MU-NLPC/Calc-aqua_rat huggingface dataset:
A batsman in his 12th innings makes a score of 115 and thereby increases his average by 3 runs. What is his average after the 12th innings if he had never been ‘not out’? Choose the correct answer:
A) 42 B) 43 C) 44 D) 82 E) 46

Solution: Let ‘x’ be the average score after 12 th innings   ⇒ 12x = 11 × (x – 4) + 115   ∴ x = 82   Answer 82
Answer: D
A train crosses a platform of 110 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?	Select.
A) A)310m
B) B)170m
C) C)180m
D) D)158m
E) E)350m

Solution: Length of the train be ‘X’   X + 110/15 = X + 250/20   4X + 440 = 3X + 750   X = 310m   310mnswer: 310m
Answer: A
What is the least number to be subtracted from 1300 to make it a perfect square? Choose one
A) 80	B) 25	C) 75	D) 63	E) 90

Solution: The numbers less than 1300 and are squares of certain number is 1225.   The least number that should be subtracted from 1300 to make it perfect square = 1300 - 1225= 
1300 - 1225 = 75
75.   ANSWER:75
Answer: C
Find the LCM of 0.6, 9.6 and 0.36.  Choose the correct choice:
A) 26.3  B) 35.6  C) 32.9  D) 25.5  E) 28.8

Solution: The given numbers are equivalent to 0.60, 9.60 and 0.36.   Now, find the LCM of 60,960 and 36. Which is equal to 2880.   The required LCM =28.80.   Answer is 28.8
Answer: E
An error 3% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is
Pick one
A) 6.04%
B) 6.14%
C) 6.23%
D) 6.26%
E) 6.09%

Solution: 100 cm is read as 102 cm.   A1 = (100 x 100) cm2 and A2 (103 x 103) cm2.   (A2 - A1) = [(103)2 - (100)2]   = (103 + 100) x (103 - 100)   = 609 cm2.   Percentage error = 6.09   6.09%
Answer: E
The H.C.F. of two numbers is 32 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:	Answers.
A) 448 B) 299 C) 421 D) 460 E) 365

Solution: Clearly, the numbers are (32 x 13) and (32 x 14).   Larger number = (32 x 14) = 448. 448nswer: Option 448
Answer: A
The diagonals of a rhombus are 15 cm and 20 cm. Find its area?	Choose the correct answer: A) 329 B) 288 C) 150 D) 238 E) 31

Solution: 1/2 * 15 * 20= 
1/2 * 15 * 20 = 150
150   Answer: 150
Answer: C
If x^2=x -1, then x^3=? Choose the correct choice:
A) 3x+2
B) 3x-2
C) 2x+1
D) -1
E) 3x+4

Solution: Given X^2 = X - 1   X^3 = X*X^2 = x*(X-1)-- Substituted from above.   = X^2 - X = X-1-X = -1.   Hence -1.
Answer: D
The product W of the first 10 prime numbers is closest to which of the following?
Choose the correct answer.
A) 6.5 x 10^7 B) 6.5 x 10^8 C) 6.5 x 10^9 D) 6.5 x 10^10 E) 6.5 x 10^11

Solution: The first 10 primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.   So, we need to find approximate value of 2*3*5*7*11*13*17*19*23*29.   # of different approximations are possible. For example:    2*5= 
 2*5 = 10
10   3*17=~50 (actually more than 50);   7*13=~100 (actually less than 100);   11*19=~200 (actually more than 200)   23*29= 
23*29 = 667
667=W   2*3*5*7*11*13*17*19=~10*50*100*200*667=10^7*667=6.67*10^9.   Answer: 6.5 x 10^9.
Answer: C
Solve the equation for x : 5x - 14 + 3x = 4 + 9 - x
Select the correct option:  A) 4  B) 5  C) 7  D) 9  E) 3

