MU-NLPC/Calc-aqua_rat huggingface dataset:
If a supermarket shows $49 of sales for apples, and on that same day there are sales of $64 in oranges. What is the ratio of sales for apples to oranges?	Choices
A) 1 : 2
B) 2 : 3
C) 4 : 7
D) 1 : 5
E) None

Solution: Solution   Let us name the apples   as A and the oranges as B.	= (A'S sales) : (B's sales)   =âˆšb : âˆša   = âˆš49 : âˆš64   = 7 : 8   Answer None
Answer: E
6 highschool boys gather at the gym for a game of mini-volleyball. Three teams of 2 people each will be created. How many ways are there to create these 3 teams?	Select the correct option:  A) 27  B) 51  C) 90  D) 45  E) 450

Solution: Arrange the 6 boys in a straight line in 6! ways.   The first three form team 1, next three form team 2 and last three form team 3. But in each team, the boys are arranged in first, second third positions so you need to un-arrange them by dividing by 3! three times (once for each team). You get 6!/(2! * 2! * 2!)   Also, there are no distinct teams - team1, team2 and team3. You just have three teams. So you also need to un-arrange the three teams by dividing by another 3!.   You get 6!/(2! * 2! * 2!) * 2! = 45   Answer (45)   You get 6!/(2! * 2! * 2!) * 2!   Answer : 45
Answer: D
A corporation paid $9 million in federal taxes on its first $50 million of gross profits and then $30 million in federal taxes on the next $150 million in gross profits. By approximately what percent did the ratio of federal taxes to gross profits increase from the first $50 million in profits to the next $150 million in profits?  Select.
A) 6%  B) 14%  C) 20%  D) 23%  E) 14%

Solution: Difference in Ratios = (30/150) - (9/50) = (1/50)   % Change = (Change (1/50) / Original ratio (7/50)) *100 = 14%   Answer - 14%
Answer: E
Harkamal purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
Choose the correct choice.
A) 1000  B) 1055  C) 1065  D) 1075  E) 1080

Solution: Cost of 8 kg grapes = 70 × 8 = 560.   Cost of 9 kg of mangoes = 55 × 9 = 490.   Total cost he has to pay = 560 + 490 = 1055.   1055)
Answer: B
Find the total number of prime factors in the expression (4)11 x (7)5 x (11)2. Choose one
A) 22 B) 29 C) 19 D) 5 E) 2

Solution: (4)11x (7)5 x (11)2 = (2 x 2)11 x (7)5 x (11)2 = 211 x 211 x75x 112   = 222 x 75 x112   Total number of prime factors = (22 + 5 + 2)= 
(22 + 5 + 2) = 29
29.   ANSWER 29 29
Answer: B
Joan took out a mortgage from hel local bank. Each monthly mortgage payment she makes must be triple the amount of the previous month's payment. If her first payment is $100, and the total amount she must pay back is $109300, how many months will it take Joan to pay back her mortgage?	Choose the correct choice from the following options:
A) 7 B) 8 C) 10 D) 11 E) 13

Solution: Joan starts off with 100 $ .. which is to be tripled every month   Her monthly payments look like this :   100 , 300 , 900 , 2700 ......... Upto 109300   This can be re written as :   100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 ...... 100 x 1093   So we have 1 , 3 , 9 , 27 ..... 109300 in GP   We know that a =1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula Tn = a3^n-1 ...)   Therefore to find the Sum of n terms of a GP we use this formula :   Sn = a (1-r^n) / 1 -r   Using this and plugging in the information we get ...   1093 = 1 - 3^n / 1-3 ; 1-3^n / -2   Cross multiplying we get   1093 x -2 = 1- 3^n   - 2186 = 1 - 3^n   - 2187 = - 3 ^n   2187 = 3 ^n (negatives cancel out)   2187 can also be re written as 3 ^ 7   Therefore ; 3 ^7 = 3 ^n   Thus n = 7 (7)
Answer: A
Mr. Karan borrowed a certain amount at 6% per annum simple interest for 9 years. After 9 years, he returned Rs. 8210/-. Find out the amount that he borrowed.	Choose the correct choice from the following answers
A) s. 5331	B) s. 5269	C) s. 5228	D) s. 5218	E) s. 52192

