 7 × 6 × 5 = 1680   Option '1680'
Answer: D
If 2994 Ã· 14.5 = 173, then 29.94 Ã· 1.45 = ?	Choose one:
A) 17.1 B) 17.3 C) 17.5 D) 17.7 E) 17.2

Solution: 29.94/ 1.45 = 299.4/14.5   = (2994/14.5) x 1/10) [ Here, Substitute 173 in the place of 2994/14.5 ]   = 173/10= 
173/10 = 173/10 = around 17.3
17.3   Answer is 17.3.
Answer: B
1764 can be expressed as a product of primes as  Choose the correct choice
A) 2 × 2 × 3 × 3 × 7 × 7
B) 2 × 3 × 3 × 3 × 7 × 7
C) 2 × 2 × 2 × 3 × 3 × 7
D) 2 × 3 × 3 × 3 × 3 × 7
E) None of these

Solution: Explanation:   It is clear that 1764 = 2 × 2 × 3 × 3 × 7 × 7   2 × 2 × 3 × 3 × 7 × 7nswer: Option 2 × 2 × 3 × 3 × 7 × 7
Answer: A
There are 600 boys in a hostel. Each plays either hockey or football or both. If 75% play hockey and 35% play football, how many play both?
Choices.
A) 120  B) 150  C) 200  D) 180  E) 60

Solution: n(A) = 75*600/100= 
75*600/100 = 450
450   n(B)= 35*600/100= 
35*600/100 = 210
210   n(AUB)= 600   n(AnB) = 450+210-600= 
450+210-600 = 60
60   Answer is 60
Answer: E
A volume of 10936 l water is in a container of sphere. How many hemisphere of volume 4l each will be required to transfer all the water into the small hemispheres?	Answers:	A) 2812	B) 8231	C) 2734	D) 4222	E) 4254

Solution: a volume of 4l can be kept in 1 hemisphere   therefore, a volume of 10936l can be kept in (10936/4) hemispheres   ans.2734   ANSWER:2734
Answer: C
The unit digit in the product (624 * 708 * 913 * 463) is:	Choose the correct choice from the following options
A) 2	B) 7	C) 6	D) 8	E) 1

Solution: Explanation:   Unit digit in the given product = Unit 8igit in (4*8*3*3) = 8   ANSWER: 8
Answer: D
In business, A and C invested amounts in the ratio 3:2, whereas the ratio between amounts invested by A and B was 3:1, If Rs 60000 was their profit, how much amount did C receive.	Pick one.
A) 10000
B) 20000
C) 15000
D) 61000
E) 26000

Solution: Explanation:   A:20000 = 3:1 = 3:1   => A:C = 3:2 = 3:2   => A:20000:C = 3:1:2   C share = (2/6)*60000= 
(2/6)*60000 = 20_000
20000   Option 20000
Answer: B
The average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 28. Which of the following integers is the higher of the remaining two integers?	Choose the correct answer.
A) 11	B) 86	C) 66	D) 55	E) 44

Solution: Let the four integers be A, B, C and D where A > B > C > D.   (A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1)   A = 93, D = 39 and B - C = 28   (1) => B + C = 276 - (A + D) = 276 - 132= 
276 - 132 = 144
144.   86 + 86 -28= 
86 + 86 -28 = 144
144   86= (144 + 28)/2= 
(144 + 28)/2 = 86
86   Answer:86
Answer: B
3 men, 4 women and 6 children can complete a work in 7 days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 days? Choose the correct option:
A) 7
B) 8
C) 6
D) 5
E) 3

Solution: Let 1 woman's 1 day work = x.   Then, 1 man's 1 day work = x/2 and 1 child's 1 day work x/4.   So, (3x/2 + 4x + + 6x/4) = 1/7   28x/4 = 1/7 => x = 1/49   1 woman alone can complete the work in 49 days.   So, to complete the work in 7 days, number of women required = 49/7= 
49/7 = 7
7.   7nswer: 7
Answer: A
If GAVE is coded as 4657 and RAT is coded as 333. How is GATE coded? Choose the correct choice from the following:
A) 4673
B) 4367
C) 4637
D) 4763
E) 4376