Solution: 3   3   8 x + x = 13 + 14   9 x = 27 => x = 3
Answer: E
By selling a watch for Rs.640/-, a man loses 20% what is that watch cost price
Choose the correct choice from the following answers
A) Rs. 700/- B) Rs. 800/- C) Rs. 880/- D) Rs. 900/- E) Rs. 990/-

Solution: 80 % ------> 640 (80 * 8 = 640)   100 % ------>800 (100 * 8 = 800)   Cost price = Rs. 800/-   Rs. 800/-
Answer: B
If r is an odd integer, which of the following must also be odd?  Pick one
A) 8r + 4  B) r + r  C) 3r + 3  D) 2r + r  E) r^2 + 1

Solution: Things to keep in mind:   Odd + odd = even   Odd + even = odd   Odd*odd = odd   Odd*even = even   On checking each option   A. 8r + 4   8r = even, 8r + 4 = even + even = even.   B. r + r   Odd + odd = even. This will be even   C. 3r + 3   3r = odd, 3r + 3 = odd + odd = even   D. 2r + r   2r = even, 2r + r = even + odd = odd   E. r^2 + 1   r^2 = odd, r^2 + 1 = odd + odd = even   Correct option: 2r + r
Answer: D
A particular store purchased a stock of turtleneck sweaters and marked up its cost by 20%. During the New Year season, it further marked up its prices by 25% of the original retail price. In February, the store then offered a discount of 7%. What was its profit on the items sold in February? Select the correct option.
A) 27.5%	B) 30%	C) 35%	D) 39.5%	E) 40%

Solution: Assume the total price = 100x   Price after 20% markup = 120x   Price after 25%further markup = 1.25*120= 
1.25*120 = 150
150x   Price after the discount= 0.93*150= 
0.93*150 = 139.5
139.5x   Hence total profit= 39.5%   Option 39.5%
Answer: D
If the radius of a circle that centers at the origin is 5, how many K points on the circle have integer coordinates?	Choose the correct choice from the following answers:
A) 4
B) 8
C) 12
D) 15
E) 20

Solution: I understand this might not be required but I used the equation of a circle.   Since the origin is at 0, x^2+y^2=5^2.   X,Y could be +/- (0,5 or 5,0) - 4 possibilities.   X,Y could be +/- (3,4 or 4,3) - 8 possibilities.   Ans: K=12
Answer: C
What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 10%?  Select
A) 20% B) 28% C) 27% D) 35% E) 70%

Solution: SP2 = 2/3 SP1   CP = 100   SP2 = 90   2/3 SP1 = 90   SP1 = 135   100 --- 35=> 35%   Answer:35%
Answer: D
RAJA and RAM can together complete a piece of work in 4 days. If RAJA alone can complete the same work in 12 days, in how many days can RAM alone complete that work ? Answers.
A) 6 days	B) 5 days	C) 7 days	D) 8 days	E) 10 days

Solution: (R6 daysJ6 days + R6 daysM)'s 1 days work = 1/4   R6 daysJ6 days 1 day work = 1/2   R6 daysM 1 day work = (1/4-1/12) = 1/6   ==>6 days   6 daysNSWER 6 days
Answer: A
Ajay spends 50% of his monthly income on household items, 25% of his monthly income on buying cloths, 15% of his monthly income on medicines and saves the remaining amount which is Rs. 9000. Find his monthly income.
Choose the correct choice from the following options: A) Rs. 90000 B) Rs. 36000 C) Rs. 50000 D) Rs. 45000 E) None of these

Solution: Savings 10 % - 9000   Expenditure 90 % - 81000   Total - 90000   Rs. 90000nswer : Rs. 90000
Answer: A
How many different pairs of numbers (s, t) such that s = 3t can be obtained if s and t are selected from the set of number {0, 1, 2, 3, 4, 5, 6, 7, 10, 11}  Choose the correct answer:
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: Given s=3t   t can take 0,1,2   and so s = 0,3,6   3 such pairs can be formed.   answer 3
Answer: C
If 0.75 : x :: 7 : 8, then x is equal to:  Options:
A) A)1.12
B) B)1.2
C) C)0.95
D) D)0.85
E) E)0.9

