MU-NLPC/Calc-aqua_rat huggingface dataset:
A certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 3 buckles is how many times that of 5 buckles and 6 buttons?	Choose the correct choice from the following choices.
A) 7/15.
B) 4/9.
C) 6/11.
D) 5/9.
E) 8/15.

Solution: 2buttons + 2buckles = 1/3(11buckles + 3buttons)   6buttons + 6buckles = 11buckles + 3buttons   3buttons = 5buckles   Weight of 3buttons and 3buckles = 5buckles + 3buckles = 8buckles   Weight of 6buttons and 5buckles = 10buckles + 5buckles = 15buckles   (3buttons and 2buckles) = x * (6buttons and 5buckles)   8 = x*15   x = 8/15   Answer: 8/15.
Answer: E
Express a speed of 180 kmph in meters per second? Choose the correct choice.
A) 10 mps B) 05 mps C) 50 mps D) 12 mps E) 11 mps

Solution: 50 mps   50 mps    180 * 5/18= 
 180 * 5/18 = 50
50 mps
Answer: C
Hammers and wrenches are manufactured at a uniform weight per hammer and a uniform weight per wrench. If the total weight of 3 hammers and 4 wrenches is one-third that of 10 hammers and 5 wrenches, then the total weight of one wrench is how many times that of one hammer? Choose the correct choice from the following options:	A) 1/2	B) 2/3	C) 1	D) 3/2	E) 1/7

Solution: x be the weight of a hammer and y be the weight of a wrench.   (3x+4y)=1/3*(10x+5y)   3(3x+4y)=(10x+5y)   9x+12y=10x+5y   7y=x   y=x/7   Ans - 1/7
Answer: E
In a bowl, the no. of marbles gets doubled after every minute. if the bowl gets filled after two hours of such process, how long do you think it will take for it to be half filled?
Choose the correct answer.
A) 1 hr 48 mins	B) 1 hr 39 mins	C) 1 hr 49 mins	D) 1hr 59 mis	E) 1 hr 58 mins

Solution: Correct Answer : D   If you go backward , if the no. of marbles gets doubled after every minute and after two hours. it is filled completely. one minute ago it would be half.
Answer: D
In a games hour 4 different types of players came to the ground? cricket 18, hockey 15, football 21, softball 15. In these 4 people play both cricket and hockey, 3people play both softball and football. 5 people play both cricket and football. How many people play only cricket?	Choose the most appropriate option:
A) 11 B) 9 C) 5 D) 3 E) 9

Solution: people play only cricket = total players in cricket- both cricket and football- both cricket and hockey.   people play only cricket = 18-4-5= 
18-4-5 = 9
9   Answer is 9
Answer: B
The average weight of A,B,C is 45 Kg. The avg wgt of A & B be 40Kg & that of B,C be 43Kg. Find the wgt of B.
Options
A) 36kg B) 84kg C) 31kg D) 45kg E) 12kg

Solution: Sol. Let A,B,c represent their individual wgts.   Then,   A+B+C=(45*3)= 
(45*3) = 135
135Kg   A+B=(40*2)= 
(40*2) = 80
80Kg & B+C=(43*2)= 
(43*2) = 86
86Kg   B=(A+B)+(B+C)-(A+B+C)   =(80+86-135)= 
(80+86-135) = 31
31Kg.   Ans: 84kg
Answer: B
Each of the positive integers a, b, and c is a three-digit integer. If each of the digits 0 through 8 appears in one of these three integers, what is the maximum possible value of the sum of a, b, and c?  Choose the correct choice from the following answers.
A) 2233  B) 2774  C) 2223  D) 2345  E) 2135

Solution: According to the stem we should use the digits 0 through 7 to construct 3 three-digit integers, so that their sum is as large as possible.   To maximize the sum, maximize the hundreds digits of a, b, and c, so make them 8, 7, and 6.   Next, minimize tens digits. Make them 5, 4, and 3.   Use the remaining digits (2, 1, and 0) for units digits.   So, a would be 852, b would be 741 and c would be 630.   741 + 852 + 630= 
741 + 852 + 630 = 2_223
2223.   Answer: 2223.
Answer: C
In a certain city , there are two football teams , 65 percent of the people prefer team (A) and the rest prefer team (B),
Team (A) is going to play against team (C) from another city. If 80 percent of people who prefer team (A) are going to attend the match , and 20 percent of the people who prefer team (B) are going to attend the match , what percent of city's people are going to attend the match ?  Choices:	A) 45%	B) 59%	C) 60%	D) 61%	E) 68%

