MU-NLPC/Calc-aqua_rat huggingface dataset:
A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 400 feet. What is its area, in square feet? Choose the most appropriate option.
A) 76,800
B) 19,600
C) 20,000
D) 20,400
E) 20,800

Solution: you can avoid a lot of work in this problem by recognizing that, with the info provided, the diagonal forms a triangle inside the rectangle with sides that have a 3:4:5 ratio.   diagonal = 200   2x + 2y = 560, or x + y = 280   a^2 + b^2 = c^2 for each the sides of the triangle   using the ratio 3:4:5 for sides, and knowing c = 400, you can deduce the following   a=240   b=320   240x320=76,800   76,800 is the answer.
Answer: A
A man cycles at a rate of 4 kmph. He cycles for 45 minutes and then takes a 15 minute break. Determine the total time taken to cover 12 kms by him.  Choose the most appropriate option:
A) 4 hours 35 minutes  B) 4 hours  C) 3 hours  D) 3 hours 45 minutes  E) 4 hours 45 minutes

Solution: Explanation:   Speed of man = 4kmph   Time for which he cycled = 45 minutes.   Distance covered = speed*time   => 4*45/60= 
4*45/60 = 3
> 3km   Total time to cover 3 km= 45 minutes + 15 minutes = 60 minutes = 1 hour   Thus 3 km is covered in 1 hour   Required distance to be covered = 12 km   Beginning from origin point, he covers 9 km in 3 hours taking 15 minutes rest after every 45 minutes. To complete 12 kms he goes another 3 km in 45 minutes.   Thus, total time he takes is 3 hours 45 minutes.   ANSWER 3 hours 45 minutes
Answer: D
An article is sold at certain price. By selling it at 2/3 of its price one losses 10%, find the gain at original price?  Choose the correct choice: A) 35 B) 25 C) 10 D) 20 E) 30

Solution: let the original Selling Price be $x. then now Selling Price = $2x/3, loss=10%   now C.P=$20x/27*27/20x*100)%=35%   35nswer 35) 35.
Answer: A
Eight machines, each working at the same constant rate, together can complete a certain job in 20 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 16 days?  Options:
A) 4  B) 6  C) 8  D) 10  E) 2

Solution: Rate of one machine = 1 job / (20*8) days   let X = number of machines needed to complete the job in 16 days   1/(8*20) * 16 * X = 1 job   X = 10   10-8= 
10-8 = 2
2   ANSW2R: 2
Answer: E
A local bank that has 11 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 11 codes?  Choose the correct option
A) 3
B) 11 ( 2 integers 4 codes)
C) 5
D) 6
E) 7

Solution: Pick any two integer.   Integers: 12   Code: 11, 12, 21, 22 = 4 Codes   Add one more integer: 3   13, 31, 33, 23, 32 = 5 Codes   Add one more integer: 4   44, 14, 41, 24, 42, 34, 43 = 7 Codes   Total = 16 Codes. Enough. Answer: 11 ( 2 integers 4 codes)   4 integers create 11 codes.
Answer: B
The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $400, by what percent is the price to be reduced?
Choose the correct option.
A) 10%  B) 15%  C) 20%  D) 25%  E) 80%

Solution: price of a coat in a certain store = $500   the price of the coat is to be reduced by $400   % change = (Final Value - Initial Value)*100 / Initial Value   % Reduction= (Reduction in Price)*100 / Initial Value   i.e. % Reduction= (400)*100 / 500= 
(400)*100 / 500 = 80
80%   Answer: Option 80%
Answer: E
On the first of the year, James invested x dollars at Proudstar bank in an account that yields 4% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year?	Choices:
A) 22.04%  B) 26.12%  C) 28%  D) 16.25%  E) 30%

Solution: Per quarter, interest = 4% So for a year, interest = 16% 16.25%ue to quarter cumulation, effective yield (YTM) would be slight higher than 16.25% Answer = 16.25% =ANSWER:16.25%
Answer: D
If the selling price of 50 articles is equal to the cost price of 40 articles, then the loss or gain percent is? Choose the correct choice from the following answers:	A) 20%	B) 80%	C) 90%	D) 22%	E) 24%

