MU-NLPC/Calc-aqua_rat huggingface dataset:
A dog breeder currently has 9 breeding dogs. 6 of the dogs have exactly 1 littermate, and 3 of the dogs have exactly 2 littermates. If 2 dogs are selected at random, what is the probability R that both selected dogs are NOT littermates?
Pick one:
A) 1/6
B) 2/9
C) 5/6
D) 7/9
E) 8/9

Solution: We have three pairs of dogs for the 6 with exactly one littermate, and one triplet, with each having exactly two littermates.   So, in fact there are two types of dogs: those with one littermate - say A, and the others with two littermates - B.   Work with probabilities:   Choosing two dogs, we can have either one dog of type B or none (we cannot have two dogs both of type B).   The probability of choosing one dog of type B and one of type A is 3/9 * 6/8 * 2 = 1/2 (the factor of 2 for the two possibilities BA and AB).   The probability R of choosing two dogs of type A which are not littermates is 6/9 * 4/8 = 1/3 (choose one A, then another A which isn't the previous one's littermate).   The required probability is 1/2 + 1/3 = 5/6.   Find the probability for the complementary event: choose AA or BB.   Probability of choosing two dogs of type A who are littermates is 6/9 * 1/8 = 1/12.   Probability of choosing two dogs of type B (who necessarily are littermates) is 3/9 * 2/8 = 1/12.   Again, we obtain 1 - (1/12 + 1/12) = 5/6.   Answer: 5/6
Answer: C
three men invested sum. and their ratio is 5:7:6. profit is 2700.then b's share Options:
A) 2000
B) 2100
C) 2200
D) 2300
E) 1050

Solution: b's share =7/18*2700= 
7/18*2700 = 1_050
1050   ANSW1050R:1050
Answer: E
An analyst will recommend a combination of 3 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 5 industrial stocks, 5 transportation stocks, and 3 utility stocks, how many different combinations of 7 stocks are possible?
--  Select
A) 12	B) 19	C) 60	D) 180	E) 300

Solution: 5C3 * 5C2 * 3C2 = 10*10*3= 
10*10*3 = 300
300.   Answer: 300.
Answer: E
When 24 is divided by the positive integer a, the remainder is 4. Which of the following statements about a must be true?
I. a is even
II. a is a multiple of 5
III. a is a factor of 20
Answers:
A) III only  B) I and II only  C) I and III only  D) II and III only  E) I, II, and III

Solution: 24= m*a + 4   m*a=20   put values of m   m=1 a=20   m=2 a=10   m=4 a=5   I. not true   II. true   III. true   D. correct
Answer: D
The Italian size of a suit jacket is N centimeters, where N is the linear distance between the armpits when the jacket is laid on a flat surface. The American size of a suit jacket is P inches, where P is twice the linear distance between the armpits when the jacket is laid on a flat surface. If, for a particular jacket, N = P +9, which of the following is closest to the value of N? (One inch is approximately 2.54 centimeters.)  Choose the correct answer:	A) 41	B) 47	C) 58	D) 65	E) 72

Solution: Since one inch is approximately 2.54 centimeters, then N centimeters is N/2.54 inches.   Next, since the American size (P inches) is twice the Italian size (N/2.54 inches), then P=2*N/2.54.   As given that N = P + 9, then N=2*N/2.54+9--> N=~41.   41nswer: 41.
Answer: A
Which of the following is closest to 1/8+1/88+1/888 Select
A) 1/8	B) 1/2.5	C) 1/5	D) 1/7.3	E) 1/9

Solution: 1/8+1/88+1/888=0.125+0.01136+0.001126= 
0.125+0.01136+0.001126 = 0.137486
0.137486=1/7.3   Answer 1/7.3
Answer: D
X Y
+Y X
________
The sum of the two digit numbers above is a three digit number PQ6, where each letter X, Y, P, and Q represents a different non zero digit. Which of the following can be the value of X?
I)	7
II)	8
III)	9	Choose the most appropriate option:
A) I only
B) II only
C) III only
D) I , II and III
E) I and II only

Solution: it can be a combination of 9,7 or 8,8   I choose I , II and III as an answer.
Answer: D
A jeweler has a 20 gram ring that is 60% gold and 40% silver. He wants to melt it down and
add enough gold to make it 80% gold. How many grams of gold should be added?	Choices.
A) 4 grams  B) 8 grams  C) 12 grams  D) 16 grams  E) 20 grams

