MU-NLPC/Calc-aqua_rat huggingface dataset:
The number of boys in a class is (7/2) times the number of girls. Which one of the following numbers cannot represent the total number of children in the class ?  Choose the correct choice from the following answers:  A) A)48  B) B)54  C) C)42  D) D)40  E) E)38

Solution: Explanation:   Let number of girls = x and number of boys = 3.5x.   Then, 3.5x + x = 4.5x = total number of students.   Thus, to find exact value of x, the total number of students must be divisible by 4.5   Answer: 54
Answer: B
What is the rate percent when the simple interest on Rs.1500 amount to Rs.250 in 5 Years? Choose the correct choice from the following answers:
A) 3.33%	B) 6%	C) 2%	D) 95%	E) 1%

Solution: Interest for 5yrs = 250   Interest for 1yr = 50   Interest rate = 50/1500 x 100 = 3.33%   3.33%nswer : 3.33%
Answer: A
If 40% of a number is 16, then the number is  Choose the correct answer:	A) number is 60	B) number is 70	C) number is 90	D) number is 40	E) None of these

Solution: Solution:   Let "a" be the number we seek. We get   40% × a = 16   2 × 40% × a = 2 × 16 = 32   80% × a = 32   10% × a = 32 : 8 = 4   100% × a = 4 × 10 = 40   a = 40   Answer number is 40
Answer: D
In how many ways can the letters of the word CAVES be arranged in a row so that the vowels appear in alphabetic order?
Choices:
A) 60
B) 30
C) 120
D) 240
E) 180

Solution: Two letters can be arranged in 2! ways.   only one combination EIU is required.   5 letters can be arranged in 5! ways.   thus 5!/ 2! * 1 = 60.   60
Answer: A
According to the directions on a packet of smoothie mix, 1 3-ounce packet of smoothie mix is to be combined with 15 ounces of water to make a smoothie. How many 3-ounce packets of smoothie mix are required to prepare 150 12-ounce smoothies?  Choose the correct option:
A) 120
B) 150
C) 180
D) 240
E) 600

Solution: This question wasn't particularly grueling, but I think it's the first where I had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the GMAT. It actually came to me by accident. Basically, if we thought that the 3 packets of powder were included in the 12 ounces of water, that would mean we would need 150 packets of smoothie mix (along with 12(150) ounces of water for a total of 150 packets. However, we know, after a more careful reading of the stimulus, that the 3 ounces are NOT included in the 12 ounces. As such, the answer has to be LESS than 150 packets, since 150 would be too much powder considering you already have 150(12) ounces of water and need less packets than water to make a smoothie. As such, the only answer less than 150 is 120, A. Does this make sense? Or am I way off base?   180
Answer: C
A palindrome is a number that reads the same forward and backward, such as 616. How many even, 4-digit numbers are palindromes?	Choose the correct choice from the following answers:
A) 40
B) 45
C) 50
D) 90
E) 2500

Solution: First recognize you only need to consider the first two digits (because the second two are just the first two flipped)   There are 90 possibilities for the first two digits of a 4 digit number, 10-99 inclusive. Everything starting with a 2,4,6,8 will be odd, which is 4/9ths of the combinations.   4/9*90= 
4/9*90 = 40
40   40NSWER:40
Answer: A
David was born 8 years after his father's marriage. His mother is 4 years younger than his father but 30 years older than David who is 8 years old. At what age did the father get married ? Select: A) 24 years B) 26 years C) 23 years D) 20 years E) 18 years

Solution: Explanation:   David's present age = 8 years.   His mother's present age = (30 + 8)= 
(30 + 8) = 38
38 years.   His father's present age= (38 + 4)= 
(38 + 4) = 42
42 years.   His father's age at the time of David's birth= (42 - 8)= 
(42 - 8) = 34
34 years.   Therefore David's father's age at the time of marriage= (34 - 8)= 
(34 - 8) = 26
26 years.   Answer: 26 years
Answer: B
I sold a book at a profit of 10%. Had I sold it for $150 more, 15% would have been gained. Find the cost price?
Choose the correct choice from the following.
A) $2000 B) $2500 C) $3000 D) $3120 E) $1540

