MU-NLPC/Calc-aqua_rat huggingface dataset:
3 candidates in an election and received 1256, 7636 and 11628 votes respectively. What % of the total votes did the winning candidate gotin that election?  Choose the correct choice from the following:
A) 56.7%
B) 55%
C) 57%
D) 60%
E) 62%

Solution: Total number of votes polled = (1256 + 7636 + 11628)= 
(1256 + 7636 + 11628) = 20_520
20520   So, Required percentage= 11628/20520 * 100 = 56.7%   56.7%
Answer: A
What is the smallest number which when increased by 3 is divisible by 9, 70, 25 and 21? Choose one.
A) 2927 B) 3147 C) 3387 D) 3567 E) 3797

Solution: When increased by 3, the number must include at least 2*3^2*5^2*7 = 3150   The answer is 3147.
Answer: B
What is the difference between the C.I. on Rs. 4000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly?  Select:
A) s.2.04
B) s.2.08
C) s.1.63
D) s.2.83
E) s.2.42

Solution: C.I. when interest is compounded yearly   = [4000 * (1 + 4/100) * (1 + (1/2 * 4)/100]   = 4000 * 26/25 * 51/50 = Rs. 4243.2   C.I. when interest is compounded half-yearly   = [4000 * (1 + 2/100)2]   = (4000 * 51/50 * 51/50 * 51/50)   = Rs. 4244.83 Difference   = (4244.83 - 4243.2)   = Rs.1.63.   Answer: s.1.63
Answer: C
Of the five-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two?	Choose the most appropriate option
A) 24440	B) 36440	C) 72440	D) 181440	E) 216440

Solution: Of the five-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two?   A. 24   B. 36   C. 72   D. 144   E. 216   Choosing the digit for p - 9 ways;   Choosing the digit for q - 8 ways;   Choosing the digit for r - 7 ways;   Choosing the digit for s - 6ways;   # of permutations of 3 digits in ppqrs - 5!/2!   Total: 9*8*7*6*5!/2!=181440.   Answer: 181440.
Answer: D
Jim is twice as old as Stephanie, who, four years ago, was three times as old as Kate. If, five years from now, the sum E of their ages will be 51, how old is Stephanie ?  Choose the correct choice from the following options:
A) 6
B) 10
C) 14
D) 20
E) 24

Solution: 1) take C (14y.o.), so mean that S=14, J=28, their sum itself is 42+10 years from now is 52, it is over the 51,   so eliminate C,D,E   2) take B (10y.o.),E= meaning S=10,J=20, so  20+10+10= 
 20+10+10 = 40
40 and for K=10-4/3=2+9= 
2+9 = 11
11, finally 40+11= 
40+11 = 51
51. It is correct   10
Answer: B
Two years ago, John put $5,000 into a savings account. At the end of the first year, his account had accrued $500 in interest bringing his total balance to $5,500. The next year, his account balance increased by 10%. At the end of the two years, by what percent has John's account balance increased from his initial deposit of $5,000 ?
Choose the correct choice from the following choices:
A) 19%	B) 21%	C) 20%	D) 22%	E) 25%

Solution: investment 5000 dollars   1 st year total gained = 500   total amount end of first year = 5500   second year account increased by 10 % = 5500*0.1= 
5500*0.1 = 550
550   therefore total amount by second year end= 6050   so total percentage increase in money = (6050-5000)*100/5000= 
(6050-5000)*100/5000 = 21
21 %   Correct Answer 21%=21%
Answer: B
if 1 is absent rest of people can be divided into 6 equal parts if 2 is absent rest of them are divided into 7 equal parts ,how many students are present
Choose the most appropriate option
A) 34
B) 35
C) 36
D) 37
E) 38

Solution: x-1/6=(x-2)/7+1,solve it ans 37   ANSWER:37
Answer: D
If the product of 12 integers is negative, at most how many of the integers can be negative?
Select the correct option: A) 2 B) 3 C) 4 D) 5 E) 11

Solution: The product of12 integers is negative   Thus an odd number of integers need to be negative to have a negative product   We are asked at most how many are required.   So, the highest odd integer before 6,i.e. 11   Correct Option : 11
Answer: E
The simple interest on a sum of money is 4/9 of the principal and the number of years is equal to the rate percent. Find the rate and the time? Choose the correct choice from the following options:  A) 6 2/3%  B) 6 2/8%  C) 6 9/3%  D) 6 2/3%  E) 6 2/1%