Solution: Gold concentration = weight of gold/total weight   0.80 =20*0.60+x/20+x   12 + x = 16 + 0.8x   0.2x = 4   x = 20 grams   correct answer 20 grams
Answer: E
At Veridux Corporation, there are 250 employees. Of these, 90 are female, and the rest are males. There are a total of 40 managers, and the rest of the employees are associates. If there are a total of 145 male associates, how many female managers are there?
Options
A) 15	B) 20	C) 25	D) 30	E) 35

Solution: 250 Employees:   90 Male, 160 Female   40 Managers, 210 Associates   145 Male Associates implies 65 Female Associates which means the remaining 25 females must be Managers   C. 25
Answer: C
A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it?
Choose the correct choice from the following:
A) 33 B) 28 C) 24 D) 97 E) 16

Solution: Explanation:   2c = Â¼ + 1/6 â€“ 1/3 = 1/12   c = 1/24 => 24 days   Answer:24
Answer: C
If two resistors, A(R1) and B(R2) stand in parallel with each other in electrical wire, the total resistor appears as R1R2/(R1+R2). If three resistors, A(R1), B(R2), and C(2R2) stand in parallel in electrical wire, what is the ratio J of the resistors’ sum of A and C to the resistors’ sum of A and B?
Choose the correct choice from the following choices
A) 2(R1+R2):(R1+2R2) B) (R1+R2):(R1+2R2) C) (2R1+R2):(R1+2R2) D) 2(R1+R2):(2R1+R2) E) 2(R1-R2):(R1+2R2)

Solution: two resistors A (r1) and B (r2).   total or sum of two resistors appear as   r1r2/r1+r2. It is looks like inversion of sum of rates.   1/r1+1/r2= r1+r2/r1r2.   same way sum of A(r1) and c(2r2)=1/r1+1/2r2   =2r2+r1/r12r2.   inversion rate = r12r2/2r2+r1.   ratio J of sum of a and c/sum of a and b=2r2r1/2r2+r1*r1+r2/r1r2   =2(r1+r2)/2r2+r1.2(R1+R2):(R1+2R2)
Answer: A
Seven men and seven women have to sit around a circular table so that no 2 women are together. In how many ways can that be done?	Pick
A) 5!*6!  B) 6!*6!  C) 5!*7!  D) 6!*7!  E) 7!*7!

Solution: The number of arrangements of n distinct objects in a row is given by n!.   The number of arrangements of n distinct objects in a circle is given by (n-1)!.   The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have: n!/n=(n-1)!   Now, 7 men in a circle can be arranged in (7-1)! ways and if we place 7 women in empty slots between them then no two women will be together. The # of arrangement of these 7 women will be 7! and not 6! because if we shift them by one position we'll get different arrangement because of the neighboring men.   So the answer is indeed 6!*7!. ANS:6!*7!
Answer: D
P is four times as fast as Q and working together, they can complete a work in 8 days. In how many days can Q alone complete the work?	Choose the correct choice from the following choices.
A) 35 days	B) 15 days	C) 10 days	D) 25 days	E) 18 days

Solution: P = 4Q   P + Q = 4Q + Q = 5Q   These 5Q people can do the work in 8 days, which means Q can do the work in 40 days.   Hence, P can do the work in 10 days.   ANSWER:10 days
Answer: C
The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher Pick:
A) 49	B) 48	C) 47	D) 50	E) 52

Solution: Total age of students is 32 Ã— 16 = 512 Years   Total age inclusive of teacher = 33 Ã— (16+1) = 561   So, Teacher's age is 561-512= 
561-512 = 49
49 Yrs   There is a shortcut for these type of problems   Teacher's age is 16+(33 Ã— 1)= 49 Years   49NSWER IS 49
Answer: A
At a dinner party, 4 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group? Pick one.
A) 1) 6  B) 2) 10  C) 3) 24  D) 4) 32  E) 5) 120