Solution: g-4 a-6 e-7 from the code gate   t - 3 from bat   ANSWER:4637
Answer: C
The perimeter of an isosceles right triangle is 4 + 4 sq rt 2. What is the length of the hypotenuse of the triangle? Choices:
A) 2.82
B) 2
C) 3
D) 4
E) 5

Solution: side of triangle is a then perimeter = a+ a +a.sqrt2 ( right angle and pythagorus) =2a +a .sqrt 2 = 4 + 4 Sqrt2 or,   a. ( 2+ sqrt2) = 4(1 + sqrt2) a= 4.( 1+sqrt2)/2+sqrt2 =4*2.414/3.414 = then hypotenuse = 2.82   2.82
Answer: A
If the numerator of a fraction is increased by 2 and the denominator is increased by 1, the fraction becomes 5⁄8 and if the numerator of the same fraction is increased by 3 and the denominator is increased by I the fraction becomes 3⁄4. What is the original fraction?	Choose the correct choice from the following choices:
A) Data inadequate
B) 2⁄7
C) 4⁄7
D) 3⁄7
E) None of these

Solution: Let the original fraction be x⁄y.   Then x+2y+1=58x+2y+1=58 or, 8x – 5y = – 11........ (i)   Again, x+3y+1=34x+3y+1=34 or, 4x – 3y = –9........ (ii)   Solving, (i) and (ii) we get x = 3 and y = 7   ∴ fraction = 3⁄7   Answer 3⁄7
Answer: D
A city had 400 migrants in the year 2000. Since then, The number of migrants in a countrythe city has doubled every 3 years. If there were 400 migrants in the country in the year 2000, What was the increase in the population of migrants during the period from 2009 to 2012?
Choices
A) 1400
B) 2300
C) 3000
D) 3200
E) 3800

Solution: The population will increase in the following order:   2000: 400   2003: 800   2006: 1600   2009: 3200   2012: 6400   3200ifference between 2009 and 2012 = 3200   Option 3200
Answer: D
A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?
Choose the most appropriate option.
A) 1260	B) 1279	C) 1023	D) 1927	E) 1298

Solution: Given that, the question paper consists of five problems. For each problem, one or two or three or none of the choices can be attempted.   Hence, the required number of ways = 45 - 1.   = 210 - 1 = 1024 - 1= 
1024 - 1 = 1_023
1023   Answer:1023
Answer: C
Three numbers are in the ratio 1:2:3 and their H.C.F is 62. The numbers are:  Pick:
A) 62, 124, 186
B) 60, 124, 186
C) 10, 20, 30
D) 62, 24, 186
E) 12, 24, 186

Solution: Let the required numbers be x, 2x and 3x. Then, their H.C.F = x. So, x = 62.   The numbers are 62, 124, 186.   62, 124, 186NSWER:62, 124, 186
Answer: A
The present age of the father is 3years more than 3 times the age of his son. Three years hence, father's age will be 10 years more than twice the age of the son. Find the present age of the father?
Answers:	A) 22years	B) 30years	C) 33years	D) 15years	E) 25years

Solution: Let the son's present age be x years   father's present age = (3x+3)   3x+3+3 = 2(x+3)+10   3x+6 = 2x+16   x = 10   father's present age = 3x+3 = 3*10+3= 
3*10+3 = 33
33 years   Answer is 33years
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 10 days. If B starts, they take a day more. How long does it take to complete the task if they both work together?
Choices.
A) 5
B) 4.5
C) 6
D) 7
E) 8

Solution: Work done by A & B in a day = x &y respectively.   When A starts:   No. of days when A works = 6No. of days when B works = 4 → 6x + 4y = 1   When B starts:   No. of days when b works = 5 No. of days when A works = 5 → 5x + 5y = 1   Solving the above two equations for xy   x = 1/10 y = 1/10   → Total work done by AB in a day = 1/10 + 1/10 = 2/10 = 1/5   → No. of days to complete the work when both work together = 5   5nswer: 5
Answer: A
In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is:	Choose the correct choice from the following options:
A) 20 liters  B) 30 liters  C) 40 liters  D) 60 liters  E) 70 liters