Solution: (x * 7) = (0.75 * 8)= 
(0.75 * 8) = 6
6/7   x= 0.85   Answer = 0.85
Answer: D
If (n+2)!/n!=90, n=?
Choose the correct option:	A) 2/131	B) 8	C) 10	D) 11	E) 12

Solution: (n+2)!/n!= 90   Rewrite as:[(n+2)(n+1)(n)(n-1)(n-2)....(3)(2)(1)]/[(n)(n-1)(n-2)....(3)(2)(1)]= 132   Cancel out terms: (n+2)(n+1) = 132   From here, we might just TEST the answer choices.   Since (10)(9) = 90, we can see that n = 8   8
Answer: B
The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is? Choose one.
A) 25.1  B) 12.2  C) 10.2  D) 11.5  E) 11.7

Solution: 1 to 11 = 11 * 10.9= 
11 * 10.9 = 119.9
119.9   1 to 6= 6 * 10.5= 
6 * 10.5 = 63
63   6 to 11= 6 * 11.4= 
6 * 11.4 = 68.4
68.4   63 + 68.4= 
63 + 68.4 = 131.4
131.4 â€“ 119.9= 11.5   6th number = 11.5   Answer: Option 11.5
Answer: D
A girl multiplies 987 by a certain number and obtains 559981 as her answer. If in the answer, both 9’s are wrong but the other digits are correct, then the correct answer will be	Choose the correct choice from the following answers.
A) 553681	B) 555181	C) 555681	D) 556581	E) None of these

Solution: 987 = 3 x 7 x 47.   So, required number must be divisible by each one of 3, 7, 47.   None of the numbers in 553681 and 555181 are divisible by 3. While 556581 is not divisible by 7.   Correct answer is 555681.   ANSWER:555681
Answer: C
In a village there are 150 men and 90 women in present time.if in next year population will be P=(a^2 +b^2)^1/2 , and in every year men are reduces 10%.what is population of after 2 year.
Choose the correct choice from the following answers.
A) 140  B) 141  C) 142  D) 143  E) 144

Solution: next year total population=[150^2+90^2]^.5=174.92=175   man decreased by 10% so total man =150*.9= 
150*.9 = 135
135   women will be= 175-135= 
175-135 = 40
40   so population after two years= [135^2+40^2]^.5=140.80=141   so population after two year= 141   ANSWER:141
Answer: B
How many factors does 25^2 have?
Choices.
A) 2 B) 8 C) 24 D) 25 E) 26

Solution: 36^2 = 6*6*6*6 = 2^4*3^4   Total factors = (4+1)*(4+1) = 4*2= 
4*2 = 8
8   Answer 8.
Answer: B
P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 50 days to complete the same work. then Q alone can do it in Choose the correct choice:
A) 20  B) 22  C) 25  D) 27  E) 30

Solution: Work done by P and Q in 1 day = 1/10   Work done by R in 1 day = 1/50   Work done by P, Q and R in 1 day = 1/10 + 1/50 = 6/50   But Work done by P in 1 day = Work done by Q and R in 1 day . Hence the above equation can be written as Work done by P in 1 day × 2 = 6/50   => Work done by P in 1 day = 3/50   => Work done by Q and R in 1 day = 3/50   Hence work done by Q in 1 day = 3/50 – 1/50 = 2/50 = 1/25   So Q alone can do the work in 25 days   Answer is 25.
Answer: C
sum of the digits of 5^2010*8^673 Choose the correct choice.
A) 7	B) 8	C) 9	D) 10	E) 11

Solution: 5^2010 * 8^673 (2^3=8) therefore   673*3= 
  673*3 = 2_019
2019=5^2010 * 2^2019   =10^2010 * 2^9 (2^9=512)   =10^2010 * 512= 512000..... upto 2010 zeroes.So the sum is 8.   ANSWER:8
Answer: B
A solution of 130 litres contains milk and water in the ratio 7:x. If thirty litres of water is added to the solution, the ratio becomes 3:2, find the value of x?	Pick.
A) 2.6
B) 2.4
C) 2.9
D) 2.8
E) 3