Solution: say the population of the city is 100 person , so there are 65 persons prefer team (A) and 35 persons prefer team(B) .   65*0.8= 
65*0.8 = 52
52 person who prefer team (A) are going to attend the match   35*0.2= 
35*0.2 = 7
7 person who prefer team (B) are going to attend the match   Thus total of   52+7= 
  52+7 = 59
59 persons are going to attend the match , which is 59 percent of population.   answer: 59%
Answer: B
Two trains, one from P to Q and the other from Q to P, start simultaneously. After they meet, the trains reach their destinations after 25 hours and 16 hours respectively. The ratio of their speeds is
Select.
A) 4:1  B) 4:2  C) 4:5  D) 4:3  E) 4:6

Solution: Ratio of their speeds = Speed of first train : Speed of second train   = √16−−√25   = 4:5   Answer is 4:5
Answer: C
In an election between two candidates first candidate got 60% of votes polled and second Candidate got 250 votes. The total number of votes polled was?  Pick.
A) votes	B) votes	C) votes	D) votes	E) votes

Solution: Total = 100 %,   First person got 60%   second person got remaining 40 % of votes.   than 40 % = 250   40% = 40×7 = 250   100% =100×7 =700 votes   votes)
Answer: A
In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 3.5), (8, 0), (0, -3.5), (-8, 0)?
Options.
A) 56	B) 88	C) 112	D) 116	E) 120

Solution: 56rea of rhombus= 1/2* D1 *D2   Length of 1st diagonal = 8+8= 
8+8 = 16
16   Length of 2nd diagonal= 3.5+3.5= 
3.5+3.5 = 7
7   56rea= 1/2*16*7= 
1/2*16*7 = 56
56   56 is the answer
Answer: A
The value of Underrot 130pi/4 + Underrot 1 is most nearly equal to which of the following integers? (Please refer to the picture below for the exact version of the question) Choose one:
A) 108
B) 114
C) 125
D) 120
E) 103

Solution: Under root (130pi/4) ~ 102   Under root (1) = 1   Hence, 102+1 = 103 is the approx answer. 103 is the correct answer.
Answer: E
A train crosses a platform of 100 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
Choose one: A) 150 B) 88 C) 77 D) 62 E) 350

Solution: Length of the train be â€˜Xâ€™   X + 100/15 = X + 250/20   4X + 400 = 3X + 750   X = 350m   Answer: 350
Answer: E
What is the 20th digit to the right of the decimal point in the decimal expansion of 1/37?
Options.
A) 0  B) 2  C) 4  D) 7  E) 9

Solution: 1/37=0.027027... So, we have a repeating cycle of 027. Every third digit (2nd, 4th, 6th, ...) to the right of the decimal point is alternating by 2, 0, 7 thus 20th digit is 2.   Answer: 2.
Answer: B
In a six-sided polygon XQRSTV ∠X measures 48° less than the average (arithmetic mean) of the remaining five angles. What does ∠X equal to, in degrees?  Select the correct option.
A) 72
B) 80
C) 88
D) 96
E) 104

Solution: The sum of interior angle in a polygon is (n-2)*180   so for a six sided figure, (6-2)*180 = 720   let the A.M of the other 5 angles be 'm'   --> m*5 + ∠X = 720, we know ∠X=m-48   --> m*5 + m - 48 = 720, solving we get m=128   hence ∠X= 128-48= 
128-48 = 80
80   Ans 80.
Answer: B
X starts a business with Rs.45000. Y joins in the business after 3 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?  Choose the correct answer.
A) 1:2  B) 2:1  C) 1:3  D) 3:1  E) 1:1

Solution: Explanation:   Ratio in which they should share the profit   = Ratio of the investments multiplied by the time period   =45000×12:30000×9   =45×12:30×9   =3×12:2×9   =2:1   Answer: Option 2:1
Answer: B
In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole?  Choose the correct choice from the following answers
A) 34 sec	B) 11 sec	C) 12 sec	D) 10 sec	E) 15 sec

Solution: Convert kmph to mps. 36 kmph = 36 * 5/18= 
36 * 5/18 = 10
10 mps.   The distance to be covered is equal to the length of the train.   Required time t= d/s = 100/10= 
100/10 = 10
10 sec.   Answer:10 sec
Answer: D
150 men consume 1050 kg of rice in 30 days. In how many days will 70 men consume 980 kg of rice? Choose the correct choice.
A) 16	B) 60	C) 66	D) 52	E) 51