Solution: Quantity of milk = 60 x	2	litres = 40 litres.   3   Quantity of water in it = (60- 40)= 
(60- 40) = 20
20 litres.   New ratio= 1 : 2   Let quantity of water to be added further be x litres.   Then, milk : water = 40 .   20 + x   Now, 40 =	1   20 + x	2   20 + x = 80   x = 60.   Quantity of water to be added = 60 litres   so the correct answer is option 60 liters)
Answer: D
A sock drawer contains seven socks, each one a different solid color. The colors of the socks are yellow, green, blue, indigo, and violet. A person reaches into the drawer, pulls out two socks, and puts a single sock on each foot. If each sock can fit either the left or the right foot, and if it matters whether a particular sock is on the left or the right foot, how many different sock fashion combinations could the person make from the five socks? Select:
A) 12
B) 15
C) 21
D) 36
E) 20

Solution: It's a question of permutation since order matters here ....   It can be deduced to-   5P2 = 5!/3! = 5*4= 
5*4 = 20
20 .........Answer is - 20
Answer: E
7 men, 5 women and 8 children were given as assignment of distributing 2000 books to students in a school over a period of 3 days. All of them distributed books on the 1st day. One of the 2nd day 2 women and 3 children remained absent and on the 3rd day 3 men and 5 children remained absent. If the ratio of the no. of books distributed in a day by a man, a woman & a child was 5 : 4 : 2 respectively, a total of approximately how many books were distributed on the second day? Choose the correct choice from the following options: A) 450 B) 490 C) 500 D) 650 E) 700

Solution: Sol. Let the books distributed by man, a woman and a child be 5x, 4x and 2x respectively.   ∴ No. of books distributed in 1st day   = 7×5x+5×4x+8×2x=71x   No. of books distributed in 1Ind day   =7×5x+3×4x+5×2x=57x   And no. of books distributed in IIIrd day   =4×5x+5×4x+3×2x=46x   71x + 57x + 46x = 2000, x = 2000/174   57x=2000/174×57=650   650
Answer: D
A total of 3000 chocolates were distributed among 120 boys and girls such that each boy received 2 chocolates and each girl received 3 chocolates. Find the respective number of boys and girls?  Choose the correct choice from the following answers:
A) 68,98 B) 60,60 C) 64,87 D) 64,09 E) 60,64

Solution: Let the number of boys be x.   Number of girls is 120 - x.   Total number of chocolates received by boys and girls = 2x + 3(120 - x) = 300   => 360 - x = 300 => x = 60.   So, the number of boys or girls is 60.   Answer:60,60
Answer: B
The product of all the prime numbers less than 25 is closest to which of the following powers of 10?  Choices:	A) 10^9	B) 10^8	C) 10^7	D) 10^8	E) 10^5

Solution: Quickly approximate   2, 3, 5, 7, 11, 13, 17, 19,23   =2.2 *10^8   10^8
Answer: D
A computer wholesaler sells 7 different computers and each is priced differently. If the wholesaler chooses three computers for display at a trade show, what is the probability (all things being equal) that the two most expensive computers will be among the three chosen for display?  Choose the most appropriate option:
A) 5/35	B) 3/28	C) 1/28	D) 1/56	E) 1/168

Solution: Since, two of the choices are prefixed, we are free to choose 1 from the rest of the 5 avilable. so 5C1 is the numerator.   Total no of ways we can choose 3 from 7 is 7c3, which is the denominator.   So, the probability: 5c1/7c3= 5/35 ans is 5/35.
Answer: A
Mike drives his new Corvette from San Francisco to Las Vegas, a journey of 640 miles. He drives the first half of the trip at an average rate of 80 miles per hour, but has to slow down for the second half of his journey. If the second half of the trip takes him 200 percent longer than the first half, what is his average rate W in miles per hour for the entire trip? Select the correct option:
A) W=26.7
B) W=30.0
C) W=40.0
D) W=53.3
E) 60.0

Solution: VERITAS PREPOFFICIAL SOLUTION   Correct Answer: C   Using the formula: Time = Distance/Rate, we find that Mike takes 4 hours to cover the first 320 miles of his trip. Since the 2nd 320 miles take 200% longer than the first, it takes Mike 8 hours longer, or 12 hours. (Note: 200% longer than the first half is not 200% of the first half.) The overall time is 4 hours + 12 hours or 16 hours. Since the definition of Average Rate = Total Distance Traveled/Total Time of Travel, Mike's average rate = 640/16 or 40 miles per hour.   Answer choice W=40.0 is correct.
Answer: C
1.A committee that includes 6 members is about to be divided into 2 subcommittees with 3 members each. On what percent of the possible subcommittees that Michael is a member of is David also a member  Choose the correct option
A) A.10% B) B.20% C) C.25% D) D.42% E) E.50%