Solution: for number of distinct arrangements of 'n' items around a circular table, we get the arrangements by way of (n-1)!   in this case, there are 4 guests, so number of distinct arrangements = 3! = 6   hence 1) 6   1) 6nswer : 1) 6
Answer: A
A woman has three blouses of different colors, four skirts of different colors, and two different pairs of shoes. She refuses to wear her pink blouse with her green skirt. How many different blouseskirt-shoe combinations could she wear?  Choose the correct choice:
A) 8	B) 12	C) 22	D) 17	E) 18

Solution: total ways = 3*4*2=24..   now its better to find the ways in which the pink blouse and green skirt are together and subtract from total to get the answer..   the ways in which the pink blouse and green skirt are together=1*1*2=2..   total ways =24-2=22..   ANSWER:22
Answer: C
In the above number, A and B represent the tens and units digits, respectively. If the above number is divisible by 65, what is the greatest possible value of B x A?  Choose the correct choice from the following answers:
A) 0	B) 10	C) 15	D) 20	E) 30

Solution: I also was confused when I was looking forabove number:D   As far as I understood, 65 is a factor of AB. In other words, the values of B (units digits can be 5 or 0. Better to have option for 5 in this case to havebigger result). Now let's try 65x1 (A=6, B=5 respectively we have =30). This is the greatest possible value of B x A.   IMO 30.
Answer: E
A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 15 per metre of cloth. What is the cost price of one metre of cloth?	Pick:	A) Rs. 80	B) Rs. 85	C) Rs. 90	D) Rs. 95	E) None of these

Solution: SP of 1m of cloth = 8925/85 = Rs. 105   CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth   = Rs. 105 - Rs. 15 = Rs. 90.   ANSWER:Rs. 90
Answer: C
In how many different ways can the letters of the word "CLAIM" be rearrangement?	Pick one:
A) 100
B) 120
C) 130
D) 143
E) 145

Solution: The total number of arrangements is   5P5 = 5! = 120   120
Answer: B
In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?  Choose the correct answer:	A) 2.5 sec	B) 2.8 sec	C) 8.5 sec	D) 2.0 sec	E) 7.5 sec

Solution: Speed = 144 * 5/18= 
144 * 5/18 = 40
40 m/sec   Time taken= 100/40= 
100/40 = 5/2 = around 2.5
2.5 sec.   2.5 secnswer:2.5 sec
Answer: A
What command is used to create a backup configuration?  Choose the most appropriate option:
A) copy running backup B) copy running-config startup-config C) config mem D) wr mem E) wr m22

Solution: Explanation:   The command to back up the configuration on a router is   Answer: Option copy running-config startup-config
Answer: B
Find the area, diameter = 13m.	Choose the correct choice from the following choices.
A) 132.00 square meter B) 132.04 square meter C) 132.78 square meter D) 132.24 square meter E) 113.43 square meter

Solution: Diameter = 13 meter.   Radius = diameter/2.   = 13/2.= 
13/2. = 6.5
6.5 meter.   Area of a circle= Ï€r2.   Here, pi (Ï€) = 3.14 meter, radius (r) = 6.5   Area of a circle = 3.14 Ã— 6.5 Ã— 6.5.   = 3.14 Ã— 42.25.   = 132.78 square meter ANSWER : 132.78 square meter
Answer: C
A wheel rotates 20 times every minute and moves 35 cm during each rotation. How many metres does the wheel move in one hour?  Pick:
A) 6 metre B) 120 metre C) 220 metre D) 1200 metre E) 420 metre

Solution: Number of times wheel moves in 1 hour = 20 * 60= 
20 * 60 = 1_200
1200   :. Distance moves= (1200*35)= 
(1200*35) = 42_000
42000 cms   In metres= 420 metre   ANSW420 metreR:420 metre
Answer: E
A truck covers a distance of 200 metres in 1 minute whereas a bus covers a distance of 100kms in 50minutes. The ratio of their speeds is?	Choose the correct choice:
A) 2:3	B) ratio 1:5	C) ratio 1:10	D) ratio 9:13	E) ratio 7:15

Solution: Ratio of speeds = (200/60) 18/5 : 60*100/50 = 12:120 = 1:10   Answer is ratio 1:10
Answer: C
A car traveling at a certain constant speed takes 30 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 30 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?
Choose the most appropriate option.
A) 16
B) 18
C) 20
D) 22
E) 24