Solution: Rate of consumption of each man = 1050/(150 * 30) = 7/30 kg/day   Let us say 70 men take x days to consume 150 kg.   Quantity consumed by each item in x days = 7x/30 kg.   Quantity consumed by 70 men in x days = (7x/30)(70)kg   (7x/30)(70) = 980   x = (980 * 30)/490 => x = 60 days   Answer:60
Answer: B
A group of hikers is planning a trip that will take them up a mountain using one route and back down using another route. They plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up, but the time each route will take is the same. If they will go up the mountain at a rate of 4 miles per day and it will take them two days, how many miles long is the route down the mountain?	Choose the correct choice from the following answers:
A) 4  B) 6  C) 8  D) 12  E) 16

Solution: D = S*T   Given condition is for UP the mountain hikers takes 4 miles per day and total 2 days... miles = 8 miles...   For DOWN speed they take = 3/2(4) = 6 miles per day and for the same 2 days... miles = 12 miles..   Answer: option 12 is correct answer
Answer: D
The ratio of three numbers is 3:4:7 and their product is 18144. The numbers are Choose one:
A) 9,12,21 B) 15,20,25 C) 18,24,42 D) 24,15,17 E) 30,12,7

Solution: Let the numbers be 3x, 4x and 7x   3x x 4x x 7x=18144   X3=216   X=6   The numbers are 18,24,42   ANSWER 18,24,42 18,24,42
Answer: C
If the radius of a circle is increased by 30% then the area is increased by: Choose the correct choice from the following answers.
A) 44%	B) 69%	C) 144%	D) 40%	E) None of the above

Solution: initially A=pi*r2   now R2=130/100r   then area=Pi*(130R/100)2   area=169R/100   that is area increases from 100 to 169=increase in area=69%   ANSWER:69%
Answer: B
Angelina walked 1200 meters from her home to the grocery at a constant speed. She then walked 480 meters to the gym at double the speed. She spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym?
Pick one:
A) 12  B) 23  C) 34  D) 48  E) 52

Solution: let the speed be X...   so time taken from home to grocery= 1200/x..   the speed to gym = 2x..   so time taken = 480/2= 
480/2 = 240
240/x..   its given 1200/x-240/x=40..   960/x=40..   x=24m/secs..   so grocery to gym=2*24= 
2*24 = 48
48m/s...   48
Answer: D
A set of pictures of butterflies contains 10 pictures. Jim bought 3 of the pictures. If 2 pictures are to be picked out from the 10 pictures, what is the probability that both pictures are not those that were already bought by Jim?	Select the correct option.
A) 14/15
B) 3/5
C) 6/13
D) 7/15
E) 7/10

Solution: Probability of first pick not one of the Jim's picture is = 7/10 (except for 3 which Jim purchased)   Probability of second pick not one of the Jim's picture is = 6/9   Total = 7/10∗6/9=7/15   Answer is 7/15   Option 7/15
Answer: D
What least number must be added to 1096, so that the sum is completely divisible by 23 ?
Pick:	A) 2	B) 1	C) 3	D) 5	E) 8

Solution: 1096/23 = 47.6--   that is   23 * 47= 
  23 * 47 = 1_081
1081   Now,   1096- 1081= 
1096- 1081 = 15
15   To get completely divided by 23 add 8 to 1096   Ans -8
Answer: E
The sum of the present ages of two persons A and B is 45. If the age of A is twice that of B, find the sum of their ages 5 years hence?	Choose the correct choice from the following:	A) 55	B) 60	C) 70	D) 80	E) 90

Solution: A + B = 45, A = 2B   2B + B = 45 => B = 15 then A = 30.   5 years, their ages will be 35 and 20.   Sum of their ages = 35 + 20= 
35 + 20 = 55
55.   55NSWER:55
Answer: A
How many 4-letter words with or without meaning, can be formed out of the letters of the word, ‘LOGARITHMS’, if repetition of letters is not allowed? Choose the correct choice from the following choices:
A) 40 B) 400 C) 5040 D) 2520 E) None of these