Solution: 115% of cost - 110% of cost = $150   5% of cost = $150   cost = 150*100/5= 
150*100/5 = 3_000
$3000   Answer is $3000
Answer: C
A marble shop contains 6 blue marbles, 6 red marbles, and 6 green marbles. If 4 marbles are purchased at random from the shop, what is the probability that the 4 marbles will be the same color?  Choose the correct choice from the following:
A) 1/68  B) 60/68  C) 13/68  D) 13/48  E) 1/48

Solution: It doesn't matter which type of card you choose, so:   Probability of choosing 1st card: 1   Probability of choosing 2nd card of the same type: 5/17   Probability of choosing 3rd card of the same type: 4/16   Probability of choosing 4th marble of the same type: 3/15   Multiply and you get 1/68   1/68nswer 1/68.
Answer: A
Faiza has 8 purses, she gives 3 purse as gift. Now how many purse she have in that?	Choose the correct choice from the following answers:
A) 2
B) 5
C) 11
D) 9
E) 4

Solution: 8-3= 
8-3 = 5
5. Answer is 5
Answer: B
In a certain diving competition, 5 judges score each dive on a scale from 1 to 10. The point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty. If a dive with a degree of difficulty of 3.2 received scores of 7.5, 7.8, 9.0, 6.0, and 8.5, what was the point value of the dive?	Choose the correct answer:
A) 68.8
B) 73.6
C) 75.2
D) 76.16
E) 81.6

Solution: 76.16egree of difficulty of dive = 3.2   Scores are 6.0 , 7.5 , 8.0 , 8.5 and 9.0   We can drop 6.0 and 9.0   Sum of the remaining scores = (7.5+7.8+8.5)= 
(7.5+7.8+8.5) = 23.8
23.8   Point of value of the dive= 23.8*3.2= 
23.8*3.2 = 76.16
76.16   Answer 76.16
Answer: D
A team of eight entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score? Choose the most appropriate option.
A) 23/35  B) 23/32  C) 23/329  D) 23/29  E) 23/291

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.   Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green   = (⁶C₁ * ⁹C₁)/¹⁵C₂ + ⁶C₂/¹⁵C₂   = (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7   = 46/70 = 23/35   23/35nswer: 23/35
Answer: A
In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr? Options
A) 2.5 sec B) 1.3 sec C) 7.6 sec D) 10 sec E) 3.6 sec

Solution: 2.5 secnswer: Option 2.5 sec   Speed = 144 * 5/18= 
144 * 5/18 = 40
40 m/sec   Time taken= 100/40= 
100/40 = 5/2 = around 2.5
2.5 sec.
Answer: A
Convert 250 inches into centimeter?
Select
A) 635cm
B) 620cm
C) 650cm
D) 610cm
E) 654cm

Solution: 1 inch = 2.54cm   250 inches = 250*2.54= 
250*2.54 = 635
635cm   635cmnswer is 635cm
Answer: A
Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $9 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 25 percent, what is the discount rate on Pony jeans?  Choose the correct answer
A) 9%
B) 10%
C) 11%
D) 12%
E) 25%

Solution: x discount on Pony jeans, (0.25-x) discount on Fox jeans.   Set the equation: 3*15(0.25-x)+2*18x=9 --> x=0.25=25%   Answer: 25%.
Answer: E
If 12 people contributed a total of $20.00 toward a gift and each of them contributed at least $1.00, then the maximum possible amount any one person could have contributed is
Choose one
A) $1.00
B) $1.25
C) $5.00
D) $9.00
E) $20.00

Solution: $9.00 for me   11 people with 1$ each -> maximum = 9
Answer: D
The ratio of sodium chloride to ammonium in 100 kg of mixed ammonium normally used by three chemists is 7: 25. The amount of sodium chloride to be added to 100 kg of mixed ammonium to make the ratio 9 :25 is Answers
A) 5 kg  B) 6.625 kg  C) 6.25 kg  D) 6.35 kg  E) 6.55 kg

Solution: sodium chloride in 100 kg = 7/32 x 100 = 21.875 kg   ammonium in 100 kg = 25/32 x 100 = 78.125 kg   Now 78.125 is 25 parts out of   (25 + 9)= 
  (25 + 9) = 34
34 parts.   Hence 9 parts= 9/25 x 78.125 = 28.125   Amount to be added = 28.125 - 21.87 5= 6.25 Kg   ANSWER:6.25 kg
Answer: C
A merchant gets a 5% discount on each meter of fabric he buys after the first 2,000 meters and a 7% discount on every meter after the next 1,500 meters. The price, before discount, of one meter of fabric is $2, what is the total amount of money the merchant spends on 4,500 meters of fabric?
Answers:
A) $8,617	B) $8,710	C) $8,810	D) $8,835	E) $8,915