Solution: Let C.P. of each article be Re. 1.   Then, C.P. of 50 articles = Rs. 50;   S.P. of 50 articles = Rs. 40.   Loss % = 10/50 * 100= 
10/50 * 100 = 20
20%.20%nswer: 20%
Answer: A
The marks obtained by Vijay and Amith are in the ratio 8:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of?
Choose the most appropriate option
A) 12:5	B) 12:1	C) 6:5	D) 12:2	E) 6:3

Solution: 8:5   3:2   -------   24:15:10   24:10   12:5   12:5nswer: 12:5
Answer: A
Solution P is 20 percent lemonade and 80 percent carbonated water by volume; solution Q is 45 percent lemonade and 55 percent carbonated water by volume. If a mixture of PQ contains 60 percent carbonated water, what percent of the volume of the mixture is P?
Choose the correct choice from the following options.
A) 20%	B) 30%	C) 40%	D) 50%	E) 60%

Solution: 60% is 20%-points below 80% and 5%-points above 55%.   So the ratio of solution P to solution Q is 1:4.   Mixture P is 1/5 = 20% of the volume of mixture PQ.   The answer is 20%.
Answer: A
A cistern has three pipes, A, B and C. The pipes A and B can fill it in 4 and 5 hours respectively and C can empty it in 2 hours. If the pipes are opened in order at 1, 2 and 3 A.M. When will the cistern be empty?  Choose the correct choice from the following answers:  A) 2 PM  B) 1 PM  C) 7 PM  D) 5 PM  E) 8 PM

Solution: 1 to 2 = 1/4   2 to 3 = 1/4 + 1/5 = 9/20   After 3 AM = 1/4 + 1/5 - 1/2 = -1/20   1/4 + 9/20 = 14/20   1 h ---- 1/20   ? ----- 14/20   14 hours ==> 5 PM   Answer:5 PM
Answer: D
The average age of twenty four boys in a class and the teacher is 15. If the teacher age is excluded, the average reduces to 14. What is the techer's age?  Choose the correct choice from the following answers.
A) 41  B) 36  C) 32  D) 39  E) 38

Solution: 25*15-24*14= 
25*15-24*14 = 39
39   ANSWER:39
Answer: D
Three candidates contested in an election and received 4136, 7636, 11628 votes respectively. What is the percentage of the total votes did the winning candidate get?
Choose the most appropriate option
A) 45%	B) 49%	C) 50%	D) 51%	E) 62%

Solution: Total number of votes polled = 4136+7636+11628= 
4136+7636+11628 = 23_400
23400   Required percentage= 11628*100/23400 = 50%   Answer is 50%
Answer: C
A student has 7 trousers and 11 shirts. In how many different ways can the student select a trouser and a shirt? Choose the correct choice: A) 68 B) 77 C) 86 D) 95 E) 104

Solution: The student can select one trouser in 7 ways.   The student can select one shirt in 11 ways.   The number of ways to select one trouser and one shirt is  7 * 11= 
 7 * 11 = 77
77 ways   The answer is 77.
Answer: B
If it is a 3x3 matrix, for which elements in first row are (V, 50, W), second row (196,X, Y)and in third row are (269, Z, 123).It is given that the sum of the numbers in each row, column, diagonal are same. Then find the value of (Y + Z). Choose the correct choice from the following answers.
A) 1012	B) 1011	C) 1212	D) 1122	E) 1021

Solution: v 50 w   196 x y   269 z 123   in 1st row and 1st column   v+196+269=v+50+w   w=415   Again, in 2nd column and 3rd row   50+x+z=269+z+123   x=342   As sum of each row column and diagonal are same.   So, 269+342+415=1026   415+y+123=1026   y=488   269+z+123=1026   z=634   y+z=488+634= 
488+634 = 1_122
1122   ANSWER:1122
Answer: D
Ross has 320 shirts, 3/4 of the shirts are green and 1/10 is without buttons. Therefore Ross has between ___ and ___ shirts with buttons that are not green.
Choose the correct answer:  A) 48 ; 80.  B) 49 ; 80.  C) 50 ; 80.  D) 51 ; 80.  E) 52 ; 80.

