MU-NLPC/Calc-aqua_rat huggingface dataset:
If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 210, what is the least possible value of n?
Pick: A) 7 B) 9 C) 11 D) 13 E) 14

Solution: 210 = 2*3*5*7, so n must be at least 7.   The answer is 7.
Answer: A
If a farmer wants to plough a farm field on time, he must plough 120 hectares a day. For technical reasons he ploughed only 85 hectares a day, hence he had to plough 2 more days than he planned and he still has 40 hectares left. What is the area of the farm field and how many days the farmer planned to work initially?	Select:
A) 483
B) 720
C) 885
D) 645
E) 287

Solution: Let x be the number of days in the initial plan. Therefore, the whole field is 120⋅x hectares. The farmer had to work for x+2 days, and he ploughed 85(x+2) hectares, leaving 40 hectares unploughed. Then we have the equation:   120x=85(x+2)+40   35x=210   x=6   So the farmer planned to have the work done in 6 days, and the area of the farm field is 120⋅6=720 hectares.   correct answer is 720)720
Answer: B
In one hour,a boat goes 8 km along the stream and 2 km against the stream.The speed of the boat in still water (in km/hr) is :
Choose one.
A) 3
B) 5
C) 8
D) 9
E) 10

Solution: Solution   Speed in still water =1/2(8+2)kmph.= 5 kmph. Answer 5
Answer: B
Shekhar started a business investing Rs.25,000 in 1999.In 2000,he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000.In 2001,Shekhar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000.What will be Rajeev’s share in the profit of Rs.1,80,000 earned at the end of 3 years from the start of the business in 1999 ?	Choices:
A) Rs.45,000  B) Rs.60,000  C) Rs.70,000  D) Rs.75,000  E) None of these

Solution: Solution   Shekhar : Rajeev : Jatin   = (25000x12+35000x12+45000x12) :(35000x24) : (35000x12)   = 1260000 : 840000 : 420000 = 3 : 2 : 1.   ∴ Rajeev’s share = Rs.(18000x2/6) = Rs. 60,000. Answer Rs.60,000
Answer: B
A sock drawer contains 5 socks, each one a different solid color. The colors of the socks are yellow, green, blue, indigo, and violet. If a person reaches into the drawer and pulls out two socks, how many different color combinations are possible in the selected pair of socks? Choose the correct answer:
A) 10 B) 15 C) 21 D) 36 E) 42

Solution: Since the order in which we select the socks does not matter, we can use combinations.   We can select 2 socks from 5 socks in 5C2 ways.   5C2 = 10   10nswer : 10
Answer: A
Find the area of circle whose radius is 7m? Choose the most appropriate option:
A) 209 B) 154 C) 278 D) 265 E) 291

Solution: 22/7 * 7 * 7= 
22/7 * 7 * 7 = 154
154   Answer: 154
Answer: B
The function f is defined for all positive integers n by the following rule: f(n) is the product of the distinct prime factors of n. If f(n) < 100 and n is not prime, what is the greatest possible value of f(n)? Select.
A) 99	B) 95	C) 91	D) 87	E) 78

Solution: A) 99 = 11*3*3 ( 99 is not product of distinct primes. 3 is repeated). so can't be the answer.   B)95 = 5*19   C)91 = 7*13   D) 87 is prime, so cannot be the answer   E) 78 = 13*2*3   largest possible n is B.   Answer is 95.
Answer: B
how many positive integers less than 9999 are such that the product of their digits is 210.
Pick one:
A) 24  B) 58  C) 26  D) 34  E) 25

Solution: The prime factorization of 210 is 2*3*5*7. So one way to make the right kind of number is to use those four digits, in any of the 4! = 24 orders you can put them in.   Notice though that we can also get 210 as a product by multiplying 5, 6 and 7. So we can make some 3-digit numbers with the right product: 3! = 6 of them to be exact.   But we can also get the right product using the digit 1 along with the digits 5, 6, and 7. Again we can arrange those digits in 4! = 24 orders.   24
Answer: A
The contents of a certain box consist of 24 apples and 30 kiwis. How many kiwis must be added to the box so that exactly 30% of the pieces of fruit in the box will be apples?	Answers.
A) 24	B) 26	C) 30	D) 46	E) 50