Solution: 4/9 P = (P*R*R)/100   R = 20/3 = 6 2/3%   6 2/3%nswer: 6 2/3%
Answer: A
The length and breadth of a rectangle is increased by 10% and 25% respectively. What is the increase in the area?
Choose the correct option:  A) 67.5%  B) 37.5%  C) 77.5%  D) 47.5%  E) 27.5%

Solution: 100 * 100= 
100 * 100 = 10_000
10000   110 * 125= 
110 * 125 = 13_750
13750   -----------   3750   10000 ------ 3750   100 ------- ?=> 37.5%   Answer:37.5%
Answer: B
A certain ornaments was marked down 10% the first week and another 30% the next week. What percent of the regular price was the final cost of the ornaments after the two markdowns? Pick one
A) 30%
B) 36%
C) 40%
D) 63%
E) 64%

Solution: If the price of the ornament is 100, and it is marked down by 10% then by 70% or charged 90% of the price first and 70% of the price of reduced price, the final price is :-   100*70*90/10000= 
100*70*90/10000 = 63
63   63% is the final price of old price.   63% is the answer
Answer: D
A number x is 4 times another number y. The percentage that y is less than x is  Choose the correct choice from the following choices:
A) 12.5%
B) 75%
C) 80%
D) 11%
E) 1%

Solution: Say y=1 and x=4.   Then y=1 is less than x=4 by (4-1)/4*100=3/4*100= 
3/4*100 = 75
75%.   Answer: 75%.
Answer: B
Two trains A and B are 100 m and 150 m long and are moving at one another at 54 Km/hr and 36 Km/hr respectively. Arun is sitting on coach B1 of train A. Calculate the time taken by Arun to completely cross Train B.
Choose the correct choice from the following answers:	A) 10 s	B) 6 s	C) 4 s	D) 8 s	E) 12 s

Solution: DETAILED SOLUTION   Speed of A = 54∗1000/60∗60 = 15 m/s   Speed of B = 36∗1000/60∗60 = 10 m/s   Relative speed = S1 + S2 = 15 + 10 m/s = 25 m/s   The length that needs to be crossed = length of train B = 150 m. Therefore time taken = 150/25= 
150/25 = 6
6s.   What is the time taken for trains to completely cross each other? The length that needs to be crossed= 100 + 150= 
100 + 150 = 250
250 m. Time taken= 250/25= 
250/25 = 10
10 s.   CORRECT ANSWER 6 s.
Answer: B
The number of positive integers valued pairs (x, y) satisfying 4x -17y = 1 and x <= 1000 (x is less than or equal to 1000) is	Choose the correct choice from the following options
A) fifty nine  B) 57  C) 55  D) 58  E) 60

Solution: 4x-17y=1   y=(4x-1)/17   x has to be a positive integer such that 1 <=x<=1000(4x-1) is a factor of 17 so that y is also a positive integer   So we need to know how many numbers in the set {3,7,11,15,....,3999} are divisible by 17   Lets try to observe the pattern   1. 3 mod 17 = 3   2. 7 mod 17 = 7   3. 11 mod 17 = 11   4. 15 mod 17 = 15   5. 19 mod 17 = 2   6. 23 mod 17 = 6   7. 27 mod 17 = 10   8. 31 mod 17 = 14   9. 35 mod 17 = 1   10. 39 mod 17 = 5   11. 43 mod 17 = 9   12. 47 mod 17 = 13   13.51 mod 17 = 0   14. 55 mod 17 = 4   15. 59 mod 17 = 8   16. 63 mod 17 = 12   17. 67 mod 17 = 16   ... and after this the remainders will repeat (this is no co-incidence that the cyclicity is also 17)   So the right choices are x=13,13+17,13+17+17,.....   The number of such numbers is 59 (highest one being 999) fifty nine
Answer: A
A trader marks his books 40% more than the cost price. If he allows 40% discount, then find his gain or loss percent? Select the correct option
A) 2% profit	B) 16% loss	C) 4% loss	D) No profit No loss	E) None of these

