MU-NLPC/Calc-aqua_rat huggingface dataset:
If a is a positive integer, then 2^a + 2^(a + 1)+ 2^(a + 2)+ 2^(a + 3)+ 2^(a + 4)+ 2^(a + 5)+ 2^(a + 6) =
Choose the correct choice:	A) 3^(a + 1)	B) 2^(a + 1)	C) 2a	D) 2a^(a + 1)	E) 127(2^a)

Solution: If a is a positive integer, then 2^a + 2^(a + 1)+ 2^(a + 2)+ 2^(a + 3)+ 2^(a + 4)+ 2^(a + 5)+ 2^(a + 6) =   2^a(1+2+4+8+16+32+64)   2^a(127)   E. 127(2^a)
Answer: E
According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 20 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?	Options:
A) 15
B) 34
C) 50
D) 67
E) 100

Solution: Orange juice concentrate: water::1:3   total quantity of orange juice = 200*6= 
200*6 = 1_200
1200 oz   so Orange juice concentrate: water :: 300 oz:900 oz   no. of 20 oz can= 300 oz/20 oz = 15   15nswer 15, 15 cans
Answer: A
40 is subtracted from 60% of a number, the result is 50. Find the number?
Choose the correct choice
A) 150 B) 992 C) 277 D) 287 E) 232

Solution: (60/100) * X – 40 = 50   6X = 900   X = 150   150nswer: 150
Answer: A
The average salaryper head of all the workers in a workshop is Rs.850, if the average salary/head of 7technician is Rs.1000 and the average salary/head of the rest is Rs.780, the totalno.of workers in the work-shop is ?
Pick one:
A) 18
B) 20
C) 22
D) 25
E) 26

Solution: Let the total number of workers be y.   So sum of salary for all workers = sum of salary of 7 technician + sum of salary for other y -7 workers.   7 x 1000 + 780(y -7) = 850 y   ⇒ 7000 + 780y - 5460 = 850y   ⇒ 70y = 1540   ∴ y = 22   So total number of workers = 22   22
Answer: C
It will take 18 days for Cameron to complete a certain task alone. He worked for 9 days before she was joined by Sandra. both of them completed the remaining task in 3 and half days. how many days will it take both of them to complete the entire job? Options
A) 6 B) 7 C) 5 D) 8 E) 9

Solution: Explanation:   Cameron and Sandra completed half work in 3.5 days   => they can complete whole work in 7 days   Answer: Option 7
Answer: B
Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 4 seconds. What is the length of the fast train? Choices:  A) 23 m  B) 22 (2/9)m  C) 27 (7/9)m  D) 29 m  E) 28 m

Solution: Relative speed = (40 - 20) km/hr =	(20 x(5/18))m/sec =	(50/9)m/sec.   Therefore Length of faster train =	((50/9)	x 4) m =	(200/9)m = 22	(2/9)	m.   22 (2/9)m
Answer: B
Two trains travelling in the same direction at 40 and 22 kmph completely pass off another in 1 minute. If the length of the first train is 125 m, what is the length of the second train?
Choose the correct choice
A) 329	B) 2698	C) 175	D) 212	E) 221

Solution: RS = 40 – 22 = 18 * 5/18= 
18 * 5/18 = 5
5 mps   T= 60 sec   D = 5 * 60= 
5 * 60 = 300
300 m   125   --------   175 m.Answer: 175
Answer: C
If a/b = 4/5, Then (5a - 3b) / (5a + 3b) = ?	Choose the most appropriate option.
A) 4  B) 2/3  C) 3  D) 1  E) 1/7

Solution: Answer   Dividing numerator as well as denominator by b, we get   Given Exp. = (5a - 3b) / (5a + 3b) = (5a/b - 3) / (5a/b + 3)   Since a/b = 4/5   this implies that   =[(5*4)/5 -3]/[(5*4)/5 +3)]   = (4- 3) / (4 + 3)   = 1/7   Option: 1/7
Answer: E
A man sells an article at a gain 15%. If he had bought it at 10% less and sold it for 4 less, he would have gained 25%. Find the cost price of the article.	Select the correct option
A) 150 B) 160 C) 170 D) 180 E) None of these

Solution: Let the C.P. be 100   First S.P. = 115   Second C.P. = 90   Second S.P = 125% of 90 = 112.50   Difference of two selling prices is 115 – 112.50 = 2.50 and C.P. of the article is 100   But actual difference is 4.   ∴ C.P. = 100⁄2.50 × 4 = 160.   Answer 160
Answer: B
What percent of 60 is 70?	Choose the correct answer:
A) 133 1⁄3
B) 75
C) 60
D) 33 1⁄3
E) 116.66