Solution: apples = (apples + kiwi + x)*0.3   24 = (30 + 24 + x)*0.3   x = 26.   Answer: 26.
Answer: B
The sum of the two digits of a number is 10. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number?	Choose the correct choice from the following options:	A) 34	B) 28	C) 12	D) 17	E) 19

Solution: Explanation:   Any two digit number can be written as (10P + Q), where P is the digit in the tens place and Q is the digit in the units place.   P + Q = 10 ----- (1)   (10Q + P) - (10P + Q) = 54   9(Q - P) = 54   (Q - P) = 6 ----- (2)   Solve (1) and (2) P = 2 and Q = 8   The required number is = 28   ANSWER IS 28
Answer: B
A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
Choices:
A) Rs.3948 B) Rs.3929 C) Rs.3927 D) Rs.3900 E) Rs.3928

Solution: Area = (l + b – d) d   (80 + 60 – 10)10 => 1300 m2   1300 * 3 = Rs.3900   Answer: Rs.3900
Answer: D
The average of 35 students in a class is 18 years. The average age of 25 students is 20. What is the average age of remaining 10 students?	Options.
A) 17 years B) 16 years C) 15 years D) 14 years E) 13 years

Solution: Sum of the ages of 14 students   = (18 * 35) - (20 * 25) = 630 - 500= 
630 - 500 = 130
130   Required average= (130/10)= 
(130/10) = 13
13 years.   Answer:13 years
Answer: E
For a group of n people, k of whom are of the same sex, the (n-k)/n expression yields an index for a certain phenomenon in group dynamics for members of that sex. For a group that consists of 20 people, 7 of whom are females, by how much does the index for the females exceed the index for the males in the group?	Choose one.
A) 0.05
B) 0.0625
C) 0.2
D) 0.3
E) 0.6

Solution: Index for females = (20-7)/20 = 13/20= 
13/20 = 13/20 = around 0.65
0.65   Index for males= (20-13/20 = 7/20= 
7/20 = 7/20 = around 0.35
0.35   Index for females exceeds males by   0.65 - 0.35= 
  0.65 - 0.35 = 0.3
0.3   Answer: 0.3
Answer: D
Find the number of square tiles to cover the floor of a room measuring 4.5 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?	Select
A) 478  B) 476  C) 472  D) 471  E) 544

Solution: 4 * 8 1/2 = 1/4 * 1/4 * x => x   = 544   Answer:544
Answer: E
In an increasing sequence of 3 consecutive integers, the sum of the first 2 integers is 561. What is last integer in the sequence?	Choose the correct choice from the following.
A) 281 B) 282 C) 275 D) 270 E) 265

Solution: Solution:   In solving this problem we must first remember that when we have 3 consecutive integers we can display them in terms of just 1 variable. Thus, we have the following:   Integer 1: x   Integer 2: x + 1   Integer 3: x + 2   We are given that the sum of the first 2 integers is 560. This means that:   x + x+1 = 561   2x + 1 = 561   2x = 560   x = 280   the last integer can be expressed and simplified as:   x+2 = 280+2= 
280+2 = 282
282   Answer: 282
Answer: B
A person borrows Rs. 9000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6 p.a for 2 years. Find his gain in the transaction per year.  Choose the correct choice from the following answers.
A) 100 rs	B) 150 rs	C) 160 rs	D) 180 rs	E) 200 rs

Solution: Gain in 2 years =   [(9000*6*2)/100]-[(9000*4*2)/100]    1080-720= 
 1080-720 = 360
360   Gain in 1 year=(360/2)= 
(360/2) = 180
180 rs   ANSWER:180 rs
Answer: D
Three numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 276. What is their H.C.F.? Choose one.
A) 18 B) 23 C) 28 D) 32 E) 36

Solution: Let the numbers be 2x, 3x, and 4x.   LCM of 2x, 3x and 4x is 12x.   12x = 276   x = 23   HCF of 2x, 3x and 4x = x = 23   The answer is 23.
Answer: B
David decides to attend a base ball game with four friends. If the party of five sits together in five consecutive seats, and David must NOT sit in between two of his friends, how many ways can the five friends be arranged?	Choose the correct choice: A) 12 B) 24 C) 36 D) 6 E) 48