Solution: Let CP of an book = 100   MP of an book = 140   Discount 40 % on 140 = 56   SP of the book = 140 - 56= 
140 - 56 = 84
84   loss= 16%   Answer : 16% loss
Answer: B
In the x- y plane, there are 4 points (0,0), (0,4), (8,4), and (8,0). If these 4 points makes a rectangle, what is the probability that x+y<4?  Choose the correct option:	A) 1/2	B) 1/3	C) 2/3	D) 1/4	E) 2/5

Solution: The line y=-x+4 intersects the rectangle and these three points of intersection (0,0), (0,4) and (4,0) form a triangle.   The points below the line y=-x+4 satisfy x+y<4.   The area of this triangle is (1/2)(4)(4)=8   The area of the rectangle is 32.   P(x+y<4) = 8/32 = 1/4   The answer is 1/4.
Answer: D
A man can row his boat with the stream at 10 km/h and against the stream in 6 km/h. The man's rate is?  Choose the most appropriate option:	A) 2 kmph	B) 7 kmph	C) 98 kmph	D) 6 kmph	E) 4 kmph

Solution: DS = 10   US = 6   S = ?   S = (10 - 6)/2= 
(10 - 6)/2 = 2
2 kmph   2 kmphnswer: 2 kmph
Answer: A
The number of boys in a class is three times the number of girls. Which one of the following numbers cannot represent the total number of children in the class ? Choose the correct option
A) 48  B) 44  C) 42  D) 40  E) 38

Solution: Explanation:   Let number of girls = x and number of boys = 3x.   Then, 3x + x = 4x = total number of students.   Thus, to find exact value of x, the total number of students must be divisible by 4.   Answer: 42
Answer: C
Find the area of a parallelogram with base 24 cm and height 16 cm? Options:
A) 298 cm2	B) 384 cm2	C) 278 cm2	D) 286 cm2	E) 276 cm2

Solution: Area of a parallelogram = base * height = 24 * 16= 
24 * 16 = 384
384 cm2   Answer:384 cm2
Answer: B
50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be:  Choose the correct choice from the following options
A) 20 cm	B) 23 cm	C) 25 cm	D) 30 cm	E) 32 cm

Solution: L*b*h=Total water displaced=200(given)   To find height i.e rise in the water level   h=200/L*B   H=25cm   answer :25 cm
Answer: C
Nails and screws are manufactured at a uniform weight per nail and a uniform weight per screw. If the total weight of one screw and one nail is half that of 6 screws and one nail, then the total weight of 3 screws, and 3 nails is how many times that of 1 screws and 5 nails?  Choose the correct answer:  A) a. 4  B) b. 5/2  C) c. 2  D) d. 3/2  E) e. 5/4

Solution: let the weight of nail be n and that of screw be s..   so s+w=1/2 * (6s+1n)...   or 1n = 4s..   lets see the weight of 3 s and 3n= 3s+3*4s=15s..   and weight of 1s and 5n3 +3*4= 
3 +3*4 = 15
15s..   and weight of 1s and 5n= 1s+5*1s=6s..   ratio1 +5*1= 
1 +5*1 = 6
6s..   ratio= 15s/6s=15/6=5/2   b. 5/2
Answer: B
A grocery shop has a sale of Rs. 6535, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?  Choose the correct option.
A) 4857
B) 4184
C) 4012
D) 4891
E) 5291

Solution: Let the sale in the sixth month =x   Then   (6535+6927+6855+7230+6562+x)/6 =6500   =>6535+6927+6855+7230+6562+x =6×6500   => 34109+x=39000   => x=39000−34109   =4891   ANSWER:4891
Answer: D
A merchant sells an item at a 20% discount, but still makes a gross profit of 20 percent of the cost. What percent P of the cost would the gross profit on the item have been if it had been sold without the discount?
Choose the correct choice: A) 20% B) 40% C) 50% D) 60% E) 75%