Solution: Total shirts = 320   Green shirts = 3/4*320= 
3/4*320 = 240
240, Non green shirts= 80   Shirts without button = 1/10*320= 
1/10*320 = 32
32, shirts with button= 288   Required: Range of shirts with buttons that are not green.   Maximum non green shirts with buttons = number of non green shirts = 80   Minimum non green shirts with buttons (48 ; 80.ll without button shirts are non green) = Non green shirts - shirts without button = 80 - 32= 
80 - 32 = 48
48   Hence the range would be (48, 80)   Correct Option: 48 ; 80.
Answer: A
If ‘+’ means ‘×’, ‘-‘ means ‘+’, ‘×’ means ‘÷’ and ‘÷’ means ‘-‘ then find the value of;
6 – 9 + 8 × 3 ÷ 20 = Choose one:
A) 6	B) 10	C) 12	D) -2	E) 8

Solution: 10 10
Answer: B
Two pillars are standing side-by-side. One pillar, which is 6 feets tall, casts a shadow that is 12 feets long. The other pillar is 4 feets tall. Compute, in feets, the length of the shadow that
the shorter pillar casts.	Options
A) 8 B) 10 C) 12 D) 16 E) 20

Solution: The ratio of shadow to height is constant, so if x is the length of the shadow, then   6/12 = 4/x and x = 8 .   correct answer 8
Answer: A
The average of 13 numbers is 60. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?
Choose the most appropriate option
A) 43 B) 30 C) 35 D) 45 E) 50

Solution: Sum of all the 13 numbers = 13 * 60= 
13 * 60 = 780
780   Sum of the first 7 of them= 7 * 57= 
7 * 57 = 399
399   Sum of the last 7 of them= 7 * 61= 
7 * 61 = 427
427   So, the 8th number= 427 + 399 - 780= 
427 + 399 - 780 = 46
46.   43NSWER 43
Answer: A
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is? Choose the correct answer
A) 3/8  B) 3/4  C) 3/5  D) 3/9  E) 3/1

Solution: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.   Answer: 3/4
Answer: B
A family made a down payment of $20 and borrowed the balance on a set of encyclopedias that cost $500. The balance with interest was paid in 24 monthly payments of $25 each. The amount of interest paid was what percent of the amount borrowed?
Choose the correct choice from the following.
A) 16%	B) 25%	C) 24%	D) 26%	E) 20%

Solution: borrowings = 500-20= 
500-20 = 480
480   total pmt= 24x25 = 600   so int = 600 - 480= 
600 - 480 = 120
120   interest in terms of borrowing= 120/480 = 25%   Answer is 25%
Answer: B
20 throws of a die produces following results
SCORE -- NUMBER OF OCCURRENCES
---1-------------------4
---2-------------------3
---3-------------------5
---4-------------------2
---5-------------------2
---6-------------------4
What is the probability K that one more throw to this series will increase the mean score?  Pick: A) 1/6 B) 1/3 C) 1/2 D) 2/3 E) 5/6

Solution: I get the mean as 67/20 --> 3.35. Thus in order to raise this mean we would need a 4,5,or 6.   Thus probability K is 1/2.1/2
Answer: C
Define e* by the equation e* = π-e. Then ((−π)*)* = Options:
A) −2π  B) -1  C) −π  D) 2π  E) 4π

Solution: for e* f(f(−π)) = f(π − (−π)) = f(π + π) = f(2π) = π − 2π = −π=−π
Answer: C
A group of 13 people plan to rent a van and agree to share equally the total cost of the rental, which is E dollars. If n of the people decide not to participate at the last minute, by how many dollars will each remaining person's share of the total cost increase?  Choose the correct choice from the following answers.
A) E/(12 - n)	B) (12 - n)/E	C) E/[12(12-n)]	D) (12-n)E/(12n)	E) nE / [13(13-n)]

Solution: total cost =nE / [13(13-n)]   no of people willing to participate initially =13   initial cost for each =nE / [13(13-n)]/13   when n people decided not to participate   Cost for each =nE / [13(13-n)]/13-n   nE / [13(13-n)]
Answer: E
Which of the following fractions can be written as the difference of reciprocals of two consecutive integers	Choose the most appropriate option:
A) 1/24	B) 7/30	C) 1/42	D) 13/56	E) 1/73