Solution: David have to sit at either of the ends.   If David sits on the left most corner, then other 5 friends can be arranged in 4! = 24   David can also sit on the other end, then another 4! ways we can arrange.   So total number of ways = 24+24= 
24+24 = 48
48   Answer : 48
Answer: E
A die is thrown three times. Events X and Y are defined as below:
X : 4 on the third throw
Y : 6 on the first and 5 on the second throw
What is the probability of X given that Y has already occurred.  Answers:
A) 1/6 B) 1/7 C) 1/8 D) 1/11 E) 1/13

Solution: The sample space has 216 outcomes.   Now X =   (1,1,4) (1,2,4) ... (1,6,4) (2,1,4) (2,2,4) ... (2,6,4)   (3,1,4) (3,2,4) ... (3,6,4) (4,1,4) (4,2,4) ...(4,6,4)   (5,1,4) (5,2,4) ... (5,6,4) (6,1,4) (6,2,4) ...(6,5,4) (6,6,4)   Y = {(6,5,1), (6,5,2), (6,5,3), (6,5,4), (6,5,5), (6,5,6)}   and X n Y = {(6,5,4)}.   Now P(Y) = 6/216   and P (X n Y) = 1/216   Then P(X|Y) = (1/216)/(6/216) = 1/6.   1/6
Answer: A
If the number of 741,61n, where n represents the ones digit, is a multiple of 3, then the value of n could be which of the following?
Choose the correct answer:
A) 7	B) 6	C) 5	D) 4	E) 3

Solution: Then for any number to be a multiple of 3,The sum of its digits should be the multiple of 3.   i.e 7+4+1+6+1+n= multiple of 3   or, 19 + n = multiple of 3.   If n=5, 19 + n =24,which is a multiple of 3.   Hence answer is 5.
Answer: C
If a-b= 8 and a^2+b^2=164, find the value of ab  Choose the correct choice from the following choices:  A) 10  B) 12  C) 50  D) 18  E) 19

Solution: 2ab = (a^2 + b^2) - (a - b)^2   = 164 - 64= 
164 - 64 = 100
100=> ab = 50   ANSWER: 50
Answer: C
In a office work is distribute between p persons. If 1/3 members are absent then work increased for each person is?	Pick one: A) 13.28% B) 14% C) 15% D) 16% E) 50%

Solution: let total % of work is 100%   total person=p   1/3 person are absent of total person . so absent person is 1/3p ie p/3.   left person is, p-p/3=2p/3.   p person do the work 100%   1 person do the work 100*p%   2p/3 person do the work (100*p*3)/2p%=150%   work increased for each person is=(150-100)= 
(150-100) = 50
50%   ANSW50%R:50%
Answer: E
The probability that a man will be alive for 10more yrs is 1/4 & the probability that his wife will alive for 10 more yrs is 1/3. The probability that none of them will be alive for 10 more yrs, is  Choose one:
A) 1/2 B) 2/3 C) 3/5 D) 4/7 E) 4/9

Solution: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/2   1/2ns.(1/2)
Answer: A
A certain college party is attended by both male and female students. The ratio of male to female students is 4 to 5. If 12 of the male students were to leave the party, the ratio would change to 1 to 2. How many total students are at the party?
Select the correct option.
A) 64  B) 72  C) 80  D) 88  E) 96

Solution: The ratio is 4:5 = 8:10, so there are 8k males and 10k females.   If 12 males left, the ratio would be 1:2 = 5:10, so there would be 5k males and 10k females.   8k-5k = 12   k = 4   8k + 10k = 32 + 40= 
32 + 40 = 72
72   The answer is 72.
Answer: B
Two pipes A and B can fill a cistern in 37 1/2 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the pipe B is turned off after?  Choose the correct answer
A) 5 min
B) 9 min
C) 10 min
D) 15 min
E) 20 min

Solution: Explanation:   Let B be turned off after x minutes. Then, part filled by (A + B) in x min + part filled by A in (30 - x) min = 1.   x(2/75 + 1/45) + (30- x) 2/75 = 1   11x + 180 - 6x = 225 => x = 9   ANSWER IS 9 min
Answer: B
A metallic sheet is of rectangular shape with dimensions 48 m x 36 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 3 m, the volume of the box (in m3) is: Choose the correct choice from the following choices:
A) 3780  B) 5120  C) 6420  D) 8960  E) 7960