Solution: Let the Market Price of the product is MP.   Let the Original Cost Price of the product is CP.   Selling Price (Discounted Price) = 100%of MP - 20%MP   = 80% of MP. ---------------- (1)   Profit made by selling at discounted price = 20% of 50%P -------------- (2)   Apply the formula:   Profit = Selling Price - Original 50%ost Price   => 20% of 50%P = 80% of MP - 100% 50%P   => MP = 12050%P/80 = 3/2 (50%P)   Now if Product is sold without any discount, then,   Profit = Selling Price (without discount) - Original 50%ost Price   = Market Price - Original 50%ost Price   = MP - 50%P   = 3/2 50%P - 50%P   = 1/2 50%P   P==50%of 50%P   Thus, Answer should be50%.
Answer: C
A florist has 3 azaleas, 4 buttercups, and 5 petunias. The florist puts two flowers together at random in a bouquet. However, the customer calls and says that she does not want two of the same flower. What is the probability that the florist does not have to change the bouquet?	Choose the correct choice from the following choices:
A) 19/66	B) 31/66	C) 47/66	D) 87/132	E) 95/132

Solution: The probability that two of the same flowers were chosen:   P(AA) = 3/12 * 2/11 = 6/132   P(BB) = 4/12 * 3/11 = 12/132   P(PP) = 5/12 * 4/11 = 20/132   The sum of these probabilities is 19/66   P(two flowers are different) = 1 - 19/66 = 47/66   The answer is 47/66.
Answer: C
A theater charges $12 for seats in the orchestra and $8 for seats in the balcony. On a certain night, a total of 350 tickets were sold for a total cost of $3,320. How many more tickets were sold that night for seats in the balcony than for seats in the orchestra?
Choose the correct option.
A) 90	B) 110	C) 120	D) 130	E) 220

Solution: Orchestra Seats - a   Balcony Seats - b   a+b = 350   and 12a + 8b = 3320   Solving equations simultaneously (Multiply Equation 1 with 8 and subtract from second equation)   4a = 3320 - 8*350 = 3320 - 2800= 
3320 - 2800 = 520
520   i.e. a= 130   and b = 350-130= 
350-130 = 220
220   More seats in balcony than orchestra= b-a = 220 - 130= 
220 - 130 = 90
90   90nswer: option 90
Answer: A
How many odd numbers between 10 and 1500 are the squares of integers?  Options:  A) 11  B) 14  C) 17  D) 20  E) 23

Solution: The numbers are the squares of 5, 7, 9,...,37 which includes 17 numbers.   The answer is 17.
Answer: C
X men can do a work in 120 days. If there were 20 men less, the work would have taken 60 days more. What is the value of X? Answers:  A) 30  B) 70  C) 80  D) 60  E) 20

Solution: 60   60   We have M1 601 = M2 602   120X = (X - 20)180   => 2X = (X - 20) 3 => 2X = 3X - 60   => X = 60
Answer: D
In a certain company, a third of the workers do not have a retirement plan. 20% of the workers who do not have a retirement plan are women, and 50% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women?
Choose the correct option:  A) 80  B) 95  C) 105  D) 120  E) 210

Solution: 20% of the workerswithoutretirement plan are women, this means 80% of the workerswithoutretirement plan are men right? Makes 100% = no retirement plan.   Then 40% of those wo have a retirement plan are men, which means 60% of those who have a retirement plan are women. These percentages are always refering to the subgroupsRetirement plan = YesandNo Retirement Plan.   Make the total workers equal x and work from there and it should be fine > x/3 have no retirement plan at all. I struggled with the question a lot, it was hard for me although usually I have no problems with sets questions like this. I believe it must be a 700+ question.   Yes, you are right. I read the question incorrectly! I glazed overnotfor some reason.   If20% of the workers who do not have a retirement plan are women,80% who do not have retirement plan are men. Also 40% who do have retirement plan are men. Since 1/3 do not have retirement plan and 2/3 do have, it becomes a simple weighted average question.   Cavg = (80*1 + 50*2)/3= 
(80*1 + 50*2)/3 = 60
60% are men   Total= 120*100/60= 
120*100/60 = 200
200   No. of women= 200 - 120= 
200 - 120 = 80
80   80
Answer: A
John purchased a paints and a buckets for Rs. 14000 &Rs. 9500 respectively. He sold the paints at a loss of 7% and the buckets at a profit of 12%. Overall how much he make a profit.
Choices
A) 258
B) 456
C) 187
D) 635
E) 160