Solution: Exp. Total new quantity = original sol + water =130+30= 
130+30 = 160
160   New ratio= 3:2, New quantity of milk =3/5*160= 
3/5*160 = 96
96 Lit,   New quantity of water= 2/5*160= 
2/5*160 = 64
64 Lit   Water present initially= (64-30)= 
(64-30) = 34
34 Lit   Ratio= 96/34 =7/x There for x = 2.4   Answer: 2.4
Answer: B
In a certain company, the ratio of the number of managers to the number of non-managers in any department must always be greater than 5 : 24. In the company, what is the maximum number of non-managers in a department that has 8 managers: Choose the most appropriate option: A) 36 B) 37 C) 38 D) 39 E) 40

Solution: M/NM > 5x/24x   M = 8   8/NM > 5x/24x   8/NM - 5x/24x > 0   (192x - 5x * NM)/(24x * NM) > 0   192x - 5x*NM > 0   5x*NM < 192x   NM < 192x/5x   NM < 38.4   Maximum number of non managers = 38   Answer: 38
Answer: C
In how many ways Q can the crew of a ten oared boat be arranged ,when of the ten persons available, 2 of whom can row only on the bow side and 3 of whom can row only on the stroke side?
Choose the correct option:
A) 1. 10!/(2! * 3!)  B) 2. 10!/(8! * 7!)  C) 3. 5!/(3! * 2!)  D) 4. (5!)^3/(3! * 2!)  E) 5. 5!/(8! * 7!)

Solution: Ans is D.   Going by the assumtion that both the Bow side and Stroke side will have 5 person each.   Five(3+2) of them had allready been selected(according to their preference), so from the remaining 5 we have to select 2 for the stroke side or 3 for the bow side.   and the 5 crew of each side can be arranged in Q= 5! ways.   Hence answer is 5C3 * 5! * 5!= (5!)^3/ 3!2!=4. (5!)^3/(3! * 2!)
Answer: D
The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 56. Find their present ages.
Choose the correct answer
A) 16,28,36	B) 8,10,20	C) 5,10,12	D) 30,32,45	E) 6,8,10

Solution: Let their present ages be 4x, 7x and 9x years respectively.   Then, (4x - 8) + (7x - 8) + (9x - 8) = 56   20x = 80 => x = 4   Their present ages are 16, 28 and 36 years respectively.   16,28,36NSWER 16,28,36
Answer: A
What is the probability of flipping a fair coin four times and the coin landing on heads on exactly one flip?	Choose the correct choice
A) 1/3
B) 1/4
C) 1/6
D) 1/12
E) 1/16

Solution: Probability = (Favorable combination)/(Total combination)   Favorable combination = (HTTT, THTT, TTHT,TTTH) ==> 4   Total combination = 16 (2^4)   Probability = (4)/(16)=1/4   (1/4)
Answer: B
Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively. In what time will they cross each other completely?
Select.
A) 11 sec
B) 15 sec
C) 19 sec
D) 12 sec
E) 20 sec

Solution: 12 sec   12 sec = 250 m + 250 m = 500 m   RS = 80 + 70= 
80 + 70 = 150
150 * 5/18= 125/3   T = 500 * 3/125= 
500 * 3/125 = 12
12 sec
Answer: D
There are three vessels of equal capacity .Vessel A contains Milk and water in the ratio 12:10 ;Vessel B contains Milk and water in the ratio 2:1 and Vessel C contains Milk and water in the ratio 3:2 .If the mixture in all the three vessels is mixed up.What will be the ratio of water to milk ?	Pick one:
A) 547/398
B) 392/598
C) 598/392
D) 210/279
E) 398/547