Solution: Solution   'LOGARITHM' contain 10 different letters.   Required number of words = Number of Arrangement of 10 letters, taking 4 at a time   = 10 P 4 = (10 × 9 × 7) = 5040 . Answer 5040
Answer: C
The average monthly income of A and B is Rs. 4050. The average monthly income of B and C is Rs. 5250 and the average monthly income of A and C is Rs. 4200. What is the monthly income of A?
Choose the correct choice:
A) 2000	B) 2500	C) 3000	D) 3500	E) 4000

Solution: Let monthly income of A = x   monthly income of B = y   monthly income of C = z   x + y = 2 × 4050 .... (Equation 1)   y + z = 2 × 5250 .... (Equation 2)   z + x = 2 × 4200 .... (Equation 3)   (Equation 1) + (Equation 3) - (Equation 2)   => x +y + x + z - (y + z) = (2 × 4050) + (2 × 4200) - (2 × 5250)   => 2x = 2(4050 + 4200 - 5250)   => x = 3000   i.e., Monthly income of A = 3000   ANSWER:3000
Answer: C
Which of the following is a divisible by 3 number ? Pick
A) 10000 B) 20000 C) 30000 D) 40000 E) 50000

Solution: Explanation :   C is divisible by 3 with out integers.   Answer : Option 30000
Answer: C
If 11 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes? Answers:
A) 10•9•8•7•6•5•4•3•2•1
B) 10•10
C) 55
D) 45
E) 36

Solution: We got #11 people who shake each other's hands once ==> a pair of 2   11!/9!2! = 11*10 / 2*1= 
11*10 / 2*1 = 55
55.   Hence answer 55.
Answer: C
A zinc-copper alloy with 5 kg of pure zinc would contain 90% of zinc. The alloy with 3 kg of 90% zinc alloy contains 84% of zinc. Calculate the weight and percentage of zinc in the zinc-copper alloy.	Choose the correct choice.
A) 2.4 kg or 80%  B) 1.4 kg or 88%  C) 4.3 kg or 60%  D) 7.4 kg or 18%  E) 1.4 kg or 60%

Solution: Right Answer Explanation:   x : 5   y : 100   90   10 : 90 – y   (90-y)/5 = 10/x = ………..(1)   In the second case,   x 3   y 90   84   6 84-y   Therefore (84-y)/3 = 6/x ………..(2)   Dividing (1) and (2)   =   810 – 9y = 2100 – 25y   16y = 1290   y = 80.625   x = 50/(90-80.625) = 50/9.375 = 5.33 kg   Quantity of zinc in x = 80.625% of x   = 0.80625 5.33   = 4.3 kg   Weight and percentage of zinc is 4.3 kg or 80.625%   4.3 kg or 60%
Answer: C
If the charge of staying in a student youth hostel $18.00/day for the first week, and $12.00/day for each additional week, How much does it cost to stay for 23 days? Choose the correct choice.
A) $318 B) $289 C) $282 D) $274 E) $286

Solution: Total number of days of stay = 23   Charge of staying in first week = 18*7= 
18*7 = 126
126 $   Charge of staying for additional days=(23-7)*12 = 16*12= 
16*12 = 192
192 $   Total charge=126 +192= 
126 +192 = 318
318$   $318nswer $318
Answer: A
If one root of the equation 2x^2 + 3x – k = 0 is 7, what is the value of k?	Choose the correct choice from the following options
A) 100  B) 110  C) 119  D) 120  E) 112

Solution: We just enter this root into the equation in order to recieve an equation to find the answer!   2*7^2+3*7-k=0   k=98+21= 
98+21 = 119
119   The answer is 119
Answer: C
Two trains running in opposite directions cross a pole placed on the platform in 47 seconds and 31 seconds respectively. If they cross each other in 33 seconds, what is the ratio of their speeds?
Choose the correct choice from the following options:	A) 1:7	B) 8:7	C) 6:7	D) 6: 5	E) 4:7

Solution: Explanation:   Let the speed of the trains be x and y respectively   length of train1 = 47x   length of train2 = 31y   Relative speed= x + y   Time taken to cross each other = 33 s   => = 33   => (47x + 31 y) = 33(x + y)   => 14x = 2y   => x/y = 2/14 = 1/7   = 1:7   1:7nswer: 1:7
Answer: A
If an object travels 400 feet in 4 seconds, what is the object's approximate speed in miles per hour? (Note: 1 mile = 5280 feet) Answers:  A) 68  B) 54  C) 87  D) 96  E) 15