Solution: Let the SP of the paints and the buckets be Rs. r and Rs. m respectively.   r = 14000(1 - 7/100) = 14000 - 980   m = 9500(1 + 12/100) = 9500 + 1140   Total SP - Total CP = r + m - (14000 + 9500) = -980 + 1140= Rs. 160   As this is positive, an overall profit of Rs. 160 was made.   160
Answer: E
1=5,2=25,3=253,4=150,5=225 then 150=?
Select.
A) 1
B) 255
C) 4
D) 445
E) 235

Solution: 1=5,2=25,3=253,4=150,5=225 then 150=?   150=4   check the fourth eqn.   ANSWER:4
Answer: C
when a no. divided by 406 it gives 115 as a remainder. when it divided by 29 what is the remainder.??? Select
A) 7 B) 28 C) 29 D) 2 E) 5

Solution: let x is divided by 406 & gives quotient y & remainder 115 then   x = 406 * y + 115   now, x / 29 = (406 * y + 115)/29 = 406 * y/29 + 115/29   => rem = 115/29 = 28   ANSWER:28
Answer: B
An article is bought for Rs.600 and sold for Rs.500, find the loss percent? Pick.
A) 16 2/8%  B) 16 8/3%  C) 19 2/3%  D) 16 2/3%  E) 11 2/3%

Solution: 600 ---- 100   100 ---- ? => 16 2/3%   Answer: 16 2/3%
Answer: D
A volunteer organization is recruiting new members. In the fall they manage to increase their number by 5%. By the spring however membership falls by 19%. What is the total change in percentage from fall to spring? Answers
A) 16.16%	B) 15.15%	C) 14.95%	D) 13.33%	E) 12.52%

Solution: (100%+5%)*(100%-19%) = 1.05*.81 = 0.8505.   1-0.8505 = 14.95% lost = -14.95%   The Answer is 14.95%   The organization has lost 14.95% of its total volunteers from fall to spring.
Answer: C
If the average (arithmetic mean) of x and y is 40, and z – x = 60, what is the average of y and z?
Choose the most appropriate option
A) 20 B) 50 C) 65 D) 70 E) 140

Solution: x+y/2 = 40   => x+y = 80   x = z - 60...sub this value   z-60+y = 80   =>z+y = 140   =>z+y/2 = 70.   ANSWER:70
Answer: D
The product of all the prime numbers less than 28 is closest to which of the following powers of 10?	Choices:  A) a) 10^9  B) b) 10^8  C) c) 10^7  D) d) 10^6  E) e) 10^8*2.23

Solution: Group these numbers so as to get product close to a multiple of 10, so they can be rewritten as (2*5)(3*7)(11*19)(13*17)*23 or 10*21*209*221*23   Now take out power of 10 from each number and rewrite   10*10*100*100*10(1*2.1*2.09*2.21*2.3) or 10^7*(1*2.1*2.09*2.21*2.3)=2.23*10^8   e) 10^8*2.23
Answer: E
Bob invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest (compounded annually) for the same 2 years at the same rate of interest and received $600 as interest. What was the annual rate of interest? Pick one:
A) 5%
B) 10%
C) 18%
D) 15%
E) 20%

Solution: First divide $550/2years to get 275$/yr non-compounding interest.   Next, subtract from the total compound after 2 years to see the interest gained in the second year. This can be done because the same amount has been invested in both accounts and the interest gained for the first year will be the same. So, $600-$275= $325.   To find the difference in interest gained, $325-$275= $50 increase in interest after the first year through compounding.   From this information we can set up the equation $275 * X% = $50.=18% giving us answer choice 18%.
Answer: C
How many seconds will a 600 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?	Select
A) 23 sec  B) 36 sec  C) 27 sec  D) 28 sec  E) 29 sec

Solution: Speed of train relative to man = 63 - 3= 
63 - 3 = 60
60 km/hr.= 60 * 5/18   = 50/3 m/sec.   Time taken to pass the man = 600 * 3/50= 
600 * 3/50 = 36
36 sec.   Answer:36 sec
Answer: B
The average expenditure of a labourer for 6 months was 85 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income i  Choose the correct choice from the following answers.
A) 70 B) 72 C) 75 D) 78 E) 80

Solution: Income of 6 months = (6 × 85) – debt   = 510 – debt   Income of the man for next 4 months   = 4 × 60 + debt + 30   = 270 + debt   ∴ Income of 10 months = 780   Average monthly income = 780 ÷ 10 = 78   Answer 78
Answer: D
Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 4 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them?	Select.
A) 28 km B) 20 km C) 65 km D) 18 km E) 16 km