Solution: % of 60 is 70?   = 70/60 = 7/6 = 116.66%   Thus 116.66 is the correct answer.
Answer: E
The dividend is 126, the quotient is 3 and the remainder is 2.
What is the divisor?	Select the correct option
A) 30  B) 35  C) 40  D) 45  E) 50

Solution: D = d * Q + R   126 = d * 3 + 2   126/3 = d + 2   42 = d + 2   42-2= 
42-2 = 40
d   40= d   Answer: 40
Answer: C
What will come in place of the x in the following Number series? 11, 14, 19, 22, 27, 30, 35, 38, 43, x
Choose the correct option:
A) 29
B) 31
C) 23
D) 46
E) 59

Solution: (46)   The pattern is + 3, + 5, + 3, + 5, …………   So the missing term is = 43 + 3= 
43 + 3 = 46
46.
Answer: D
Stacy and Heather are 10 miles apart and walk towards each other along the same route. Stacy walks at constant rate that is 1 mile per hour fast than heather's constant rate of 5 miles/hour. If Heather starts her journey 24 minutes after Stacy, how far from the original destination has Heather walked when the two meet?.	Choose one:
A) 6.0 mile  B) 3.0 mile  C) 4.0 mile  D) 3.45 mile  E) 12 mile

Solution: Ss - Stacy's speed = 6m/hr   Sh - Heather's speed = 5m/hr   In 24 minutes Stacy will cover = (24/60)*6= 
(24/60)*6 = 12/5 = around 2.4
2.4miles   Now since both are walking in opposite directions, add their speeds - 6+5=11m/hr and distance to cover is  10 -2.4= 
 10 -2.4 = 7.6
7.6   Time taken= Distance/ Speed = 7.6/11 = 0.69 hrs   Heather will cover = 5*0.69= 
5*0.69 = 3.45
3.45 miles.   Answer 3.45 mile
Answer: D
In a km race, A beats Bby 28 metres or 7 seconds. Find A's timeoverthe course Choose the correct choice from the following choices
A) 4 min	B) 3 min. 3sec	C) 4 min.4 sec	D) 5 min. 3 sec	E) 4 min. 3 sec

Solution: Clearly, B covers 28 m in 7 seconds.   :. B's time over the course = (278 x 1000) sec = 250 seconds.   :. A's time over the course = (250 - 7-) sec = 243 sec   = 4 min. 3 sec.   Option 4 min. 3 sec
Answer: E
At a monthly meeting, 1/3 of the attendees were males and 4/5 of the male attendees arrived on time. If 5/6 of the female attendees arrived on time, what fraction of the attendees at the monthly meeting did not arrive on time?
Answers:
A) 1/6 B) 2/15 C) 3/20 D) 7/30 E) 8/45

Solution: Males who did not arrive on time are 1/5*1/3 = 1/15 of the attendees.   Females who did not arrive on time are 1/6*2/3 = 1/9 of the attendees.   The fraction of all attendees who did not arrive on time is 1/15 + 1/9 = 8/45   The answer is 8/45.
Answer: E
If Scott has earned 364 dollars by working 4 hrs/day a week at a constant daily rate for 1 weeks, which of the following represents his daily wage? Answers:
A) 15
B) 14
C) 13
D) 12
E) 11

Solution: Scott total earning = 364   No days he worked = 4 * 7= 
4 * 7 = 28
28   Rate= 1 week   Daily wage = total / (Rate * days)   = 364/(4*7*1)= 
364/(4*7*1) = 13
13   13 is correct answer...
Answer: C
Of the people who responded to a market survey, 360 preferred Brand X and the rest preferred Brand Y. If the respondents indicated a preference for Brand X over Brand Y by ratio of 9 to 1, how many people responded to the survey?  Choose the correct choice from the following options
A) 80 B) 160 C) 240 D) 360 E) 400

Solution: Ratio = 9:1 => 9x respondents preferred Brand X and x preferred Brand Y   Since, no. of respondents who preferred Brand X = 360 => 9x=360 => x=40   Hence Total no. of respondents = 360 + 40= 
360 + 40 = 400
400   Hence 400 is the answer.
Answer: E
In a group of 5 boys and 3 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?  Choose the correct choice from the following choices:
A) 60  B) 50  C) 80  D) 30  E) 120