Solution: Explanation:   Let us assume Mr. Karan borrowed amount is Rs. A. (the principal)   By formula of simple interest, S.I. = PRT / 100   Where P = The principal, R = Rate of interest as a %, T = Time in years   S.I. = (P * 6 * 9)/100 = 54 P/100   Amount = Principal + S.I.   8210 = P + (54P/100)   8210 = (100P + 54P)/100   8210 = 154P/100   P = (8210 * 100)/154 = Rs. 5331.169   s. 5331NSWER: s. 5331
Answer: A
If G is a negative integer, which of the following must be a negative integer?  Answers:	A) G + 1	B) G/2+3	C) G^4	D) G – y	E) G^11

Solution: We need to check each option here:   A. G + 1   This will depend on the value of G. Nothing can be said   B. G/2+3   This will depend on the value of G. Nothing can be said   C. G^4   This will always be positive. Even powers of negative numbers are positive and odd powers are negative   D. G – y   This will depend on the value of G. Nothing can be said   E. G^11   This will always be negative. G^11ven powers of negative numbers are positive and odd powers are negative   Correct Option: G^11
Answer: E
Mary has 1803 dollars with her. What is the amount that she should keep with her inorder to distribute the same among nine kids equally?
Pick:  A) 3  B) 0  C) 10  D) 2  E) 6

Solution: The answer is 3. (1803-3=1800). 1800 is divisible by nine which gives an answer of 20.So,she will be distributing 20 each for the nine kids and the remaining 3 will be left with her. So the answer is 3=3
Answer: A
Circles X and Y are concentric. If the radius of circle X is two times that of circle Y, what is the probability that a point selected inside circle X at random will be outside circle Y? Select the correct option:
A) 13
B) Pi/3
C) Pi/2
D) 5/6
E) 3/4

Solution: Small circle radius = a, so area = PI a ^ 2   Large circle radius = 2a, so area =4. PI a ^ 2   Area of shaded region = 4PI a^2 - PI a^2 = 3 PI a^2   So, probability = ( 3 PI a^2 ) / (4 PI a^2 )   = 3/4 = Answer = 3/4
Answer: E
The average age of three boys is 15 years. If their ages are in ratio 3:5:7, the age of the youngest boy is  Choices:
A) 21 years	B) 18 years	C) 15 years	D) 9 years	E) None

Solution: Solution: Sum of ages of three boys = 45 years   Now, (3x+5x+7x) = 45   Or, 15x = 45   Or, x = 3   So, age of youngest boy = 3x = 3*3= 
3*3 = 9
9 years.   Answer: Option 9 years
Answer: D
A snail, climbing a 66 feet high wall, climbs up 4 feet on the first day but slides down 2 feet on the second. It climbs 4 feet on the third day and slides down again 2 feet on the fourth day. If this pattern continues, how many days will it take the snail to reach the top of the wall?
Choose the correct choice from the following choices
A) 42
B) 63
C) 77
D) 80
E) 91

Solution: total transaction in two days = 4-2= 
4-2 = 2
2 feet   in 62 days it will climb 62 feet   on the 63rd day , the snail will climb 4 feet , thus reaching the top   therefore , total no of days required=63   63
Answer: B
A jar of 364 marbles is divided equally among a group of marble-players today. If 2 people joined the group in the future, each person would receive 1 marble less. How many people are there in the group today?
Select the correct option.
A) 20 B) 22 C) 24 D) 26 E) 28

Solution: 364 = 26*14 = 28*13   There are 26 people in the group today.   The answer is 26.
Answer: D
Mary replaced 20% of an 60% juice concentrate with water. Upon finding the resultant juice too sweet, she further replaced 30% of this solution with water, then fine tuned it by replacing 10% of that solution with water.
What is the final juice concentration Mary liked best?	Choose one.
A) 25.5%  B) 41.68%  C) 30.24%  D) 21%  E) 39.54%

Solution: The answer can be quickly calculated as: (60)(0.8)(0.7)(0.9)   How it works: By calculating how much juice is removed from an assumed 100 ml mixture, we can find out the final percentage.   In step 1, 20% of a 60% juice concentrate is replaced with water. With 100 ml of juice concentrate, this translates to removing 20% of juice, or rather keeping 80% of it. Hence, we multiply 60x0.8 = 48 ml.   In step 2, 30% of the solution is mixed with water. This translates to keeping 70% of the concentrate. Hence, 48x0.7 = 33.6 ml.   Finally in step 3, 10% of the solution is replaced with water. This means 90% of the concentrate remains. So, final amount of concentrate = 33.6x0.9 = 30.24 ml.   30.24 ml of concentrate in a 100 ml solution makes 30.24%   Answer: 30.24%
Answer: C
A can contains a mixture of liquids A and B is the ratio 7:5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many liter M of liquid A was contained by the can initially?  Choose the correct option: A) 10 B) 20 C) 21 D) 25 E) 27