Solution: for first 2000 metres he does not get any discount   amount = 2*2000= 
2*2000 = 4_000
$4000   for next 1500 metres he gets 5% discount   amount= 2*1500 - (1/20)*3000= 
2*1500 - (1/20)*3000 = 2_850
$2850   for the nest 1000 metres he gets 7% discount   amount= 2*1000 - 7*20= 
2*1000 - 7*20 = 1_860
$1860   total amount= $4000 + $2850 + $1860 = $8710   ANSWER:$8,7104000 +  2850 +  1860= 
4000 +  2850 +  1860 = 8_710
$8710   ANSWER:$8,710
Answer: B
A cycle is bought for Rs.900 and sold for Rs.990, find the gain percent?  Pick one
A) 39% B) 20% C) 23% D) 74% E) 10%

Solution: 900 ---- 90   100 ---- ? =>   10%   Answer:10%
Answer: E
There are equal numbers of male and female horses in a ranch.The number of brown horses is 30% more than the number of female brown horses.What percentage of female horses are brown if the total number of male horse is ten times more than the number of brown male horses.	Pick one: A) 30 B) 33.3 C) 55.1 D) 32.1 E) 20

Solution: Since we are dealing in percentage let us pick 100 as the number of brown female horses.   That means that the total number of brown horses is= 130 (30% more),   therefore the number of brown male horses is 30.   The total number of male horses is 10x the number of brown male= 30*10= 
30*10 = 300
300 male horses.   female horses are 50% of the horses, and because there are 300 male horses, then there must also be 300 female horses.   Therefore percentage of female horses that are brown= 100/300*100=33.3   Correct option is 33.3
Answer: B
Which one of the following is a composite number?
Pick:
A) 31  B) 61  C) 85  D) 73  E) 2

Solution: 85 is divisible by 5,17. So, it is a composite number.   85
Answer: C
Suppose that f(x) is a function such that for every real number x,i)f(x)+f(1-x) = 12 and (ii) f(1+x) = 3+f(x). Then f(x)+f(-x)
must equal  Choices:
A) 8  B) 9  C) 10  D) 11  E) 12

Solution: Since (ii) holds for every real number x, it will remain valid if we replace x with   -x. Therefore, f(1-x) = 3+f(-x). Now, from (i), 12 = f(x)+f(1-x) = f(x)+3+f(-x)   so that f(x) + f(-x) = 12-3= 
12-3 = 9
9. (Observe that f(x)= 3x + 4 satisfies the conditions   in the problem.)   correct answer 9
Answer: B
A and B can do a work in 15days, B and C in 30days, C and A in 45days. If A,B and C work together , they will complete the work in?
Choices.
A) 10days  B) 16days  C) 20days  D) 25days  E) 22days

Solution: A+16days 1day work = 1/15   16days+C 1day work = 1/30   C+A 1day work  +  1= 
 +  1 = 1
1/30   C+A 1day work = 1/45   Adding we get 2(A+16days+C)  +  1= 
 +  1 = 1
1/45   Adding we get 2(A+16days+C)= 1/15 + 1/30 + 1/45 = 11/90   A+16days+C 1 day work = 11/180   A,16days,C can finish the work in 180/11 days = 16days approximately   Answer is 16days
Answer: B
In 1996, the property tax of a community is increased by 6% over the 1995 tax.
An additional surcharge of $200 is also added for a special project.
If the Petersons' 1996 tax totals $2108, find their property tax for the year 1995 Select:	A) 1600	B) 1800	C) 1900	D) 2000	E) 2500

Solution: Tax for the year 1996= 2108   Surcharge add : 200   ie 2000-200= 
2000-200 = 1_800
1800   1800*6%=108+2000= 
108+2000 = 2_108
2108   so the answer is 1800
Answer: B
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is? Choose the correct choice from the following answers:
A) 13 km/hr B) 50 km/hr C) 17 km/hr D) 18 km/hr E) 12 km/hr