Solution: Required number of ways = 5801*3803 + 5802*3802 + 5803*3801 + 5804   = 15+30+30+5= 
15+30+30+5 = 80
80   Answer is 80
Answer: C
By investing Rs. 1620 in 8% stock, Michael earns Rs. 135. The stock is then quoted at
Choose the most appropriate option.
A) 46	B) 96	C) 35	D) 87	E) 13

Solution: To earn Rs. 135, investment   = Rs. 1620.   To earn Rs. 8, investment   = Rs. 96.   Market value of Rs. 100 stock   = Rs. 96.   Answer: 96
Answer: B
A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?	Select the correct option:
A) 150	B) 277	C) 272	D) 278	E) 121

Solution: Length of the train be ‘X’   X + 150/15 = X + 250/20   4X + 600 = 3X + 750   X = 150m   150nswer: 150
Answer: A
The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?
Choose the correct option:  A) 289 cm  B) 800 cm  C) 829 cm  D) 288 cm  E) 289 cm

Solution: Area of the square = s * s   = 5(125 * 64)   => s = 25 * 8= 
25 * 8 = 200
200 cm   Perimeter of the square= 4 * 200= 
4 * 200 = 800
800 cm.   Answer: 800 cm
Answer: B
A car traveled the first quarter of a certain distance at thrice the speed it traveled the remaining distance. What proportion of the total time traveled, was the time taken to travel the first quarter of the distance? Choices:
A) 1/4 B) 1/5 C) 1/6 D) 1/7 E) 1/10

Solution: These problems can be solved through algebra or sly number picking. Being a big fan of solving problems with numbers, let's pick a total distance divisible by 4 (say 40) so we can break it up into quarters, and a speed that can easily be one-third, say 10. Each quarter is thus 10 kilometers (or miles or feet or angstroms for all it matters), and the runner's speed is 10 km/h for the first quarter and 3 1/3 km/h for the remaining quarters.   He'll take 1 hour to do the first quarter and then 3 hours for the second quarter,3 hours for the third and 3 hours for the fourth. On total he will take 10 hours to complete this race, of which 1 hour was spent on the first quarter. So 1/10. Answer 1/10.
Answer: E
In how many ways can 7 identical beads be stung into a ring?  Choose the correct choice from the following options
A) 7! B) 5! C) 6! D) 6!/2 E) 3!

Solution: since the arrangement is either clockwise or anticlockwise, we have 6!/2 ways. Ans:( 6!/2 )
Answer: D
On Teacher's Day, sweets were to be equally distributed among 190 children in a school. Actually, on the Teacher's day, 70 children were absent and therefore each child got 14 sweets extra. How many sweets did each child get on that day?  Choose the correct choice from the following:
A) 18  B) 22  C) 28  D) 32  E) 38

Solution: Total Children = 190.   Let each student gets x chocolates if all were present.   So, Total chocolates = 190x.   70 students were absent. So, no of extra chocolates distributed among 120 students,   = 14 *70= 
14 *70 = 980
980.   Now,   Total chocolates= 190x   120 * (x +14) = 190   120x + 1680 = 190x   70x = 1680   x = 24.   Total no of chocolates = 24 * 190= 
24 * 190 = 4_560
4560.   No of chocolates each student gets on that day= 4560/120= 
4560/120 = 38
38.   ANSW38R : OPTION 38
Answer: E
The probabilities of solving a question by 3students A, B & C are 1/2,1/3 &1/4, respectively. The probability that the problem will be solved is?  Select the correct option
A) 1/2	B) 3/4	C) 3/7	D) 4/5	E) 5/7

Solution: Sol. First, we find the probability of not solving the problem x PTO x = (1 — D x - D x - D   1 2 3 1 =iXiX71=4;   1 3 Required probability 3/4   3/4
Answer: B
In a department store prize box, 40% of the notes give the winner a dreamy vacation; the other notes are blank. What is the approximate probability that 3 out of 5 people that draw the notes one after the other, and immediately return their note into the box get a dreamy vacation?	Choose the correct choice from the following answers:
A) 0.12	B) 0.23	C) 0.35	D) 0.45	E) 0.65

Solution: The probability of winning is 40% = 40/100 = 2/5.   The probability of NOT winning is 60% = 3/5.   P(WWWNN)=5!3!2!∗(25)3∗(35)2=144625≈23P(WWWNN)=5!3!2!∗(25)3∗(35)2=144625≈23 (we multiply by 5!3!2!5!3!2!, because WWWNN scenario can occur in several ways: WWWNN, WWNWN, WNWWN, NWWWN, ... the # of such cases basically equals to the # of permutations of 5 letters WWWNN, which is 5!3!2!5!3!2!).   Answer: 0.23.
Answer: B
A is 7/2 times as fast as B. If A gives B a start of 80 m, how long should the race course be so that both of them reach at the same time?  Choose the correct choice from the following
A) 140 metre B) 180 metre C) 190 metre D) 240 metre E) 12 metre