Solution: 12:10=>12x+10x=22x   2:112 +10= 
12 +10 = 22
22x   2:1=>2y+1y=3y   3:22 +1= 
2 +1 = 3
3y   3:2=>3z+2z=5z   22x3 +2= 
3 +2 = 5
5z   22x=3y=5z   Take LCM of 22,3,5=330   Or simply;   x=15   y=110   z=66   So,   Ratio of Water:Milk=(10x+y+2z)/(12x+2y+3z)=392/598   Ans:392/598
Answer: B
If v and y are integers, then vy(v + y) is Choose one:
A) Always positive
B) Always negative
C) Positive when v is positive
D) Negative when v is negative
E) It cannot be determined by the information given

Solution: Given v and y are integers, then vy(v + y)   Let's take even as 2 / -2 and odd as 3 / -3..we get the following.. and IMO option D is correct answer..   I presume its Option E if am not missing anything.   v=-3 and y=1   vy(v + y) is positive = 6
Answer: E
A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. If field has a length that is twice its width, find the area of the field in square meters. Pick
A) 56,000 square meters
B) 32,000 square meters
C) 65,000 square meters
D) 20,000 square meters
E) 43,000 square meters

Solution: Let us first find the distance d jogged   distance = rate * time = (12 km / hr)* 30 minutes   = (12 km/hr) * 0.5 hr = 6 km   The distance of 6 km corresponds to 10 perimeters and therefore 1 perimeter is equal to   6 km / 10 = 0.6 km = 0.6 * 1000= 
0.6 * 1000 = 600
600 meters   Let L and W be the length and width of the field. The length is twice the width. Hence   L= 2 W   The perimeter is 600 meters and is given by   2 (L + W) = 600   Substitute L by 2 W   2 (2 W + W) = 600   Simplify and solve for W   4 W + 2 W = 600   6 W = 600   W = 100   Find L   L = 2 W = 200   Find the area A of the rectangle   A = L * W = 200 * 100 = 20,000 square meters correct answer 20,000 square meters
Answer: D
In expressing a length of 55.471 km as nearly as possible with the three significant digits, find the percentage error
Choose the most appropriate option:
A) 0.52%	B) 0.24%	C) 0.052%	D) 0.024%	E) None of these

Solution: Explanation:   Error = (55.5 - 55.471)= 
(55.5 - 55.471) = 0.029
0.029   Required percentage=   0.029/ 55.471Ã—100=0.052   Option 0.052%
Answer: C
Two trains start from A & B and travel towards each other at
speed of 40kmph and 50kmph resp. At the time of the meeting the
second train has traveled 130km more than the first.the distance
between them.
Choose one.
A) 1170 km	B) 1180 km	C) 1270 km	D) 1280 km	E) 1350 km

Solution: Let the distance traveled by the first train be x km   then distance covered by the second train is x + 130km   x/40 = x+130 / 50   x= 520   so the distance between 1170 km & B is x + x + 130 = 1170 km   1170 kmnswer is 1170 km.
Answer: A
The total of the ages of Jayant, Prem and Saransh is 93 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. What is the present age of Saransh?  Choose the correct choice from the following options:  A) 24 years  B) 31 years  C) 34 years  D) 38 years  E) None

Solution: Solution   Let the ages of Jayant, Prem and Saransh 10 years ago be 2x, 3x and 4x years respectively. Then,   (2x + 10)+(3x + 10)+(4x + 10)	= 93.   ‹=›9x = 63   x = 7.   ∴ Prem's present age = 3x + 10 = 31 years.   Answer 31 years
Answer: B
A man sells an article at 15% loss. Had he sold it for Rs. 420/- more he could have gained 20%. What is the cost price of the article?	Choose the most appropriate option:	A) Rs.420/-	B) Rs.400/-	C) Rs.900/-	D) Rs.1200/-	E) None of these

Solution: Explanation:   Short cut method:   Loss =====> 15 %   Profit ====> 20 %   ~   ----------------   35 % ---------> Rs. 420/-   100 % --------> Rs. 1200/-   Answer: Option Rs.1200/-
Answer: D
Average of first six multiples of 15 is  Choose the correct answer.
A) 9.5
B) 44.5
C) 52.5
D) 15.75
E) 17.7