Solution: Speed of the train relative to man = (125/10) m/sec   = (25/2) m/sec. [(25/2) * (18/5)] km/hr   = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed   = (x - 5) km/hr. x - 5 = 45 ==> x   = 50 km/hr.   Answer:50 km/hr
Answer: B
If the cost price of 40 articles is equal to the selling price of 25 articles, what is the % profit or loss made by the merchant? Pick one:
A) 25% loss
B) 25% profit
C) 20% loss
D) 60% profit
E) 75% profit

Solution: Let the cost price of 1 article be $1.   Therefore, cost price of 40 articles = 40 * 1= 
40 * 1 = 40
$40   The selling price of 25 articles= cost price of 40 articles = $40.   Now, we know the selling price of 25 articles. Let us find the cost price of 25 articles.   Cost price of 25 articles = 25 * 1= 
25 * 1 = 25
$25.   Therefore, profit made on sale of 25 articles= Selling price of 25 articles - cost price of 25 articles   = 40 - 25= 
40 - 25 = 15
$15.   As the profit is in the positive, the merchant has made a profit of $15.   Therefore, % loss= loss/cp * 100   % loss = 15/25 * 100= 
15/25 * 100 = 60
60%profit.   60% profit
Answer: D
27 is a perfect cube. When x is added to the prime factor of 27, the result is a prime number. What is x?	Choices:
A) 1
B) 3
C) 5
D) 8
E) 11

Solution: 27 is 3*3*3   then   A 3+1= 
3+1 = 4
4   B   3+3= 
  3+3 = 6
6   C   3+5= 
  3+5 = 8
8   8 3+8= 11   E   3+11= 
  3+11 = 14
14   here 8 is the only addition that gives a prime number.
Answer: D
If 12 men do a work in 80 days, in how many days will 20 men do it?
Choose the correct choice from the following options.
A) 18 days
B) 38 days
C) 42 days
D) 48 days
E) 44 days

Solution: 12 * 80 = 20 * x   x = 48 days   ANSWER:48 days
Answer: D
A life insurance company insured 25,000 young boys, 14,000 young girls and 16,000 young adults. The probability of death within 10 years of a young boy, young girl and a young adult are 0.02, 0.03 and 0.15 respectively. One insured person dies. What is the probability that the dead person is a young boy? Options.
A) 36/165  B) 25/166  C) 26/165  D) 32/165  E) 33/165

Solution: The number of young boys that will die = 0.02 x 25,000 = 500   The number of young girls that will die = 0.03 x 14,000 = 420   The number of young adults that will die = 0.15 x 16,000 = 2400   The required probability = The number of young boys who will die / The total number of people who will die.   = 500 / (500 + 420 + 2400) = 25/166   ANSWER:25/166
Answer: B
Integer x is equal to the product of all even numbers from 2 to 60, inclusive. If y is the smallest prime number that is also a factor of x-1, then which of the following expressions must be true?  Choose the most appropriate option
A) 0<y<4 B) 4<y<10 C) 10<y<20 D) 20<y<30 E) y>30

Solution: x = the product of all even numbers from 2 to n, where n is any even integer value from 2 to 60 including.   If x = 2, x - 1 = 2! -1   If x = 2x4, x - 1 = 2! (2^2) - 1   If x = 2x4x6, x - 1 = 3! (2^3) - 1   If x = 2x4x6x8, x - 1 = 4! (2^4) - 1   .   .   .   .   If x = 2x4x6x.......x60, x - 1 = 30! (2^30) - 1   Lets find y, a smallest prime factor of (x-1):   If y were 2, [(30!) (2^30) -(1)] would be divisible by 2 however thats not the case.   If y were 3, [(30!) (2^30) -(1)] would be divisible by 3 however thats not the case.   If y were 5, [(30!) (2^30) -(1)] would be divisible by 5 however thats not the case.   .   .   .   .   .   If y were 29, [(30!) (2^30) -(1)] would be divisible by 29 however thats not the case.   If none of the primes under 31 is a factor of (x-1), (x-1) must have a prime factore above 30.   ANSWy>30R:y>30
Answer: E
If a function f is defined by f(x)= -1/x for all non zero numbers x. If f(a) = -1/2 and f(ab) = 1/8 then b= ?  Choose the correct choice from the following options
A) -1/4
B) 1/4
C) 4
D) -4
E) 12