Solution: Speed of 140 metre : Speed of B = 7⁄3 : 1 = 7 : 3   It means, in a race of 7 m, 140 metre gains  (7-3)= 
 (7-3) = 4
4 metre   If 140 metre needs to gain 80 metre, race should be of 7/4×80= 140 metre   140 metrenswer is 140 metre
Answer: A
If x represents the sum of the interior angles of a triangle and y represents the sum of the interior angles of a regular pentagon, then the addition x and y is equal to the sum of the interior angles of what geometric shape?	Choose one: A) Hexagon B) Square C) Rhombus D) Trapezoid E) Pentagon

Solution: Sum of angles of Triangle= 180*(3-2)= 
180*(3-2) = 180
180=> using formula sum of angles of polygon = 180*(n-2) where n is the number of sides in a polygon   Sum of angles in Pentagon = 180*(5-2)= 
180*(5-2) = 540
540   Difference= 180 +540= 
180 +540 = 720
720=> Hexagon   hence (Hexagon).
Answer: A
A dog is tied to a tree by a long nylon cord. If the dog runs from the due North side of the tree to the due South side of the tree with the cord extended to its full length at all items, and the dog ran approximately 30 feet, what was the approximate length of the nylon cord W, in feet?	Select the correct option.
A) 30  B) 25  C) 15  D) 10  E) 5

Solution: Because the cord was extended to its full length at all items, the dog ran along a semi-circular path, from north to south.   The circumference of a full circle is 2*pi*r, but since we only care about the length of half the circle, the semi-circle path is pi*r.   W=pi*r = 30. Round pi = 3, then r = 10.   Chord is about 10 feet long.10
Answer: D
There are two circles, one circle is inscribed and another circle is circumscribed over a square. What is the ratio of area of inner to outer circle?	Choose the correct answer
A) 1:2
B) 2:3
C) 2:1
D) 1:4
E) 1:3

Solution: For simplicity consider side of the square as 1. Now radius of inner circle =1/2. Formula for diagonal of the square = side*sqrt(2) = 1*sqrt(2). Half the diagonal = (1/2)*sqrt(2) = 1/sqrt(2). We got radiuses of both circles. So calculate areas and find ratio. Inner circle area= pi*(1/2)^2 and Outer circle = pi*(1/sqrt(2))^2. Divide both, you will get ratio as 1:2   1:2NSWER:1:2
Answer: A
In how many ways a hockey team of eleven can be elected from 16 players? Options
A) 4368  B) 4267  C) 5368  D) 4166  E) None

Solution: Solution   The required number of selections   = 3C1 × 4C1 × 2C1 (6C3 + 6C2 + 6C0) = 42 × 4!   4368nswer 4368
Answer: A
The average age of an adult class is 40 years. 2 new students with an avg age of 32 years join the class. Therefore decreasing the average by 4 year. Find what was the original strength of class?
Answers:
A) 10	B) 12	C) 16	D) 2	E) 22

Solution: Let original strength = y   Then , 40y + 2 x 32 = ( y + 2) x 36   â‡’ 40y + 64 = 36y + 72   â‡’ 4y = 8   âˆ´ y = 2   2
Answer: D
A cyclist rides a bicycle over a route which is 1/3 uphill, 1/3 level, and 1/3 downhill. If the cyclist covers the uphill part of the route at the rate of 8 km per hour and the level part at the rate of 12 km per hour, what rate in km per hour would the cyclist have to travel the downhill part of the route in order to average 12 km per hour for the entire route? Choose the correct choice:
A) 16
B) 20
C) 24
D) 28
E) 32

Solution: Let V be the speed on the downhill section.   Let D be the distance of each of the three equal sections.   Total time T = T1+T2+T3 and 3D/T = 12 km/hour   3D / (D/8 + D/12 + D/V) = 12   1/4 = 1/8 + 1/12 + 1/V   1/V = 1/24 and so V = 24 km/h   The answer is 24.
Answer: C
The 30 members of a club decided to play a badminton singles tournament. Every time a member loses a game he is out of the tournament. There are no ties. What is the minimum number of matches that must be played to determine the winner ? Choose the correct option:	A) 15	B) 29	C) 61	D) 72	E) None of these