Solution: Difference of reciprocals means 1 has to be in the numerator;   So option BD can be ignored   For option A, BE, we require to search two consecutive numbers whose product is the denominator   24 = 4 * 6 ......... Ignore   42 = 6* 7 ........ Answer   73 = 6 * 9 ................ Ignore   Answer = 1/42
Answer: C
A gardener grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 197 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year?  Choose the correct choice from the following answers.
A) 9801	B) 10,000	C) 14,400	D) 12,696	E) can not be determined

Solution: Let the side for growing cabbages this year be X ft. Thus the area is X^2.   Let the side for growing cabbages last year be Y ft. Thus, the area was Y^2.   The area would have increased by 197 sq ft as each cabbage takes 1 sq ft space.   X^2 - Y^2 = 197   (X + Y)(X - Y) = 197   197 is a prime number and thus it will be (99+98)*(99-98).   Thus X = 99 and Y = 98   X^2 = 99^2 = 9801   The answer is 9801.
Answer: A
A man has Rs. 440 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?  Answers
A) 45	B) 82.5	C) 75	D) 90	E) 105

Solution: Let number of notes of each denomination be x.   Then x + 5x + 10x = 440   16x = 440   x = 27.5.   Hence, total number of notes = 3x = 82.5.   Answer = 82.5
Answer: B
Seven people went to a restaurant for dinner. Six of them spent $9 each on their meals and the seventh person spent $12 more than the average expenditure of all seven people. What was the total amount of money that the seven people spent?
Choose the correct answer:	A) $71	B) $73	C) $75	D) $77	E) $79

Solution: Let T be the total amount of money spent.   6*9 + (T/7 + 12) = T   66 = 6T/7   T = (7*66)/6= 
(7*66)/6 = 77
77   The answer is $77.
Answer: D
A printer numbers the pages of a book starting with 1 and uses 3189 digits in all. How many pages does the book have ?  Choose the correct choice:
A) 1000
B) 1074
C) 1075
D) 1080
E) 1090

Solution: No.of digits in 1-digit page nos=1*9= 
1*9 = 9
9   " " 2-digit "=2*90= 
2*90 = 180
180   3-digit "=3*900= 
3*900 = 2_700
2700   " " 4-digit "=3189-(9+180+2700)= 
3189-(9+180+2700) = 300
300   therefore no.of 4-digit page no's=300/4= 
300/4 = 75
75   total no.of pages=999+75= 
999+75 = 1_074
1074   ANSWER:1074
Answer: B
If x = 1- 5t and y = 2t - 1, then for what value of t does x = y?
Choose the correct choice from the following answers.
A) 5/2  B) 3/2  C) 2/3  D) 2/7  E) 0

Solution: We are given x = 1 – 5t and y = 2t – 1, and we need to determine the value for t when x = y. We should notice that both x and y are already in terms of t. Thus, we can substitute 1 – 5t for x and 2t – 1 for y in the equation x = y. This gives us:   1 – 5t = 2t – 1   2 = 7t   2/7 = t   The answer is 2/7.
Answer: D
In the biology lab of "Jefferson" High School there are 4.32*10^6 germs, equally divided among 10,800 Petri dishes. How many germs live happily in a single dish?	Choose the correct answer.
A) 100  B) 200  C) 400  D) 1000  E) 5000

Solution: 4.32*10^6/ 10800==> 43.2*10^3/108==> 43200/108= 
43200/108 = 400
400   ANSWER:400
Answer: C
A train 300 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?	Choose the correct choice from the following answers:
A) 298 m
B) 268 m
C) 500 m
D) 267 m
E) 1000 m

Solution: Speed = 78 * 5/18 = 65/3 m/sec.   Time = 1 min = 60 sec.   Let the length of the train be x meters.   Then, (300 + x)/60 = 65/3   x = 1000 m.   Answer: 1000 m
Answer: E
A shop produces sarongs. The daily average production is given by 5n + 20, where n is the number of workers aside from the owner. In the first k days, 500 units are produced, and then 5 workers are added to the team. After another k days, the cumulative total is 1100. How many workers were part of the latter production run?	Choose the correct choice from the following choices:
A) 26  B) B)10  C) C)11  D) D)15  E) E)23.5