Solution: As A:B::7:5 ---> only option C is a multiple of 7 and hence it is a good place to start. Also A:B::7:5 means that , A = (712)*Total and B = (5/12)*Total   If A = 21 , B = 15 ---> remove 9 litres ---> you remove (7/12)*9 of A ---> A remaining = 21-(7/12)*9 = 63/4   Similarly, for B, you remove (5/12)*9 ---> B remaining = 15 - (5/12)*9 = 45/4 and then add 9 more litres of B ---> 9+45/4 = 81/4   Thus A/B (final ratio) = (45/4)/(81/4) = 7:9 , the same as the final ratio mentioned in the question.   Hence C is the correct answer.   A/B = 7/9 = (7x-(7/12)*9)/ (5x-(5/12)*9+9), where 7x and 5x are initial quantities of A and B respectively.   Thus, 7/9 = (7x-(7/12)*9)/ (5x-(5/12)*9+9) ---> giving you x=3. Thus A (original) M= 7*3 = 21.21
Answer: C
A person want to give his money of $1000 to his 4 children A,B,C,D in the ratio 2:4:3:1. What is the A+D share?	Select the correct option: A) $100 B) $200 C) $300 D) $500 E) $600

Solution: A's share = 1000*2/10= 
1000*2/10 = 200
$200   D's share= 1000*1/10= 
1000*1/10 = 100
$100   A+D= $300   Answer is $300
Answer: C
An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 12 o'clock noon?  Choose the correct choice from the following answers:  A) 180°  B) 120°  C) 160°  D) 170°  E) 150°

Solution: The angle traced by the hour hand in 12 hours is 360°, which is 30° per hour.   In 4 hours, the angle traced by the hour hand is 4×30° = 120°   The answer is 120°.
Answer: B
Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?	Choose the correct choice from the following choices.
A) 20/9  B) 40/9  C) 50/9  D) 60/9  E) 80/9

Solution: one day work of A = 1/8   one day work of 40/9 = 1/10   so one day work of A and 40/9 together = 1/8 + 1/10 = 9/40   so total days required = 40/9   ANSWER:40/9
Answer: B
A letter lock consists of five rings each marked with three different letters. The number of distinct unsuccessful attempts to open the lock is at the most?
Choose one:
A) 277  B) 269  C) 242  D) 177  E) 123

Solution: Since each ring consists of three different letters, the total number of attempts possible with the five rings is   = 3 * 3 * 3 * 3 * 3 = 216. Of these attempts, one of them is a successful attempt.   Maximum number of unsuccessful attempts = 243 - 1= 
243 - 1 = 242
242   Answer:242
Answer: C
It takes 3 workers a total of 9 hours to build a giant machine with each worker working at the same rate. If 3 workers start to build the machine at 11:00 AM, and one extra worker per hour is added beginning at 2:00 PM, at what time will the machine be complete?  Choose the correct choice from the following choices:
A) 5:15  B) 5:26  C) 5:37  D) 5:48  E) 5:59

Solution: 3 workers build 1/9 of a machine in one hour.   1 worker builds 1/27 of a machine in one hour.   In the first 3 hours, 3 workers build 3*(1/27)*3=9/27 of a machine   From 2:00 to 3:00, 4 workers build another 4/27. The total is 13/27.   From 3:00 to 4:00, 5 workers build another 5/27. The total is 18/27.   From 4:00 to 5:00, 6 workers build another 6/27. The total is 24/27.   To build another 3/27, 7 workers need (3/7)*60 minutes which is about 26 minutes.   The machine is complete at about 5:26.   The answer is 5:26.
Answer: B
Indu gave Bindu Rs.3750 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest? Options:	A) s.6	B) s.2	C) s.5	D) s.3	E) s.4

Solution: 3750 = D(100/4)2   D = 6   s.6NSWER:s.6
Answer: A
Of the five numbers in a sequence, the first term is 10,000, and each of the following terms is 60% of the previous term. What is the value range of the five numbers?  Choose the correct choice from the following choices:
A) 8,704
B) 9,750
C) 9,975
D) 9,984
E) 10,736