Solution: Explanation:   Clearly, every member except one (i.e. the winner) must lose one game to decide the winner. Thus, minimum number of matches to be played = 30 - 1= 
30 - 1 = 29
29.   Answer: 29
Answer: B
If $120 invested at a certain rate of simple interest amounts to $180 at the end of 3 years,How much will $150 amount to at the same rate of interest in 6 years? Choose one:
A) $190
B) $180
C) $200
D) $240
E) $300

Solution: 120 amounts to 180 in 3 years.   i.e (principal + interest ) on 120 in 3 years = 180   120 + 120*(r/100)*(3) = 140 => r = 50/3   150 in 6 years = principal + interest   =300   Answer is $300.
Answer: E
A man purchased 15 pens, 12 books, 10 pencils and 5 erasers. The cost of each pen is Rs.36, each book is Rs.45, each pencil is Rs.8, and the cost of each eraser is Rs.40 less than the combined costs of pen and pencil. Find the total amount spent?
Choose the most appropriate option
A) Rs.1100
B) Rs.1120
C) Rs.1140
D) Rs.1160
E) None of these

Solution: Cost of each eraser = (36 + 8 -40) = Rs.4   Required amount = 15 * 36 + 12 * 45 + 10 * 8 + 5 * 4   540 + 540 + 80 + 20 = Rs.1180   ANSWNone of theseR:None of these
Answer: E
If M is the mean of x,y,z ; then what is the mean of x,z and y  Select the correct option
A) M B) 3M C) 10M D) M+10 E) M-10

Solution: order only changed   So new mean is M.   Mnswer (M)
Answer: A
A boy incurs 5% loss by selling a book for Rs. 1000. At what price should the book be sold to earn 5 % profit? Choose the correct choice
A) 1105.26 B) 1105.29 C) 1105.22 D) 11105.21 E) 1103.26

Solution: Explanation:   Let the new selling price be Rs. x   (100 – loss %) /1000 = (100 + gain %) / x   (100 – 5) / 1000 = (100 + 5) / x   x = (105 × 1000) / 95 = 105000 / 95   x = 1105.26.\   1105.26NSWER: 1105.26
Answer: A
Uncle Bruce is baking chocolate chip cookies. He has 36 ounces of dough (with no chocolate) and 14 ounces of chocolate. How many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20% chocolate?	Choose the correct choice.
A) 3
B) 6
C) 7.2
D) 5
E) 9

Solution: Answer is D.   x/x+36=1/5   x=9   14-9= 
14-9 = 5
5
Answer: D
Robert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15 kmph. At what speed musthe travel to reach A at 1 PM?
Pick one
A) 40 km
B) 45 km
C) 60 km
D) 65 km
E) 70 km

Solution: Let the distance travelled by x km.   Then, x - x = 2   10 15   3x - 2x = 60   x = 60 km.   Time taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs.   10   So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.   Required speed = 60 kmph. = 12 kmph.   5   60 km
Answer: C
If $30,000 interest is invested in x percent simple annual interest for 10 years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years?  Choose the correct answer:
A) 5000 x  B) 7000 x  C) 6000 x  D) 3000 x  E) 8000 x

Solution: 30000*x/100*10 = 3000 x   Answer : 3000 x
Answer: D
A driver took a trip consisting of three segments at three different speeds. The driver drove a distance of (3D) at a speed of (2V), then a distance of (4D) at a speed of (3V), then a distance of D at a speed of (6V). In terms of D and V, what was the total time of the trip?  Pick one: A) 3D/V B) 4D/V C) 5D/V D) 6D/V E) 7D/V

Solution: The total time of the trip was:   3D/2V + 4D/3V + D/6V =   18D/12V + 16D/12V + 2D/12V =   36D/12V = 3D/V   The answer is 3D/V.36 /12= 
36 /12 = 3
3D/V   The answer is 3D/V.
Answer: A
Qames can eat 25 marshmallows is 20 minutes. Dylan can eat 25 in one hour. In how much time will the two eat 150 marshmallows?  Select the correct option.
A) 40 minutes.
B) 1 hour and 30 minutes.
C) 1 hour.
D) 1 hour and 40 minutes.
E) 2 hours and 15 minutes.