Solution: Distance = Relative Speed * Time   = (4 + 3) * 4= 
(4 + 3) * 4 = 28
28 km   [ They are travelling in the opposite direction, relative speed= sum of the speeds].   28 kmnswer: 28 km
Answer: A
The sum of ages of 5 children born 1 year different each is 50 yrs. What is the age of the Elder child? Choose the correct choice from the following options:
A) 8
B) 9
C) 16
D) 17
E) 18

Solution: Let the ages of children be x, (x + 1), (x + 2), (x + 3) and (x + 4) years.   Then, x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 50   5x = 40   x = 8   x+4= 8+1= 
8+1 = 9
9   Answer : 9
Answer: B
Of the books standing in a row on a shelf, an atlas is the 30th book from the left and the 33rd book from the right. If 4 books to the left of the atlas and 4 books to the right of the atlas are removed from the shelf, how many books will be left on the shelf?  Answers
A) 54
B) 57
C) 58
D) 61
E) 63

Solution: 100%. There are total of   30+33-1= 
  30+33-1 = 62
62 books and   4+4= 
  4+4 = 8
8 books are removed, thus 62-8= 
62-8 = 54
54 books are left.   54nswer: 54.
Answer: A
The length of rectangle is thrice its breadth and its perimeter is 96 m, find the area of the rectangle?  Pick one:	A) 156	B) 432	C) 288	D) 355	E) 478

Solution: Explanation:   2(3x + x) = 96   l = 36 b = 12   lb = 36 * 12= 
36 * 12 = 432
432   Answer: 432
Answer: B
The area of the rectangle ABCD is 30. The points E and F are on the diagonal AC as shown,
and 2(AE + FC) = 3 EF. What is the area of △BEF ? Choices: A) 5 B) 6 C) 9 D) 10 E) cannot be determined

Solution: We have EF =   2/5AC. Thus, the ratio of the areas of 46EF and 46AC is   2/5   correct answer 6
Answer: B
In a shop 30% of the articles are sold at a profit of 40% and the remaining at a loss of 20%.what is the overall profit/loss?	Choose one:	A) 2% loss	B) 5% loss	C) 15% profit	D) 3% profit	E) no profit, no loss

Solution: 30*1.4+70*0.8/100=0.98   2% lossNSWER:2% loss
Answer: A
How many different pairs of positive integers (a, b) satisfy the equation 1/a+1/b=30/51 ?  Choose the correct choice:
A) 6  B) 3  C) 2  D) 1  E) 0

Solution: There is no certain way to solve 2 unknown with 1 equation. The best way is to look at the question and retrospect the most efficient way. In this question, a and b are only positive integers. So that is a big relief. Now, we can start with putting a=1,2,.. and so on till the time we are confident about one of the options.   So, we start with   a=1, we get b as -ve. out   a=2, we get b as 6. Yes (Now (a,b) = (2,6). We can directly see that (a,b)=(6,2) will also satisfy. So we have 2 possible solutions)   a=3, we get b as 3. Yes (Now we have 3 possible solutions)   a=4, we get b as fraction. Out   a=5, we get b again as some fraction. Out   a=6 already taken.   We have A,B options left. C,D,E are out.   A is 6. To have 6 as the answer, we will need one more pair like2,6and one more solution where a=b.   When a=b, we have only 1 solution = 1. So, one more solution, where a=b is not possible.   So, answer will be 1.
Answer: D
When positive integer x is divided by 10, the quotient is y and the remainder is 3. When 2x is divided by 7, the quotient is 3y and the remainder is 1. What is the value of 11y – x? Choose the correct option
A) 2
B) -2
C) 3
D) -3
E) 4

Solution: (1) x = 10y+3   (2) 2x = 21y+1   (2)-(1): x=11y-2   11y-x=2   The answer is 2.
Answer: A
A train of length 110 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?	Choose the correct choice.
A) 3  B) 7  C) 6  D) 8  E) 1

Solution: Explanation:   Distance = 110 m   Relative speed = 60 + 6= 
60 + 6 = 66
66 kmph (Since both the train and the man are in moving in opposite direction)= m/sec = m/sec   Time taken to pass the man = = 6 s   Answer: 6) 6
Answer: C