Solution: The daily average production is given by 5n + 20- given   In the first k days, 500 units are produced   = (5n+20)K =500   k = 500/5n+20...................................1   5 workers were added = 5(n+5)+20 = 5n +45   cumulative is 1100 .. thus for the current period = 1100 -500= 
1100 -500 = 600
600   (5n+45)K= 600   k = 600/5n+45........................................2   equate 1 and 2   500/5n+20 = 600 /5n+45   500(5n+45) = 600(5n+20)   2500n + 22500 = 3000n + 12000   -500n = -10500   n = 21   thus n+5 = 26   hence 26
Answer: A
A piece of ribbon 4 yards long is used to make bows requiring 15 inches of ribbon for each. What is the maximum number of bows that can be made?  Choose the correct choice from the following options:
A) 8  B) 9  C) 10  D) 11  E) 12

Solution: 1 Yard = 36 inches   Total length of ribbon = 4 yards = 4*36= 
4*36 = 144
144   Length of ribbon needed for 1 bow= 15 inches   Max number of bows that can be made = 144 / 15= 
144 / 15 = 48/5 = around 9.6
9.6   Answer 9
Answer: B
If BURNER is coded as CASOIS then how will ALIMENT be coded?  Choose the correct choice:	A) BKJLFMU	B) EKOLIMS	C) EMONIOU	D) BRJSFTU	E) EROSITU

Solution: You take the next consonant or vowel in alphabetical sequence.   Watch:   b - c (next consonant in sequence)   u - a (aeiou, u cycles back to beginning, or a)   r - s   n = o   e = i (next vowel)   r = s   therefore:   a = e (next vowel)   l = m   i = o   m = n   e = i   n = o   t = u   EMONIOU   ANSWER:EKOLIMS
Answer: B
The total of a company's assets in 1994 was 50% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of the company's assets in 1992 was N dollars, what were the company's assets in 1994?  Choices.
A) 5.5N  B) 7.5N  C) 9.5N  D) 11.5N  E) 13.5N

Solution: In 1992, the company's assets were N.   In 1993, the company's assets were N + 4N = 5N.   In 1994, the company's assets were 5N + 2.5N = 7.5N.   The answer is 7.5N.5  + 2.5= 
5  + 2.5 = 7.5
7.5N.   The answer is 7.5N.
Answer: B
If the set S is composed of the following numbers {99, 100, 100, 105, 106, 112, 127}, which of the following is largest?  Choose the correct choice from the following options:  A) The average (arithmetic mean) of set S  B) The median of set S  C) The mode of set S  D) The range of set S  E) The standard deviation of set S

Solution: A) 99, 100, 100, 105, 106, 112, 127 = 749 and its mean is   749/7= 
  749/7 = 107
107.   B) The list is of 7 numbers and median is 105.   C) Mode is number of repetition of a number in the list , here it is 100.   D) Range= Max value - min value = 127 -99= 
127 -99 = 28
28.   E) SD= square root of (sum of ( mean of series - number)^2 ) / n =>< 100   IMO option The average (arithmetic mean) of set S is correct answer..
Answer: A
What is the dividend. divisor 13, the quotient is 17 and the remainder is 1	Pick: A) 222 B) 224 C) 226 D) 228 E) 230

Solution: 222 = d * Q + R   222 = 13 * 17 + 1   222 = 221 + 1   222 = 222
Answer: A
if the price of a book is first decreased by 15% and then increased by 10%, then the net change in the price will be :  Answers:
A) 10 B) 388 C) 6.5 D) 29 E) 22

Solution: Explanation:   Let the original price be Rs. 100.   Decreased by 15% = 85   Then increased 10% on Rs 85 = 85 + 8.5= 
85 + 8.5 = 93.5
93.5   Net change in price= 100 - 93.5= 
100 - 93.5 = 6.5
6.5   Answer : 6.5
Answer: C
A truck covers a distance of 360 km at a certain speed in 8 hours. How much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 14 km more than that travelled by the truck ? Choices.
A) 6 hours
B) 5 hours
C) 7 hours
D) 8 hours
E) None

Solution: Explanation :   Speed of the truck = Distance/time = 360/8= 
360/8 = 45
45 kmph   Now, speed of car= (speed of truck + 18) kmph = (45 + 18)= 
(45 + 18) = 63
63 kmph   Distance travelled by car= 360 + 81= 
360 + 81 = 441
441 km   Time taken by car= Distance/Speed = 441/63 = 8 hours.   Answer – 8 hours
Answer: D
A car crosses a 600m long bridge in 5 mins. What is the speed of car in km per hr?	Choose the correct choice from the following answers
A) 7 km/hr	B) 7.2 km/hr	C) 7.5 km/hr	D) 8 km/hr	E) 8.5 km/hr