Solution: A,B, C is too low so I eliminated those answers, E was too high of a number, so I chose D.42% as my final answer.D.42%
Answer: D
A father was as old as his son's present at the time of your birth. If the father's age is 36 years now, the son's age 5years back was? Select the correct option:
A) 10 years	B) 12 years	C) 14 years	D) 13 years	E) 20 years

Solution: Let the son's present age be x years. Then, (36 - x) = x   2x = 36.   x = 18.   Son's age 5 years back (18 - 5)= 
(18 - 5) = 13
13 years.   13 years
Answer: D
A man can row 6 kmph in still water. When the river is running at 3 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
Choose the most appropriate option
A) 5.75
B) 4.5
C) 5.76
D) 5.74
E) 5.71

Solution: M = 6   S = 3   DS = 9   US = 3   x/9 + x/3 = 1   x = 2.25   D = 2.25 * 2= 
2.25 * 2 = 4.5
4.5 Answer: 4.5
Answer: B
A credit card number has 6 digits (between 1 to 9 inclusive). The first two digits are 12 in that order, the third digit is bigger than 6, the fourth digit is divisible by 3, and the fifth digit is 2 times the sixth. How many different credit card numbers are possible? Choose the correct choice from the following:
A) 18  B) 24  C) 36  D) 48  E) 72

Solution: The first two digits are fixed.   The third digit can be 7, 8, or 9 so there are 3 choices.   The fourth digit can be 3, 6, or 9 so there are 3 choices.   The fifth digit depends entirely on the sixth digit.   The sixth digit can be 1, 2, 3, or 4 so there are 4 choices.   The number of possibilities is  3*3*4= 
 3*3*4 = 36
36   The answer is 36.
Answer: C
an article whose initial cost is Rs 400 is subjected for discounts of 25%, 15%, and 40% what is the amount the customer have to pay?	Answers.
A) 103	B) 113	C) 123	D) 143	E) 153

Solution: 0.75*0.85*.60*400= 
0.75*0.85*.60*400 = 153
153   ANSW153R:153
Answer: E
John went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?	Choose the most appropriate option: A) 19.7 B) 21 C) 21.4 D) 21.5 E) 22.5

Solution: Total cost of the items he purchased = Rs.25   Given that out of this Rs.25, 30 Paise is given as tax   => Total tax incurred = 30 Paise = Rs.30/100   Let the cost of the tax free items = x   Given that tax rate = 6%   ∴ (25−30/100−x)6/100 = 30/100   ⇒ 6(25 −0.3 −x) = 30   ⇒ (25 − 0.3 − x) = 5   ⇒ x = 25 − 0.3 − 5 = 19.7   19.7
Answer: A
The difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number T?	Choose the most appropriate option.
A) 60	B) 80	C) 40	D) 120	E) 160

Solution: (1 + 1/8)x - (1 - 1/4)x = 30   (9/8)x - (3/4)x = 30   x = 80=T   Answer: 80
Answer: B
Barbata invests $2400 in the National Bank at 4%. How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment?	Select:
A) 1200 B) 3000 C) 2400 D) 3600 E) 2450

Solution: Let the additional invested amount for 8% interest be x;   Equation will be;   2400+0.04*2400+x+0.08x = 2400+x+0.06(2400+x)   0.04*2400+0.08x = 0.06x+0.06*2400   0.02x = 2400(0.06-0.04)   x = 2400*0.02/0.02= 
2400*0.02/0.02 = 2_400
2400   Ans:2400
Answer: C
A goods train runs at the speed of 72 kmph and crosses a 240 m long platform in 26 seconds. What is the length of the goods train?
Choose the most appropriate option:  A) 230 m  B) 270m  C) 643m  D) 280m  E) 270m

Solution: Speed =	(72 x	5/18)m/sec	= 20 m/sec.   Time = 26 sec.   Let the length of the train be x metres.   Then,	x + 240/26	= 20   x + 240 = 520   x = 280.   Answer:280m
Answer: D
Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?	Choose the correct choice from the following options
A) 8 ½ sec	B) 6 ½ sec	C) 2 ½ sec	D) 7 ½ sec	E) 9 ½ sec