Solution: 1st number= 10,000   2nd number = 60% of 10,000= 6000   3rd number= 60% of 6000= 3600   4th number = 60% of 3600= 2160   5th number= 60% of 2160= 1296   Range = 10,000-1296= 8704   8,704 is the answer
Answer: A
A property decreases in value every year at the rate of 6 1/4% of its value at the beginning of the year its value at the end of 3 years was Rs.21093. Find its value at the beginning of the first year?  Answers
A) 25600.24	B) 25600.28	C) 25600.243	D) 25600.21	E) 25600.23

Solution: 6 1/4% = 1/16   x *15/16 * 15/16 * 15/16 = 21093   x = 25600.24   25600.24nswer: 25600.24
Answer: A
Five years ago, John’s age was half of the age he will be in 8 years. How old is he now? Choices:
A) 14years	B) 15years	C) 16years	D) 17years	E) 18years

Solution: Let John=j,j-5=(j+8)/2,then j=18years   ANSW18yearsR:18years
Answer: E
9. On level farmland, two runners leave at the same time from the intersection of two country roads. One runner jogs due north at a constant rate of 8 miles per hour while the second runner jogs due east at a constant rate that is 2 miles per hour slower than the first runner's rate. How far apart, to the nearest mile, will they be after 1/2 hour ?  Choose the correct choice from the following:
A) 5	B) 7	C) 8	D) 12	E) 14

Solution: If runner 1 is going north and runner 2 is going east they are like two sides of a 90 degree triangle.   Side 1 = 8 m/h --> 4 m in 1/2 hr   Side 2 = 6 m/h --> 3 m in 1/2 hr   to complete this right angle triangle   d^2 = 4^2 + 3^2   d^2 = 25   = 5   5nswer option 5
Answer: A
The probability that A speaks truth is 3/5 and that of B speaking truth is 1/7. What is the probability that they agree in stating the same fact?
Choose the correct choice from the following answers.
A) 18/35 B) 18/38 C) 18/36 D) 18/16 E) 15/35

Solution: If both agree stating the same fact, either both of them speak truth of both speak false.   Probability   = 3/5 * 1/7 + 2/5 * 6/7   = 3/35 + 12/35   = 15/35   Answer: 15/35
Answer: E
Given a square of length 2m. Its corners are cut such that to represent a regular octagon. Find the length of side of octagon
Choose the correct option
A) 2	B) 3	C) 4	D) 5	E) 7

Solution: Let x is the side of the octagon and x + 2y is the side of the square.   In the given octagon, y2+y2=x2⇒2y2=x2⇒y=x2–√y2+y2=x2⇒2y2=x2⇒y=x2   But x2–√+x+x2–√=2x2+x+x2=2   ⇒2–√x+x=2⇒2x+x=2   ⇒x=22–√+1=22–√+1×2–√−12–√−1=2(2–√−1)⇒x=22+1=22+1×2−12−1=2(2−1)   2nswer:2
Answer: A
If the selling price is quintupled,the profit is hexatrupled,what is the percentage of profit?? Select.
A) 50%	B) 100%	C) 150%	D) 200%	E) 250%

Solution: we can make two equations from the given info..   let selling price be S and cost price be C..   so profit=P=S-C...   if S is doubled profit is tripled..   so 6P=5S-C..   or S=5P...   therefore C=P..   % of profit=P/P=100%   100%
Answer: B
How many different 6 digit numbers can be formed from the number 745698 by re-arranging its digits so that the odd digits occupy even position
Answers:
A) 15
B) 12
C) 8
D) 7
E) 36

Solution: There are 3 odd numbers which have to be placed at 3 even places =3!=6 ways   There are 3 even numbers which have to be placed at 3 odd places. So 3! = 6ways   so total number of ways of arranging all these numbers are 6 * 6= 
6 * 6 = 36
36 ways   Answer:36
Answer: E
A car traveled from San Diego to San Francisco at an average speed of 45 miles per hour. If the journey back took twice as long, what was the average speed of the trip?
Options.
A) 30. B) 32. C) 36. D) 42. E) 44.