Solution: 30 * T = 1 km => T = 1/30 km/h   V*(T+30/3600) = 1   V (1/30 + 30/3600) = 1   V (150/3600) = 1   V = 24 km/h   The answer is 24.
Answer: E
As part of a promotion designed to attract visitors, an amusement park gives out 24,600 free tickets per year. Usually, the number of tickets given away each month is constant. Due to an employee error, only 95,00 tickets were given out in the first four months of the year. How many tickets should the amusement park give out in the fifth month so that it will begin the sixth month back on its regular giveaway schedule?  Select
A) 600	B) 750	C) 500	D) 400	E) 700

Solution: 24600/12= 
24600/12 = 2_050
2050   2050*5= 
2050*5 = 10_250
10250   10250-9500= 
10250-9500 = 750
750   Answer 750
Answer: B
A reduction of 50% in the price of apples would enable a man to obtain 80 more for Rs.55, what is reduced price per dozen?  Choose the correct choice from the following choices:
A) 1
B) 3
C) 4
D) 7
E) 10

Solution: 4   55*(50/100) = 28 --- 64   ? --- 12 => Rs.4
Answer: C
What percent of 30 is 80?	Choose the correct option.
A) 133 1⁄3	B) 75	C) 266.66	D) 33 1⁄3	E) 25

Solution: To find out the % of 80 in 30   Do 80/30 = 266.66%   Answer 266.66)
Answer: C
Find large number from below question The difference of 2 no.'s is 1365. On dividing the larger no. by the smaller, we get 6 as quotient and the 15 as remainder?	Select:
A) 1245  B) 1430  C) 1540  D) 1600  E) 1635

Solution: Let the smaller number be x. Then larger number = (x + 1365).   x + 1365 = 6x + 15   5x = 1350   x = 270   Large number = 270+1365= 
270+1365 = 1_635
1635   1635
Answer: E
A car traveled 75% of the way from town A to town B at an average speed of 50 miles per hour. The car travels at an average speed of S miles per hour for the remaining part of the trip. The average speed for the entire trip was 50 miles per hour. What is S ?	Pick:  A) 10  B) 20  C) 25  D) 30  E) 50

Solution: Total distance = 100 miles (easier to work with %)   75% of the distance = 75 miles   25% of the distance = 25 miles   1st part of the trip →  75/50= 
 75/50 = 3/2 = around 1.5
1.5   2nd part of the trip → 25/S= t   Total trip → (75+25)/50 = 1.5 + t » 100/50 = 1.5 + t » 2 = 1.5 + t » t = 0.5   Back to 2nd part of the trip formula: 25/S = 0.5 » S =50   Ans 50
Answer: E
The amounts of time that three secretaries worked on a special project are in the ratio of 1 to 2 to 5. If they worked a combined total of 128 hours, how many hours did the secretary who worked the longest spend on the project?
Answers:
A) 90
B) 70
C) 56
D) 16
E) 14

Solution: 8x = 128   => x = 16   Therefore the secretary who worked the longest spent 16 x 5 = 90 hours on the project   Option (90)
Answer: A
Mr. Kramer, the losing candidate in a two-candidate election, received 942,568 votes, which was exactly 45 percent of all votes cast. Approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast?  Choose the correct choice from the following answers.
A) 9%	B) 12%	C) 15%	D) 17%	E) 20%

Solution: Let me try a simpler one.   Lets assume that candidate got 45% votes and total votes is 100.   Candidate won = 45   Remaining = 55   To get 50%, candidate requires 5 votes from 100 which is 5% and 5 votes from 55.   5/55= 1/11 = .09 = 9%   Which is approx 9%. Hence the answer is 9%.
Answer: A
If x is the product of three consecutive positive integers, which of the following must be true?
I. x is an integer multiple of 3.
II. x is an integer multiple of 6
III. x is an integer multiple of 2	Pick one:
A) a) I only	B) b) II only	C) c) I and II only	D) d) I and III only	E) e) I,II and III