Solution: 70 + 50= 
70 + 50 = 120
120 * 5/18= 100/3 mps   7 ½ sec = 150 + 100= 
150 + 100 = 250
250 m   T= 250 * 3/100   = 15/2   = 7 ½ sec   Answer: 7 ½ sec
Answer: D
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 choices
A) 288
B) 150
C) 188
D) 166
E) 122

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
Answer: B
At what rate percent on simple interest will Rs.750 amount to Rs.900 in 4 years?
Choose the correct option:
A) 6%
B) 2%
C) 4%
D) 5%
E) 3%

Solution: 150 = (750*4*R)/100   R = 5%   Answer: 5%
Answer: D
Two trains are moving at 90 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
Choose the correct choice from the following answers.
A) 42/5 sec  B) 45/8 sec  C) 40/6 sec  D) 37/6 sec  E) 42/4 sec

Solution: 70 + 90 = 150 * 5/18 = 400/9 mps   D = 150 + 100= 
150 + 100 = 250
250 m   T= 250 * 9/400 = 45/8 sec   Answer:45/8 sec
Answer: B
George can fill Q cans of paint in 3 minutes. If there are R cans of paint in one gallon, how many gallons can George fill in 45 minutes? Choose the most appropriate option.
A) 30R/Q.  B) 15R/Q  C) 30Q/R  D) 5Q/R  E) 15Q/R

Solution: George can fill Q cans of paint in 3 minutes.   So in 45 mins , he can fill  45/3= 
 45/3 = 15
15Q cans.   R cans= 1 gallons   => 15Q cans = 15Q/R gallons.   Hence the answer is 15Q/R.
Answer: E
In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 6 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?	Pick.
A) 33
B) 44
C) 48
D) 52
E) None of these

Solution: Let the capacity of the can be T litres.   Quantity of milk in the mixture before adding milk = 4/9 (T - 6)   After adding milk, quantity of milk in the mixture = 6/11 T.   6T/11 - 6 = 4/9(T - 6)   10T = 594 - 264 => T = 33.   33NSWER:33
Answer: A
Martha takes a road trip from point A to point B. She drives x percent of the distance at 70 miles per hour and the remainder at 50 miles per hour. If Martha's average speed for the entire trip is represented as a fraction in its reduced form, in terms of x, which of the following is the numerator?  Choose the correct choice from the following options
A) 110
B) 35,000
C) 1,100
D) 3,000
E) 30,000

Solution: total distance = d   total time taken = x/(100*70) + (100-x)/(100*50)   speed = distance / time   gives numerator = 35000   Answer : 35,000
Answer: B
A pet store regularly sells pet food at a discount of 10 percent to 30 percent from the manufacturer’s suggested retail price. If during a sale, the store discounts an additional 20 percent from the discount price, what would be the lowest possible price of a container of pet food that had a manufacturer’s suggested retail price o f $ 40.00?  Choose one:
A) $ 10.00	B) $ 11.20	C) $ 22.40	D) $ 16.00	E) $ 18.00

Solution: For retail price = $40   First maximum discounted price = 40 - 30% of 40 = 40-12= 
40-12 = 28
28   Price after additional discount of 20%= 28 - 20% of 28 = 28 - 5.6= 
28 - 5.6 = 22.4
22.4   Answer: Option $ 22.40
Answer: C
Beth received 4/10 of the votes cast in a certian election. What franction of the other votes cast would she have needed in order to have received 1/2 of the votes cast? Answers.
A) 1/6  B) 2/7  C) 3/10  D) 7/20  E) 1/2

Solution: Let the total votes be 10. Beth received 4 votes, other votes  10-4= 
 10-4 = 6
6. In order to have received 1/2 of the votes she needed 5 votes so 1 more, which is 1/6 of the other votes.   1/6nswer: 1/6.
Answer: A
The population of a town is 8100. It decreases annually at the rate of 10% p.a. What was its population 2 years ago?
Choose the most appropriate option:
A) 9000	B) 8000	C) 8500	D) 9500	E) 10000

Solution: Formula :   ( After =100 denominator   Ago = 100 numerator)   8100 × 100/90 × 100/90 = 10000   10000)
Answer: E