Solution: Explanation:   Average=15(1+2+3+4+5+6) / 6=315 / 6= 
315 / 6 = 105/2 = around 52.5
52.5   Option 52.5
Answer: C
A bag contains 6 black and 6 white balls. One ball is drawn at random. What is the probability that the ball drawn is white? Answers:
A) 4 B) 4/3 C) 4/5 D) 4/9 E) 1/2

Solution: Let number of balls = (6 + 6)= 
(6 + 6) = 12
12.   Number of white balls= 6.   P (drawing a white ball) = 6/12 = 1/2   Hence Answer is 1/2
Answer: E
For a race a distance of 224 meters can be covered by P in 8 seconds and Q in 32 seconds. By what distance does P defeat Q eventually?	Choose the most appropriate option:  A) 672m  B) 6738m  C) 634m  D) 671m  E) 636m

Solution: Explanation:   This is a simple speed time problem. Given conditions:   =>Speed of P= 224/8= 
224/8 = 28
28m/s=>Speed of Q=224/32= 
224/32 = 7
7m/s=>Difference in time taken = 24 seconds   Therefore, Distance covered by P in that time= 28m/s x 24 seconds = 672 metres   672mNSWER: 672m
Answer: A
In a game of billiards, A can give B 40 points in 80 and he can give C 60 points in 80. How many points can B give C in a game of 100? Choose the correct choice:
A) 50	B) 55	C) 60	D) 65	E) 70

Solution: A scores 80 while B score 40 and C scores 20.   The number of points that C scores when B scores 100 = (100 * 20)/40= 
(100 * 20)/40 = 50
50.   In a game of 100 points, B gives (100 - 50)= 
(100 - 50) = 50
50 points to C   50nswer:50
Answer: A
A certain quantity of 45% concentration solution is replaced with 20% concentration solution such that the concentration of the combined amount is 35%.
What's the ratio of the amount of solution that was replaced to the amount of solution that was not replaced? Choose the correct choice from the following answers
A) 1:3  B) 1:2  C) 2:3  D) 2:1  E) 3:1

Solution: 20% - - - - - - - - - 35% - - - - - - 45%   From 20 to 35 =15   From 35 to 45 = 10   So the ratio is 15/10 = 3 to 2   2:3 it is
Answer: C
If P and Q are positive integers, P - 1 is divisible by 2 and Q - 3 is divisible by 4, all of the following could be the value of P - Q Except?  Choices
A) 9
B) 2
C) 4
D) 6
E) 12

Solution: P-1 = 2Q   => P = 2Q + 1 = 1,3,5,7,9,11,13,15,17,19,21,23,25   Q-3 = 4P   => Q = 4P + 3 = 3,7,11,15,19,23,27,31,35,39,43,47   2=5-3   4=11-7   6=17-11   12=23-11   So , we can see that all the answer choices are possible here except 9
Answer: A
Three boys picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical? Choose the correct choice from the following options:
A) A)4^30
B) B)2^30
C) C)1^30
D) D)3^30
E) E)6^30

Solution: Each Mango can be given to any one of the four people or in other words..1 mango can be divided into 3 ways...so all 30 can be divided in 3^30 ways   ANS:3^30
Answer: D
Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?	Choose the correct choice from the following options:	A) Rs. 150	B) Rs. 300	C) Rs. 250	D) Rs. 200	E) None of these

Solution: Explanation :   Let the amount paid to X per week = x   and the amount paid to Y per week = y   Then x + y = 550   But x = 120% of y = 120y/100 = 12y/10   ∴ 12y/10 + y = 550   ⇒ y[(12/10) + 1] = 550   ⇒ 22y/10 = 550   ⇒ 22y = 5500   ⇒ y = 5500/22 = 500/2 = Rs.250   Answer : Option Rs. 250
Answer: C
In expressing a length of 61.472 km as nearly as possible with the three significant digits, find the percentage error ?  Choose the correct choice from the following.
A) 0.35% B) 0.4% C) 0.045% D) 0.6% E) None of these