Solution: Clearly, l = (48 - 6)= 
(48 - 6) = 42
42 m,   b= (36 -6)= 
(36 -6) = 30
30 m,   h= 8 m.   Volume of the box = (42 x 30 x 3) m3 = 3780 m3. 3780nswer: Option 3780
Answer: A
A and B are integers. The expression (A+1)(B+1) is even. What can be said about A and B?  Choose the most appropriate option.
A) They are both even numbers. B) At least one of them is even C) At least one of them is odd. D) They are both odd. E) Nothing can be said surly on A and B

Solution: Odd x Odd = Odd   Odd x Even = Even   Even x Even = Even   To fulfill condition Either (A+1) or (B+1) needs to be Even   So either A or B needs to be odd   Or At Least one of them is odd.   ANSWER:At least one of them is odd.
Answer: C
Using only the digits from 0 to 6 , how many 5 digit codes can be constructed, if the first digit can not be 4 and no digits is used more than once ? Choose the correct choice from the following choices:
A) 1800 B) 2160 C) 7776 D) 720 E) 820

Solution: 5*6*5*4*3= 
5*6*5*4*3 = 1_800
1800   1800NSWER:1800
Answer: A
A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 550-mile journey? Assume that the train makes no intermediate stops. Choices
A) 8
B) 8.5
C) 9
D) 9.5
E) 10

Solution: A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 550-mile journey? Assume that the train makes no intermediate stops.   I think the easiest way to solve this problem would be simply to count the number of miles it travels per hour (and in total)   Hour miles/hour Total miles   1 10 10   2 20 30   3 30 60   4 40 100   5 50 150   6 60 210   7 70 280   8 80 360   9 90 450   10 100 550   It takes a total of nine hours to cover the 550 mile distance.   ANSW10R: 10
Answer: E
Group A has 1 boys and 2 girls, group B has 3 boys and 2 girls and group C has 2 boys and 5 girls. One student is selected from each of the group. Find the probability that one girl and two boys are among the three selected?  Choose the correct choice from the following options:  A) 3/41  B) 152/18  C) 29/105  D) 219/315  E) 202/735

Solution: Group A has 1 boy and 2 girls; 3   Group B has 3 boys and 2 girls; 5   Group C has 2 boys and 5 girls. 7   Selected group should have one girl and two boys.   Girl from A, boy from B, boy from C: 2/3*3/5*2/7 = 4/35;   Boy from A, girl from B, boy from C: 1/3*2/5*2/7 = 4/105;   Boy from A, boy from B, girl from C: 2/7*3/5*5/7 = 6/49.   Sum = 4/35 + 4/105 + 6/49 = 202/735.   Answer: 202/735.
Answer: E
How much is 50% of 40 is greater than 4/5 of 25?	Answers.
A) 0  B) 67  C) 88  D) 12  E) 66

Solution: (50/100) * 40 – (4/5) * 25   = 0   0nswer: 0
Answer: A
A person distributed 10% of his income to his 2 children each. He deposited 20% of his income to his wife's account. He donated 10% of remaining amount to an orphan house.Finally he has $500. Find his total income?  Choose one:  A) $900  B) $1000  C) $1200  D) $1150  E) $1500

Solution: 2 children got = 2*10= 
2*10 = 20
20%   wife got= 20%   orphan house = 10%   total = 20+20+10= 
20+20+10 = 50
50%   remaining= 100-50= 
100-50 = 50
50%   50%= 500   100% = 500*100/50= 
500*100/50 = 1_000
$1000   Answer is $1000
Answer: B
If a new town has 300 residents, and the population doubles every 10 years, what will be its population after 75 years?	Choose the correct answer:  A) 6034 residents  B) 9051 residents  C) 54306 residents  D) 15075 residents  E) 18102 residents

Solution: 300*2^(75/10)=300*2^7.5=100*181.02=54306   The answer is 54306 residents.
Answer: C
3 men or 6 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work? Answers
A) 15/7 days
B) 15/4 days
C) 17/4 days
D) 15/6 days
E) 12/4 days

Solution: 3M = 6W ---- 20 days   12M + 8W -----?   24W + 8 W = 32W ---?   6W ---- 20 32 -----?   6 * 20  24  + 8= 
 24  + 8 = 32
32W ---?   6W ---- 20 32 -----?   6 * 20= 32 * x => x = 15/4 days Answer: 15/4 days
Answer: B
Find the area, diameter = 12m. Choose the correct choice from the following options.
A) 113.00 square meter	B) 113.04 square meter	C) 113.08 square meter	D) 113.24 square meter	E) 113.43 square meter