Solution: 1 mile = 5280 feet   => 1 feet = 1/5280 miles   If the object travels 400 feet in 4 sec   then it travels 400/4 * 60 * 60 feet in 1 hour (1 hr = 60 min * 60 sec)   = 3600 * 100 feet in 1 hour   = 360000 feet in 1 hr   = 360000/5280 miles in 1 hour   = 36000/528 miles/hr ~ 68 miles/hr   68nswer - 68
Answer: A
How many meters of carpet 50cm, wide will be required to cover the floor of a room 30m * 20m?
Choose the correct choice from the following
A) 3387	B) 2888	C) 2788	D) 1200	E) 2881

Solution: 50/100 * x = 30 * 20 => x   = 1200   Answer: 1200
Answer: D
In an organisation there are 1000 employees out of which 250 earn below 10k$ and 500 earn between 10k$ and 50k$. What is the total percentage of employees who earn less than 50k$?	Pick one.
A) 66%  B) 75%  C) 70%  D) 50%  E) 82%

Solution: total percentage = (250+500)/1000= 
(250+500)/1000 = 3/4 = around 0.75
0.75   75%
Answer: B
What smallest number should be added to 4456 so that the sum is completely divisible by 6 ?
Choose the correct choice from the following choices:
A) 9
B) 5
C) 2
D) 7
E) 1

Solution: Explanation:   6)4456(742   42   --------   25   24   -------   16   12   -----   4   ------   Required number = (6-4)= 
(6-4) = 2
2.   Answer: 2) 2
Answer: C
The length of a rectangular floor is more than its breadth by 200%. If Rs.529 is required to paint the floor at the rate of Rs.3/sq m, what would be the length of the floor? Options
A) 12
B) 18
C) 20
D) 22
E) 23

Solution: Let the length and the breadth of the floor be l m and b m respectively.   l = b + 200% of b = l + 2b = 3b   Area of the floor = 529/3 = 176.33 sq m   l b = 176.33 i.e., l * l/3 = 176.33   l^2 = 529 => l =23   23
Answer: E
A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 500 m long?	Choose the correct choice from the following choices
A) 266 Sec  B) 170 Sec  C) 776 Sec  D) 166 Sec  E) 997 Sec

Solution: L = S*T   S= 1200/120= 
1200/120 = 10
10 m/Sec.   Total length (D)= 1700 m   T = D/S   T = 1700/10= 
1700/10 = 170
170 Sec   Answer: 170 Sec
Answer: B
The Italian size of a suit jacket is N centimeters, where N is the linear distance between the armpits when the jacket is laid on a flat surface. The American size of a suit jacket is P inches, where P is twice the linear distance between the armpits when the jacket is laid on a flat surface. If, for a particular jacket, N = P + 16, which of the following is closest to the value of N? (One inch is approximately 2.54 centimeters.)  Choose the correct choice from the following
A) 36  B) 47  C) 58  D) 65  E) 72

Solution: Since one inch is approximately 2.54 centimeters, then N centimeters is N/2.54 inches.   Next, since the American size (P inches) is twice the Italian size (N/2.54 inches), then P=2*N/2.54.   As given that N = P + 16, then N=2*N/2.54+16 --> N=~72.   Answer: 72.
Answer: E
Find the average of first 100 natural numbers?  Choose the correct option:
A) 50.5
B) 52
C) 60.5
D) 75
E) 65

Solution: Sum of first 100 natural numbers = 100*101/2= 
100*101/2 = 5_050
5050   Required average= 5050/100= 
5050/100 = 101/2 = around 50.5
50.5   50.5nswer is 50.5
Answer: A
If r and s are positive integers and r-s=6, which of the following has the greatest value T?
Choices:
A) 2r B) 2s C) r +s D) 2r-s E) 2s-r

Solution: The simplest way to do this is to assume values.   We are told that r and s are positive integers T.   Also, r-s = 6 => r = 6+s   Hence r is 6 more than s.   Let s be 10. Hence r = 16.   Option 2r: 2r = 2*16= 
2*16 = 32
32   Option B: 2s= 2 * 10= 
2 * 10 = 20
20   Option C: r + s= 16 + 10= 
16 + 10 = 26
26   Option D: 2r - s= 2(16) - 10 = 32 - 10= 
32 - 10 = 22
22   Option E: 2s - r= 2(10) - 16 = 20 - 16= 
20 - 16 = 4
4   Hence option 2r is the greatest.
Answer: A
Of the 16 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 16 temporary employees are women, how many of the possible groups of 4 employees consist of 3 women and one man?  Choose one
A) 22  B) 35  C) 56  D) 110  E) 105