Solution: f(a) = -1/2 = -1/a, and thus a = 2   f(ab) = 1/8, and thus ab = -8   2b = -8   b = -4   The answer is -4.
Answer: D
The equal amounts of money are deposited in two banks each at 15% per annum for 3.5 years and 5 years respectively. If the difference between their interests is Rs.144, find the each sum?
Choose the correct option:	A) Rs.648	B) Rs.640	C) Rs.629	D) Rs.620	E) Rs.622

Solution: (P*5*15)/100 - (P*3.5*15)/100 = 144   75P/100 – 52.5P/100 = 144   22.5P = 144 * 100   => P = Rs.640   Answer: Rs.640
Answer: B
What is the place value of 9 in the numeral 2934?	Select the correct option: A) 600 B) 900 C) 700 D) 760 E) 768

Solution: Option '900'    9 * 100= 
 9 * 100 = 900
900
Answer: B
A certain football team played seven games and scored an average of 5 goals per game. If, in the team’s first five games, it scored 5, 4, 2, 5, and 4 goals, what was the average (arithmetic mean) number of goals scored over the last two games?  Options.
A) 5	B) 1	C) 2	D) 7.5	E) Cannot be determined from the information given.

Solution: Avg goals for total of 7 games = 5   So A+B+C+7.5+E+F+G/7=5   and A+B+C+7.5+E+F+G = 35   Given A+B+C+7.5+E = 20   So F+G = 15   So average (arithmetic mean) number of goals scored over the last two games is 15/2= 
15/2 = 15/2 = around 7.5
7.5   Correct answer is 7.5) 7.5
Answer: D
The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent? Pick:
A) 18 9/11% B) 18 2/11% C) 18 2/81% D) 19 2/11% E) 38 2/11%

Solution: 13 CP = 11 SP   11 --- 2 CP   100 --- ? =>18 2/11%   Answer: 18 2/11%
Answer: B
The weight of four dogs is determined to be 25 pounds, 31 pounds, 32 pounds and 28 pounds respectively. The weight of a fifth dog is determined to be y pounds. If the average (arithmetic mean) weight of the first four dogs is the same as that of all five dogs what is the value of y?	Pick: A) 31 B) 29 C) 35 D) 37 E) 39

Solution: Total weight of the 4 dogs = (25+31+32+28) = 132   Avg = 116/4= 
116/4 = 29
29   Total weight of 5 dogs= 116+y or 4(29)+y   Average of 5 dogs as per Question = 29   Equation:   4(29) + y = 5 (29), or y = 29.   Choose 29
Answer: B
List I: 3, 6, 14, 19
List II: x, 3, 14, 8, 19
Select the correct option
A) 6	B) 7	C) 8	D) 9	E) 10

Solution: We start by calculating the median of the numbers of list I: 3, 6, 14, 19. We see that the numbers in the list are in order already and, since we have an even number of numbers, the median is the average of the two middle numbers.   median = (6 + 14)/2   median = 20/2= 
20/2 = 10
10   The median of list I is 7.   Looking at list II: x, 3, 6, 14, 19, we see that we have an odd number of terms. Thus, when the list is ordered from least to greatest the median must be the middle term. Since the medians of the two lists must be equal, we know that the median of list II must be 10 and therefore x is 10.   The answer is 10.
Answer: E
If by selling an article for Rs.60, a person loses 1/7 of money, what would he have gained or lost % by selling it for Rs.77?  Choose the correct option.
A) 5%  B) 10%  C) 13%  D) 14%  E) 20%

Solution: Sol. CP - = EC7 = 70 1-7 6 77-70 % Profit = 100 = 10%   10%
Answer: B
In a certain math department, students are required to enroll in either Calculus or Trigonometry, each of which is offered in beginner and advanced courses. The number of students enrolled in Trigonometry is 50% greater than the number of students enrolled in Calculus, and 70% of Calculus students are enrolled in the beginner course. If 4/5 of students are in the beginner courses, and one student is selected at random, what is the probability that an advanced Trigonometry student is selected?
Select the correct option
A) 8%  B) 16%  C) 20%  D) 24%  E) 40%

Solution: Let x be the number of students in calculus.   Then the number of students in trigonometry is 1.5x   The number of students on beginner calculus is 0.7x   The number of students in beginner trigonometry is 4/5*(2.5x) - 0.7x = 1.3x   The number of students in advanced trigonometry is 0.2x   The percentage in advanced trigonometry is 0.2x / 2.5x  4/5*(2.5 ) - 0.7= 
 4/5*(2.5 ) - 0.7 = 1.3
1.3x   The number of students in advanced trigonometry is 0.2x   The percentage in advanced trigonometry is 0.2x / 2.5x= 8%   The answer is 8%.
Answer: A
The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost? Choose one:
A) Rs.1014 B) Rs.1140 C) Rs.999 D) Rs.1085 E) Rs.1185