Solution: Speed = 600 m/sec.   5 x 60   = 2 m/sec.   Converting m/sec to km/hr (see important formulas section)   = 2 x 18 km/hr   5   = 7.2 km/hr   7.2 km/hr
Answer: B
A can contains a mixture of liquids A and B is the ratio 7:5. When 12 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 of liquid A was contained by the can initially? Choose one.
A) 25  B) 27  C) 29  D) 28  E) 31

Solution: Ci*Vi = Cf*Vf   (7/12)*(V1 - 12) = (7/16)*V1   (V1 - 12)/V1 = 3/4   12 accounts for the difference of 1 on ratio scale so Initial volume = V1 = 4*12= 
4*12 = 48
48 litres.   7/12 of the initial mixture was liquid A so liquid A was   (7/12)*48= 
  (7/12)*48 = 28
28 litres.   Answer : 28
Answer: D
10% of the inhabitants of village having died of cholera.,a panic set in , during which 25% of the remaining inhabitants left the village. The population is then reduced to 4050. Find the number of original inhabitants. Pick one.
A) 600 B) 6500 C) 6000 D) 6500 E) 7000

Solution: Let the total number of orginal inhabitants be x.   ((75/100))*(90/100)*x)=4050  (27/40)*x=4050   x=((4050*40)/27)= 
((4050*40)/27) = 6_000
6000.   ANSWER 6000 6000
Answer: C
John found that the average of 15 numbers is 40. If 12 is added to each number then the mean of number is?	Choose the correct choice from the following options
A) 52 B) 45 C) 65 D) 78 E) 64

Solution: (x+x1+...x14)/15 = 40   52   Option 52
Answer: A
Two numbers are respectively 20% and 60% more than a third number. The percentage that is first of the second is?
Choose the correct choice from the following options
A) 34% B) 68% C) 51% D) 75% E) 83%

Solution: I II III   120 160 100   160----------120   100-----------? => 75%   Answer:75%
Answer: D
If a train runs at 40 kmph ,it reach its destination late by 11 minutes but if it runs at 50kmph it is late by 5 minutes only . the correct time for a train to complete its journey is?
let the correct time to complete the journey be x min
distance covered in(x+11)min. at 40 kmph
distance covered in(x+5)min. at 50 kmph
(x+11)/60*40=(x+5)/60*50
x=19min
Choose the correct choice from the following answers.
A) 19 min
B) 19hrs
C) 52min
D) 126min
E) 52min

Solution: let the correct time to complete the journey be x min   distance covered in(x+11)min. at 40 kmph   distance covered in(x+5)min. at 50 kmph   (x+11)/60*40=(x+5)/60*50   x=19min   19 minnswer(19 min)
Answer: A
The traffic lights at 3 different roads change after every 14 sec, 72 sec, 108 sec respectively. If they all change simultaneously at 9:15 AM then at what time will they again change simultaneously.	Answers.
A) 9:22:12 B) 9:42:15 C) 10:15:24 D) 9:40:12 E) 10:01:20

Solution: LCM of 14,72,108 = 1512 = 25mnts 12sec   The lines will change every 25m 12sec   The light will change again after 9:15 AM is = 9:15+0:25:12 = 9:40:12   Answer is 9:40:12
Answer: D
How many positive 5-digit integers have the odd sum Q of their digits?
Choose the correct answer:  A) 9*10^2  B) 9*10^3  C) 10^4  D) 45*10^3  E) 9*10^4

Solution: We are looking at numbers between 10000 and 99999 both inclusive.   There are 90000 numbers.   Now for   10000 : sum of digits is odd;   10001 :sum of digits is even;   10002 : sum of digits is odd ; so on and so forth. So every alternate number is such that the sum of digit is odd.   (Exception for the above statement :   When it is 10009 the sum is even and for 10010 again the sum is even; But if you look at 10019 :sum is odd; 10020 : sum is odd   and this pattern continues so basically the number of odd sum of digits and even sum of digits are equal)   This means exactly half of the numbers will have odd sum Q of their digits. i.e 45000   Answer :45*10^3
Answer: D