Solution: The answer should be D i.e. X will be an integer and multiple of 3 and 6.   Let us take example n, n+1, n+2 as 3 three consecutive positive integers.   In a sequence of consecutive integers a number is multiple of 3 after every interval of 2 numbers i.e 3,4,5,6 Or 8,9,10,11,12   Hence in a product of 3 consecutive integers, the product is always divisible by 3.   Now, in a consecutive sequence every alternate is an even number, and when an even number is multiplied by 3 we will have 6 as one of the multiple also.   Now for a number to be a multiple of 4 we need at least 2 2's. this is only possible if the first number of three consecutive positive integers is an even number so that 3 is also even and we have 2 2's. But incase the sequence starts with odd we will have one 2 hence, the divisibility by 4 depends on the first number to be even   Answerc) I and II only
Answer: C
Consider a sequence of numbers given by the expression 7 + (v - 1) * 5, where n runs from 1 to 80.What is the sum of this series ?	Choose the correct option:	A) 409	B) 1636	C) 16360	D) 16000	E) 15360

Solution: terms in this sequence are 7,12,17----402   now since this is an a.p. with a common difference of 5. therefore its sum can be given as   v(a+l)/2----------------1)   v= total no. of terms =80   a= first term=7   l= last term=402   subsituting values in the expression 1 we have   80(7+402)/2   = 40(409)   =16360=16360
Answer: C
In a hostel, the number of students decreased by 9% and the price of food increased by 20% over the previous year. If each student consumes the same amount of food then By how much should the consumption of food be cut short by every student, so that the total cost of the food remains the same as that of the previous year?  Choose the correct choice:
A) 19%
B) 15%
C) 25%
D) 40%
E) 8.4%

Solution: Cost of food (C) = Food consumed per student (F) * Number of students (N) * Price of food (P)   Originally,   C = FNP   When number of students decrease by 8%, and the price of food increases by 20%,   C = F(new) * (0.91N) * (1.2P)   => F(new) = F/(0.91*1.2)   => F(new) = 0.915F   Therefore the new cost of food must be 91.5% of the old cost, or the cost of food must decrease by 8.4% (option 8.4%)
Answer: E
1!+2!+3!+4!+5!+..100! is divided by 24. Find the remainder?  Answers:
A) 5	B) 8	C) 9	D) 11	E) 13

Solution: By applying rule 2, we divide the terms of the above expression individually, and add them to get the final remainder. But from 4! onwards all the terms leave a remainder 0 when divided by 24.   So the remainder = 1 + 2 + 6 + 0 + 0....... = 9   9
Answer: C
The positive integers x and y leave remainders of 2 and 3, respectively, when divided by 6. x > y. What is the remainder when x– y is divided by 6?	Choose the correct answer.
A) 4  B) 2  C) 1  D) 5  E) 3

Solution: Let's test out some values of p and q that satisfy the given information.   x leaves are remainder of 2 when divided by 6   So, x COUL5 equal 8   y leaves are remainder of 3 when divided by 6   So, y COUL5 equal 3   What is the remainder when x – y is divided by 6?   So, x - y = 8 - 3= 
8 - 3 = 5
5, and when we divide 5 by 6, we get 0 with remainder 5   Answer: 5
Answer: D
If equation |x/2| + |y/2| = 1 encloses a certain region on the coordinate plane, what is the area of this region? Choose the most appropriate option.
A) 8
B) 50
C) 100
D) 200
E) 400

Solution: The equation can be reduced to intercept form as |x/2| + |y/2| = 1, so these are lines in four quadrants with x and y intercept as 2, so it is a rhombus with diagonals of 4 each and hence area = 1/2*d1*d2 = 1/2*4*41/2* 1* 2= 
1/2* 1* 2 = 1
1/2*4*4= 
1/2*4*4 = 8
8. 8nswer 8.
Answer: A
The average of 5 numbers is 6.8. If one of the numbers is multiplied by a factor of 4, the average of the numbers increases to 9.2. What number is multiplied by 4?  Choose the correct choice from the following answers: A) 1.5 B) 3.0 C) 3.9 D) 4.0 E) 6.0

Solution: The average of 5 numbers is 6.8   The sum of 5 numbers will be 6.8 x 5 = 34   The average of 5 number after one of the number is multiplied by 4 is 9.2   The sum of the numbers will now be 9.2 x 5 = 46   So the sum has increased by  46-34= 
 46-34 = 12
12   Let the number multiplied by 4 be n   Then,   4n= n+12   or 3n = 12   or n = 4   Answer:- 4.0
Answer: D
If the true discount on a certain sum due 6 months hence at 15% is Rs. 120, what is the banker’s discount on the same sum for the same time and at the same rate?  Choose the correct choice from the following:
A) 100  B) 115  C) 120  D) 129  E) None