Solution: Diameter = 12 meter.   Radius = diameter/2.   = 12/2.= 
12/2. = 6
6 meter.   Area of a circle= πr2.   Here, pi (π) = 3.14 meter, radius (r) = 6.   Area of a circle = 3.14 × 6 × 6..   = 3.14 × 36.   = 113.04 square meter or 113.04 m2. ANSWER : 113.04 square meter
Answer: B
A salesman’s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1200 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 1200 more than that by the previous schema, his sales were worth?
Choices
A) 12028	B) 12000	C) 12019	D) 16000	E) 12012

Solution: [1200 + (X-4000) * (2.5/100)] - X * (5/100)   = 600   X = 16000   Answer: 16000
Answer: D
The speed of a boat in still water is 24 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 15 minutes is Select.
A) 1.6 km B) 2 km C) 3.6 km D) 6.75 km E) None of these

Solution: Explanation:   Speed downstreams	=(24 + 3)= 
(24 + 3) = 27
27 kmph.   6.75 kmistance travelled= (27 x 15/60)km   = 6.75 km   Option 6.75 km
Answer: D
Mr Yadav spends 60% of his monthly salary on consumable items and 50% of the remaining on clothes and transport. He saves the remaining amount. If his savings at the end of the year were 48456, how much amount per month would he have spent on clothes and transport?	Choose the correct choice from the following choices
A) 4038  B) 8076  C) 9691.2  D) 4845.6  E) None of these

Solution: ∵ 4038mount, he have spent in 1 month on clothes transport = 4038mount spent on saving per month   ∵ 4038mount, spent on clothes and transport   = 48456⁄12 = 4038   4038nswer 4038
Answer: A
A Japanese rock band made ¥3 million on their first album with sales of ¥12 million, and made ¥5 million on their second album with sales of ¥30 million. By approximately what percent did the ratio of profit to sales decrease from the first album to second album?	Choose the most appropriate option
A) 24%
B) 27%
C) 30%
D) 33%
E) 36%

Solution: Solution:   This is a percent decrease problem. We will use the formula: percent change = (new – old)/old x 100 to calculate the final answer.   We first set up the ratios of profits to sales. The first ratio will be for the first album, and the second ratio will be for the next album. Because all of the sales are in millions, we do not have to express all the trailing zeros in our ratios.   First album   profit/sales = 3/12 = 1/4   Second album   profit/sales = 5/30 =1/6   We can simplify each ratio by multiplying each by the LCM of the two denominators, which is 12. Keep in mind that we are able to do this only because our answer choices are expressed in percents.   First album   profit/sales = (1/4) x 12 = 3   Next 2 Million   profit/sales = (1/6) x 12 = 2   We can plug 3 and 2 into our percent change formula:   (2 – 3)/3 x 100   =-1/3 x 100 so approximately a 33% decrease.   Answer 33%.
Answer: D
The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream?
Choose the correct choice
A) 15
B) 19
C) 14
D) 18
E) 16

Solution: The ratio of the times taken is 2:1.   The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1)= 
(2+1)/(2-1) = 3
3/1= 
3/1 = 3
3:1   Speed of the stream= 42/3= 
42/3 = 14
14 kmph.   Answer:14
Answer: C
A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 800 m long?
Answers
A) 266 Sec	B) 200 Sec	C) 776 Sec	D) 166 Sec	E) 997 Sec

Solution: L = S*T   S= 1200/120= 
1200/120 = 10
10 m/Sec.   Total length (D)= 2000 m   T = D/S   T = 2000/10= 
2000/10 = 200
200 Sec   Answer: 200 Sec
Answer: B
If y exceeds x by 20%, then x is less than y by?
Options.
A) 16%	B) 16 1/3 %	C) 16 2/3 %	D) 16 3/5 %	E) None of these

Solution: Explanation:   X=100	y=120   120------20   100-------? => 16 2/3%   ANSWER IS 16 2/3 %
Answer: C
3 candidates in an election and received 2500, 5000 and 15000 votes respectively. What % of the total votes did the winningcandidate got in that election?  Choose the correct choice.
A) 45%	B) 50%	C) 57%	D) 66.6%	E) 65.6%