Solution: Explanation :   Error = (61.5 - 61.472)= 
(61.5 - 61.472) = 0.028
0.028   Required percentage= 0.028/61.472100=0.045   Answer : 0.045%
Answer: C
The cost per unit of electricity during a 4 year period is as follows:
Year 1, $1 per unit;
Year 2, $1.5 per unit;
Year 3, $2 per unit;
Year 4, $2.5 per unit.
If a factory spent equal dollars on electricity each year, what was the average cost of a unit of electricity during the 4 year period?	Choose the correct choice from the following.
A) $1.66 B) $1.46 C) $1.36 D) $1.56 E) $1.26

Solution: Let money spent each year = $15   Units bought first year = 15   Units bought second year = 10   Units bought third year = 7.5   Units bought fourth year = 6   Total number of units = 38.5   Total money spent = 15*4= 
15*4 = 60
60   Average= 60/38.5 = 1.56   Answer : $1.56
Answer: D
By selling 10 pencils for a rupee a man loses 25%. How many for a rupee should he sell in order to gain 25%? Select the correct option:	A) 6	B) 9	C) 10	D) 89	E) 81

Solution: 75% --- 10   125% --- ?     75/125 * 10= 
  75/125 * 10 = 6
6   6nswer: 6
Answer: A
A does a work in 10 days and B does the same work in 15 days. In how many days they together will do the same work?  Select:	A) 2 days	B) 6 days	C) 5 days	D) 7 days	E) 1 days

Solution: 6 days   6 days   A's 1 day work = 1/10; 6 days's 1 day work = 1/15   (A + 6 days)'s 1 day work = (1/10 + 1/15) = 1/6   So, both together will finish the work in 6 days.
Answer: B
1,257
1,275
1,527
........
........
+7,521
The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,2,5 and 7 exactly once in each integer. What is the sum E of the 24 integers ?	Answers:
A) 26,996
B) 44,406
C) 60,444
D) 66,660
E) 99,990

Solution: This is the way i solved it :   Total no. of different combos = 24, total digits 4 therefore each digit must repeat  24/4= 
 24/4 = 6
6 times in each row .. So the right most row would add up to 1x6 + 2x6 + 5x6 + 7x6= 6+12+30+42= 
6+12+30+42 = 90
90 .. Each row would add up to 90, so 90 in the first means we have 9 that carries over and we get 0 , the second time its 90+9 and 9 stays and one 9 goes to the row to the left, so the last two digits of the SUM E should be 90 (E) .. We could go on and solve the exact number but since only one answer choice has the last digits as 90 we needn't go any further..
Answer: E
A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 3 more days. How many days would it have taken the second carpenter to do the complete job working alone?
Choose the correct choice from the following answers
A) 4 2/3 B) 7 C) 9 D) 14 E) 24

Solution: A carpenter worked only 1 day on something that takes him 6 MORE days.   Means;   Carpenter finishes his work in 7 days.   Let his buddy finish the same task in x days.   Respective rates per day:   1/7 AND 1/x   To complete 1 work:   First guy worked for 5 days @ rate=1/7 per day.   Second one worked for 3 days @ rate=1/x per day   Expression:   Days*Rate=Work   4*1/7+3*1/x=1   4x+21=7x   3x=21   x=7 days.   Ans:7
Answer: B
A can do a piece of work in 4 hours . A and C together can do it in just 2 hours, while B and C together need 3 hours to finish the same work. B alone can complete the work in --- hours.
Choose the most appropriate option.
A) 12 hours	B) 6 hours	C) 8 hours	D) 10 hours	E) 15 hours

Solution: Work done by 12 hours in 1 hour = 1/4   Work done by B and C in 1 hour = 1/3   Work done by 12 hours and C in 1 hour = 1/2   Work done by 12 hours,B and C in 1 hour = 1/4+1/3 = 7/12   Work done by B in 1 hour = 7/12 – 1/2 = 1/12 => B alone can complete the work in 12 hours   Option 12 hours
Answer: A