Solution: Sol.   B.G. = S.I. on T.D. = Rs. [120 * 15 * 1/2 * 1/100] = Rs. 9.   ∴ (B.D.) - (T.D.) = Rs.9.   ∴ B.D. = Rs. (120 + 9) = Rs. 129   Answer 129
Answer: D
A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 32, then how old is B? Options:
A) 17 years  B) 19 years  C) 29 years  D) 10 years  E) 12 years

Solution: Let C's age be x years.   Then, B's age = 2x years.   A's age = (2x + 2) years.   (2x + 2) + 2x + x = 32   5x = 30 => x = 6   Hence, B's age = 2x = 12 years.   Answer: 12 years
Answer: E
In the first 12 overs of a cricket game, the run rate was only 4.5. What should be the run rate in the remaining 38 overs to reach the target of 360 runs?
Choose the correct choice from the following answers:
A) 9.55  B) 6.25  C) 6.75  D) 8.05  E) 7.25

Solution: Required run rate = 360 - (4.5 x 12)	/38	=	306/38 = 8.05 Option 8.05
Answer: D
The S.I. on a certain sum of money for 3 years at 8% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is?  Choose the correct choice from the following answers:
A) 288
B) 276
C) 1750
D) 2887
E) 2991

Solution: C.I. = [4000 * (1 + 10/100)2 - 4000]   = (4000 * 11/10 * 11/10 - 4000) = Rs. 840.   Sum = (420 * 100)/(3 * 8) = Rs. 1750.Answer: 1750
Answer: C
Alyssa and her six cousins went to a party. There are sixteen pieces of
pizza for them to eat.
Is there any
pizza left over?
Select:
A) 5  B) 4  C) 3  D) 2  E) 1

Solution: 16/7 = 2 R 2 Each girl will get 2 pieces of pizza and there will be 2   pieces left over.   correct answer 2
Answer: D
A change-making machine contains one-rupee, two-rupee and five-rupee coins. The total number of coins is 300. The amount is Rs. 960. If the numbers of one-rupee coins and two-rupee coins are interchanged, the value comes down by Rs. 40. The total number of five-rupee coins is  Options.
A) 100
B) 140
C) 60
D) 150
E) None of these

Solution: Explanation :   Let the number of 5 rupee , 2 rupee and 1 rupee coins be x, y and z respectively.   x + y + z = 300.   5x + 2y + z = 960 .......(i)   5x - y + 2z = 920 ......(ii)   On subtracting (ii) from (i) we get,   y - z = 40.   And, x + 2y = 340.   Using the options,   if x= 140, y= 100 and z= 60, this satisfies all the given conditions.   Answer : 140
Answer: B
The ratio between the present ages of A and B is 5:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago? Choose the correct choice from the following options:	A) 3:1	B) 2:3	C) 4:3	D) 5:4	E) 2:4

Solution: Let the present ages of A and B be 5x and 3x years respectively.   Then, (5x - 4)/(3x + 4) = 1/1   2x = 8 => x = 4   Required ratio = (5x + 4):(3x - 4) = 24:8 = 3:1   3:1NSWER 3:1
Answer: A
How many positive integers less than 50 have a reminder 2 when divided by 7? Choose the correct choice:  A) 3  B) 4  C) 5  D) 6  E) 7

Solution: take the multiples of 7 and add 2   0X7+2=2 ....6X7+2=44   there are 7 numbers   answer 7
Answer: E
Alex deposited x dollars into a new account that earned 5 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ? Choose the correct option:	A) w/(1+1.08)	B) w/(1.08+1.16)	C) w/(1.16+1.24)	D) w/(1.05+1.05^2)	E) w/(1.08^2+1.08^2)

Solution: Account at the end of the first year would be 1.05x dollars. At this time x dollars was deposited, hence the account at the beginning of the second year would be (1.05x+x) dollars. Account at the end of the second year would be (1.05x+x)*1.05=w --> x(1.05^2+1.05)=w --> x=w/(1.05+1.05^2).   Answer: w/(1.05+1.05^2).
Answer: D