Solution: another approach :   one scenario : [WWWM]   now we have 5 ways for the first women , 4 ways for the 2nd women and , 3 ways for the third women.   and 11 ways to select one man   so   5*4*3*11= 
  5*4*3*11 = 660
660   now the three women are same so combinations with win them are irrelevant the 3 women can we arranged in 3! ways   hence 660/3!= 660/6= 
660/6 = 110
110   110
Answer: D
Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?  Choose the correct answer:
A) 288 B) 277 C) 209 D) 992 E) 612

Solution: (800*3*3)/100= 
(800*3*3)/100 = 72
72   920 + 72= 
920 + 72 = 992
992   Answer: 992
Answer: D
A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 10% less than the price each head sold for the day before.what was the gross profit C on this shipment?
Choose the correct choice from the following choices.
A) a) $100 B) b) $115 C) c) $125 D) d) $130 E) e) $135

Solution: I recommend one should use fractions to solve this one rather than converting it into decimals   Sol:   1500 heads -> $600   1 head -> $600/1500   1 head -> $(2/5)   25% more of (2/5) -> 125/100 * 2/5 = $(1/2)   He sold   2/3*1500= 
  2/3*1500 = 1_000
1000 heads for $(1/2) per head   Total revenue by selling 1000 heads= 1000 * 1/2= 
1000 * 1/2 = 500
$500   Heads left: 500   c) $125ost per head: 90% of the previous price: 90/100 * 1/2= $(9/20)   Total revenue by selling 500 heads = 9/20 * 500= 
9/20 * 500 = 225
225   Total revenue after selling 1500 cabbage heads - 225+500= $725   Money spent on the purchase: $600   Profit c) $125= 725-600= 
725-600 = 125
$125   Ans:c) $125
Answer: C
At a certain high school, a student’s popularity is determined by his or her locker number. Whoever has the locker number with the greatest number of distinct prime factors is the most popular student in the school. If Raja,Kamal, Baskar, and Divya get lockers with the numbers 350, 400, 150, and 420, respectively, who is the most popular student?	Choose the correct choice from the following options:
A) Divya
B) Kamal
C) Baskar
D) Raja
E) They have equal popularity

Solution: Distinct prime factors of 350 (Raja) : 2,5,7   Distinct prime factors of 400 (Kamal): 2 and 5.   Distinct prime factors of 150 (Baskar): 2,3, and 5   Distinct prime factors of 420 (Divya): 2,3,5 and 7.   So most popular student - Divya   Divyanswer Divya
Answer: A
The no. of gift pack bought by Dexter is 1 more than the price, in rupees, of each gift pack. The amount of Rs.380 which Dexter had, fell shorof the required amount. What is the amount by which he might have fallen short? Choose one
A) 40	B) 45	C) 54	D) 65	E) 70

Solution: Let the price of gift pack be 'aa'   Then number of packs bought =a+1=a+1   Hence total cost is a(a+1)a(a+1)   It is given that 380<a(a+1)380<a(a+1)   If a=19a=19, the total cost =19×20=380=19×20=380   Dexter would not have fallen short, If:   a=20a=20, a(a+1)=420a(a+1)=420   So he would have fallen short by Rs 40.   This is the minimum amount by which he may have fallen short.   40
Answer: A
A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet? Choose the correct choice from the following options:
A) 10.60 p.m
B) 10.20 p.m
C) 10.30 p.m
D) 10.10 p.m
E) 10.50 p.m

Solution: D = 70 * 1 ½ = 105 km   RS = 85 – 70 = 15   T = 105/15= 
105/15 = 7
7 h     3.30 + 7= 
  3.30 + 7 = 10.3
10.30 p.m.   Answer: 10.30 p.m
Answer: C
A bus leaves Santa Barbara at 6:00 a.m. traveling east at 50 miles per hour. At 2:00 p.m. a plane leaves Santa Barbara traveling east at 450 miles per hour. At what time will the plane overtake the bus? Pick:
A) 2:45 p.m.	B) 3:15 p.m.	C) 3:30 p.m.	D) 3:45 p.m.	E) 3:00 p.m.

Solution: At 2:00pm, the bus is 400 miles ahead of plane   The plane travels at 450 mph, which gains 400 mph on bus     400/400= 
  400/400 = 1
1 hour   2:00 + 1:00= 3:00   The plane will overtake bus at 3:00pm   Answer:3:00 p.m.
Answer: E