Solution: Rate =Output/Time   Qames Rate=25/20=5/4   Dylan Rate=25/60=5/12   1 hour.ombined rate = 5/4+5/12= 20/12   1 hour.ombinedRate*1 hour.ombinedTime= 1 hour.ombinedOutput   20/12*t=150   t=90 mins => 1 hr 30 min
Answer: C
A person incurs loss for by selling a watch for Rs1140.at what price should the watch be sold to earn a 5% profit ?	Pick one:
A) 1205 B) 1260 C) 1300 D) 1340 E) 1450

Solution: let the new sp be Rsx.then   (100-loss%) : (1st sp)=(100+gain%) (2nd sp)   {(100-5)/1400}={(100+5)/x}=> x={(105*1140)/95= 
(105*1140)/95 = 1_260
1260.   ANSWER 1260
Answer: B
In a garden, there are 10 rows and 17 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is
Answers:
A) 20 m
B) 22 m
C) 34 m
D) 26 m
E) 28 m

Solution: Explanation:   Each row contains 17 plants.   There are 15 gapes between the two corner trees (16 x 2) metres and 1 metre on each side is left.   Therefore Length = (32 + 2)= 
(32 + 2) = 34
34 m.   Answer: 34 m
Answer: C
A car traveling with 5/75/7 of its actual speed covers 4242 km in 11 hr 4040 min 4848 sec. What is the actual speed of the car? Choose the correct choice from the following: A) 30 km/hr B) 35 km/hr C) 25 km/hr D) 40 km/hr E) 45 km/hr

Solution: Explanation:   time =1=1 hr 4040 min 4848 sec   =1=1 hr +4060+4060 hr +483600+483600 hr   =1+23+175=12675hr=1+23+175=12675hr   distance =42=42 km   speed=distancetime=42(12675)speed=distancetime=42(12675) =42Ã—75126=25 km/hr=42Ã—75126=25 km/hr   â‡’57â‡’57 of the actual speed =25=25   â‡’â‡’ Actual speed =25Ã—75=35 km/hr   Answer is 35 km/hr
Answer: B
The average of 45 results is 10. The average of first 22 of them is 16 and that of last 22 is 20. Find the 23 result?  Choose the correct answer.
A) 600
B) 480
C) 538
D) 650
E) 560

Solution: 23th result = sum of 45results - sum of 44 results   10*45-16*22+20*22 = 450-352+440= 
450-352+440 = 538
538   Answer is 538
Answer: C
In a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class?	Choose one:
A) 12.5 Yrs  B) 14.2 Yrs  C) 12.3 Yrs  D) 12.6 Yrs  E) 12 Yrs

Solution: Total age of 50 students   (30X 13+20 X 12) = 630   Average = 630/50= 
630/50 = 63/5 = around 12.6
12.6 Years   ANSWER IS 12.6 Yrs
Answer: D
A car started running at a speed of 30 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 11 hours of the journey.	Choose the most appropriate option
A) 342 km
B) 352 km
C) 642 km
D) 440 km
E) 382 km

Solution: The total distance covered by the car in the first 11 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 +48 + 50 = sum of 11 terms in AP whose first term is 30 and last term is 50 = 11/2 [30 + 50] = 440 km.   ANSWER:440 km
Answer: D
F and E are midpoints of AB and AD respectively. If the side of square ABCD is 8, what is the area of triangle CEF?
Choose the correct answer:
A) 8√2	B) 9√3	C) 18	D) 16√2	E) 24

Solution: Area of Shaded figure = Area of Square - (Area of Triangle AEF + Area of Triangle FBC + Area of Triangle EDC )   = 8*8 - (1/2 * 4 * 4 + 1/2 * 4 * 8 + 1/2 * 4 * 8 )= 
8*8 - (1/2 * 4 * 4 + 1/2 * 4 * 8 + 1/2 * 4 * 8 ) = 24
24.   Answer 24.
Answer: E
The cash difference between the selling prices of an article at a profit of 4% and 8% is Rs 3. The ratio of two selling prices is  Pick one:	A) 51:52	B) 52:54	C) 53:54	D) 54:55	E) None of these

Solution: Explanation:   Let the Cost price of article is Rs. x   Required ratio = (104% of x) / (108% of x)   =104/108   =52/54 = 52:54.   Answer: 52:54
Answer: B
A walks around a circular field at the rate of one round per hour while B runs around it at the rate of eleven rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other after___ minutes?  Pick one.
A) 6 min B) 12 min C) 10 min D) 15 min E) 16 min

Solution: Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two.   Relative speed of A and B = 11 - 1= 
11 - 1 = 10
10 rounds per hour.   Time taken to complete one round at this speed= 1/10 hr = 6 min.   6 min
Answer: A