Solution: Let the time taken be = x   One way distance = 45x   Total distance traveled = 2 * 45= 
2 * 45 = 90
90x   Total time taken= x + 2x = 3x   30.verage speed = 90x/3x = 30   30.nswer: 30.90 /3= 
90 /3 = 30
30   30.nswer: 30.
Answer: A
In how many no. between 100 and 1000 at least one of their digits is 7?
Pick one.
A) 900 B) 648 C) 720 D) 252 E) 729

Solution: Let's count the number of occurrences with only one 7:   (1) 7XX:  1 * 9 * 9= 
 1 * 9 * 9 = 81
81   (2) X7X: 8 * 1 * 9= 
8 * 1 * 9 = 72
72   (3) XX7: 8 * 9 * 1= 72   81 + 72 + 72= 
81 + 72 + 72 = 225
225   At this point we can already see that the answer must be D since the choice are very dispersed.   Anyways, let's count number of occurrences with two 7s:   (1) 77X: 1 * 1 * 9= 
1 * 1 * 9 = 9
9   (2) X77: 8 * 1 * 1= 8   (3) 7X7: 1 * 9 * 1 = 9   9 + 8 + 9= 
9 + 8 + 9 = 26
26   Number 777 is missing. So the total becomes   225 + 26 + 1= 
225 + 26 + 1 = 252
252   252 is the correct answer.
Answer: D
1,236
1,263
1,326
.....
....
+6,321
The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,2,3,6 exactly once in each integer. What is the sum of these 24 integers?  Options: A) 63,332 B) 67,772 C) 71,112 D) 75,552 E) 79,992

Solution: In each of the units, tens, hundreds, and thousands place, each digit will appear 6 times.   Then the sum equals 6(1111)+6(2222)+6(3333)+6(6666) = 79,992   The answer is 79,992.
Answer: E
The total number of students in Grades 1 and 2 is 30 more than the total number of students in grades 2 and 5. How much lesser is the number of students in Grade 5 as compared to Grade 1? Pick:
A) 20 B) 30 C) 10 D) 40 E) 15

Solution: (Grade 1 + Grade 2) - (Grade 2 + Grade 5) = 30   Grade 1 - Grade 5 = 30   Answer: 30
Answer: B
One card is drawn at random from a pack of 48 cards. What is the probability that the card drawn is a face card?  Choose the correct option: A) 1/4 B) 1/7 C) 1/8 D) 1/5 E) 2/5

Solution: Clearly, there are 52 cards, out of which there are 12 face cards.   P (getting a face card) =	12/48 = 1/4   1/4
Answer: A
A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?  Select the correct option.
A) 50	B) 45	C) 20	D) 73	E) 27

Solution: 50+B+C = 500   50+C = 200   B+C = 350   --------------   50+B+2C = 550   50+B+C = 500   ----------------   C = 50   50nswer:50
Answer: A
Kelly and Jody packed boxes with books. If Jody packed 20% of the total number of boxes, what was the ratio of the number of boxes Kelly packed to the number that Jody packed? Options:
A) 1 to 6
B) 4 to 1
C) 2 to 5
D) 3 to 5
E) 2 to 3

Solution: Explanation:   If Jody packed 20% of the boxes then Kelly packed 80%. The ratio of the number of boxes Kelly packed to the number Jody packed is thus 80%/20%=4/1   Answer: Option 4 to 180 /20= 
80 /20 = 4
4/1   Answer: Option 4 to 1
Answer: B
8k8
+ k88
--------
1,6y6
If k and y represent non-zero digits within the integers above, what is y? Choose the correct choice:
A) 6  B) 7  C) 8  D) 9  E) 17

Solution: 8k8   k88   --------   16y6   Trial and error or just plug-in method might be the shortest way to solve this problem. Though you can narrow down the possible values of k to just two: 7 and 8 --> 8**+7**=16** or 8**+8**=16** (k can not be less than 7 or 9, as the result won't be 16**). After that it's easy to get that k=7 and y=6.   6nswer: 6.
Answer: A
A and B partner in a business. A contribute 1/4 of the capital for 15 months and B received 2/3 of the profit. For how long B's money was used? Select the correct option:  A) 5 months  B) 10 months  C) 8 months  D) 12 months  E) 7 months