Solution: a2 = 3136 => a = 56   56 * 4 * 3= 
56 * 4 * 3 = 672
672 – 6= 666 * 1.5= 
666 * 1.5 = 999
999   ANSWER:Rs.999
Answer: C
When a merchant imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that the merchant paid was $94.50, what was the total value of the item?
Pick
A) $2,350	B) $2,850	C) $3,250	D) $3,400	E) $3,750

Solution: Let x be the value in excess of $1,000.   0.07x = 94.5   x = $1,350   The total value was $1,350 + $1,000 = $2,350.   The answer is $2,350.
Answer: A
A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container.
Choose the correct choice from the following.
A) 26.34 litres  B) 27.36 liters  C) 28 litres  D) 29.16 litres  E) cannot be determined

Solution: Solution   Amount of milk left after 3 operations   [40 (1-4/40)3] litres = (40x9/10x9/10x9/10)= 29.16 litres   Answer 29.16 litres
Answer: D
If the average of 744, 745, 747, 748, 749, 752, 752, 753, 755 and x is 750, what is the value of x? Choose the correct choice from the following options:  A) 750  B) 752  C) 754  D) 755  E) 756

Solution: Sum of the deviations of the numbers in the set from the mean is always zero   744, 745, 747, 748, 749, 752, 752, 753, 755   mean is 750   so the list is -6-5-3-2-1+2+2+3+5... this shud total to zero   but this is -5 , hence we need a number that is 5 more than the mean to get a +5 and make it zero   hence the answer is  750 + 5= 
 750 + 5 = 755
755   755
Answer: D
Two bullet trains of equal lengths take 10 seconds and 30 seconds respectively to cross a telegraph post. If the length of each bullet train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
Choose the correct answer
A) 13 sec.
B) 14 sec.
C) 12 sec.
D) 15 sec.
E) 19 sec.

Solution: Speed of the first bullet train = 120/10 m/sec = 12 m/sec.   Speed of the second bullet train = 120/30 m/sec = 4 m/sec.   Relative speed = (12 + 4)= 
(12 + 4) = 16
16 m/sec.   Required time= (120 + 120)/16= 
(120 + 120)/16 = 15
15 sec.   15 sec.
Answer: D
What will be the length of the mini-train, if it crosses a pole in 3 sec while travelling at a speed of 75 kmph? Choose the correct answer.
A) 60 m  B) 65 m  C) 63.5 m  D) 64 m  E) 62.5 m

Solution: 62.5 mxplanation:   D = 75 * 5/18 * 3= 
75 * 5/18 * 3 = 125/2 = around 62.5
62.5 m   Answer: Option 62.5 m
Answer: E
30 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780. The bigger part is :	Pick one:
A) 33
B) 34
C) 26
D) 10
E) 19

Solution: Explanation:   Let the two parts be (30- x) and x.   Then, 10 (30 - x) + 22x = 780   => 12x = 480   => x = 40.   Bigger part = (30- x) = 10.   Answer: 10) 10
Answer: D
Find the least number which when divided by 20,25,35,40 leaves remainder 14,19,29,34 respectively. Choose the correct choice from the following answers:
A) 1394 B) 1450 C) 1245 D) 2564 E) 1256

Solution: The difference of 20-14= 
20-14 = 6
6 , 25-19= 6 , 35-29 = 6 , 40-34 = 6   LCM of 20,25,35,40 = 1400   Required number = 1400 - 6= 
1400 - 6 = 1_394
1394   1394nswer is 1394
Answer: A
Two trains are running in opposite directions with the same speed. If the length of each train is 180 m and they cross each other in 12 sec, then the speed of each train is?
Choose the correct choice from the following
A) 54
B) 31
C) 36
D) 25
E) 24

Solution: Let the speed of each train be x m/sec.   Then, relative speed of the two trains = 2x m/sec.   So, 2x = (180 + 180)/12 => x = 15   Speed of each train = 15 m/sec.   = 15 * 18/5= 
15 * 18/5 = 54
54 km/hr.   54nswer: Option 54
Answer: A