Solution: Total number of votes polled = (2500 + 5000 + 15000)= 
(2500 + 5000 + 15000) = 22_500
22500   So, Required percentage= 11628/20400 * 100 = 66.6%   66.6%
Answer: D
Two musicians, Maria and Perry, work at independent constant rates to tune a warehouse full of instruments. If both musicians start at the same time and work at their normal rates, they will complete the job in 45 minutes. However, if Perry were to work at twice Maria’s rate, they would take only 30 minutes. How long would it take Perry, working alone at his normal rate, to tune the warehouse full of instruments?	Choices
A) 1 hr 30 min B) 1 hr 45 min C) 2 hr D) 2 hr 20 min E) 3 hr

Solution: Sol:   Lets Perry Rate be P and Rate of Maria be M   (rate)*(time)= Work or rate = work/time   first equation=> P+M = 1/45   converting it to hrs P+M= 1/(45/60) => 1/(3/4) =>4/3   second equation => M+2M =>1/30   converting it to hrs 3M=1/(30/60) =>1/(1/2)= 
1/(1/2) = 2
>2   therefore M= 2/3 and P=2/3   Rate of Perry = 2/3   time= work/rate (work = 1 job)   Time= 1.5 hrs   1 hr 30 minnswer 1 hr 30 min
Answer: A
Danny drove his old car 100 kilometers, from his home to a friend. To prevent the engine from overheating, he stopped his car for 13 minutes every time he completed 40 kilometers of continuous driving. When the car was moving, Danny drove it at an average speed of 60 kilometers per hour. What was Danny's average speed on that trip? Choose the correct option:
A) 37.5 kilometers per hour  B) 47.6 kilometers per hour  C) 50 kilometers per hour  D) 75 kilometers per hour  E) 100 kilometers per hour

Solution: Time taken to reach first 40 km is 40/60 = 2/3 hr   Time taken to reach next 40 km is 40/60 = 2/3 hr   Time taken to reach next 20 km is 20/60 = 1/3 hr   Danny stopped twice on his way at 40 km from starting point and at 80km from the starting point...   Each stop was of 13min , so two 13min break = 2*13/60 => 13/30 hr   Total time taken to reach 100 km is (2/3 + 2/3 + 1/3+13/30 ) =21/10 hrs   So, Average speed is 100/(21/10) = 47.6km/hour   Answer will be 47.6 kilometers per hour
Answer: B
The function g(p) is defined for integers p such that if p is even, g(p) = p/2 and if p is odd, g(p) = p + 5. Given that g(g(g(g(g(p))))) = 19, how many possible values for p would satisfy this equation? Choose the correct choice from the following answers.
A) 1	B) 5	C) 7	D) 8	E) 11

Solution: Let me define terms:   in g(p) = R   p is argument, R is result, g() is function,   in g(g(g(g(g(p))))), g1 is inner most, g5 is outermost for identification.   From definition of function g, we can deduce that:   If Result is even then two possibilities for argument = 1 Even 1 Odd   If Result is odd then one possibility for argument = 1 Even   Since final result = 19 = Odd   Possibilities:   g1:1 Even   g2: 1*(Even,Odd ) =1 Even 1 Odd   g3: 1*(Even,Odd) + 1 Even =2 Even 1 Odd   g4: 2*(Even, Odd) + 1 Even =3 Even 2 Odd   g5: 3*(Even, Odd) + 2 Even =5 Even 3 Odd = Total 8   Ans 8 it is!
Answer: D
Jill invests $10000 in an account that pays an annual rate of 3.96%, compounding semi-annually. Approximately how much Q does she have in her account after two years?  Choose the correct option:
A) $10079.44
B) Q=$10815.83
C) $12652.61
D) $14232.14
E) $20598.11

Solution: PS. I guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8%   Hence Q=$10815.83 the answer
Answer: B
What is the least value of x. So that 30x55 is divisible by 3?
Choices:
A) 4
B) 5
C) 1
D) 2
E) 7

Solution: The sum of the digits of the number is divisible by 3, then the number is divisible by3.   3 + 0+ x + 5 + 5 = 13+ x   Least value of x may be 2   Therefore  13+ 2= 
 13+ 2 = 15
15 is divisible by 3.   2
Answer: D