Solution: B received 2/3 of the profit.   Then A received remaining 1/3 of the profit.   => A : 10 months =1/3:2/3=1:2   Let the total capital =x   Then A's capital =x4   10 months's capital =x–x/4=3x/4   Assume 10 months's money was used for b months   Then A:10 months =x/4×15:3x/4×b   ⇒15x/4:3bx/4=1:2   ⇒15:3b=1:2   ⇒5:b=1:2   ⇒5×2=1×b   ⇒b=10   Answer is 10 months.
Answer: B
I. a2 - 2a - 8 = 0,
II. b2 = 9 to solve both the equations to find the values of a and b? Choose the most appropriate option:
A) If a < b B) If a ≤ b C) If the relationship between a and b cannot be established D) If a > b E) If a ≥ b

Solution: Explanation:   I. (a - 4)(a + 2) = 0   => a = 4, -2   II. b2 = 9   => b = ± 3   -2 < 3, -2 > -3, 4 > 3, 4 > -3,   No relation can be established between a and b.   If the relationship between a and b cannot be established)
Answer: C
A, B and C can do a work in 7 days, 8 days and 12 days respectively. In how many days can all three of them working together, complete the work? Choose the correct choice.
A) 2 50/59  B) 2 5/59  C) 2 2/50  D) 2 2/59  E) 2 1/59

Solution: Work done by all three of them in one day = 1/7 + 1/8 + 1/12 = 59/168   The number of days required = 168/59 = 2 50/59 days.   2 50/59nswer:2 50/59
Answer: A
Five bells commence tolling together and toll at intervals of 2, 4, 6, 8,10 seconds respectively. In 60 minutes, how many times do they toll together?  Choose one.
A) 41
B) 10
C) 31
D) 16
E) 17

Solution: L.C.M of 2,4,6,8,10 is 240. i.e after each 2 min they will toll together.So in 60 min they will toll 30 times.As they have initially tolled once,The answer will be  30+1= 
 30+1 = 31
31.   ANSWER:31
Answer: C
In a school with 5 classes, each class has 2 students less than the previous class. How many students are there in the largest class if the total number of students at school is 100?  Choose the correct choice from the following choices:
A) 24
B) 25
C) 26
D) 27
E) 28

Solution: Let x be the number of students in the largest class.   Then x + (x-2) + (x-4) + (x-6) + (x-8) = 100   5x -20 = 100   5x = 120   x = 24   The answer is 24.
Answer: A
A wheel that has 6 cogs is meshed with a larger wheel of 7 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions made by the larger wheel is:	Options
A) 9 B) 10 C) 6 D) 18 E) 7

Solution: Explanation :   Let the required number of revolutions made by larger wheel be x.   Then, More cogs, Less revolutions (Indirect Proportion)   7:6::21:x => 7 * x = 21 * 6   => x = (21 * 6)/7   => x = 18   Answer : 18
Answer: D
0.009/x=0.1. find the value of X
Choose the most appropriate option
A) 0.0009	B) 0.09	C) 0.9	D) 9	E) 90

Solution: x=0.009/0.1= 
0.009/0.1 = 0.09
0.09   ANSWER:0.09
Answer: B
If 36 men can do a piece of work in 25 hours, in how many hours will 10 men do it? Choose the correct choice from the following choices.
A) 22
B) 38
C) 60
D) 88
E) 90

Solution: Explanation:   Let the required no of hours be x. Then   Less men , More hours (Indirect Proportion)   \inline \fn_jvn \therefore 10:36 ::25:x \inline \fn_jvn \Leftrightarrow (10 x X)=(36 x 25) \inline \fn_jvn \Leftrightarrow \inline \fn_jvn x=\frac{36\times 25}{10}=90   Hence, 10 men can do it in 90 hours.   Answer: 90) 90
Answer: E
w, b, c, and d are positive integers. If the remainder is 9 when w is divided by b, and the remainder is 5 when c is divided by d, which of the following is NOT a possible value for b + d? Choose the correct choice from the following answers:
A) 20	B) 19	C) 18	D) 16	E) 15

Solution: When w is divided by b remainder is 9 that means b is greater than or equals to 10, similarly d is greater than or equals to 6.   b + d cannot be 15, hence 15 is the answer.
Answer: E
Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 19 MPH between the 2 friends until the friends meet. How many miles does the pigeon travel?
Choose the correct choice from the following choices: A) 54 B) 57 C) 60 D) 36 E) 96

Solution: 57   57   It takes 3 hours for the friends to meet; so the pigeon flies for 3 hours at 19 MPH = 57 miles
Answer: B