MU-NLPC/Calc-aqua_rat huggingface dataset:
For positive x and y if x/y is n% of y, then what percent must x be of y?  Choices
A) (y × n)%	B) (n/y)%	C) (√n)%	D) (n^2)%	E) (100 – n)%

Solution: Solution -   The statement x/y is n% of y means that: x/y = (n / 100) × y   In order to find what percent must x be of y i.e., we need to divide x by y.   x/y %=(n / 100) × y *100 ---->(y*n)%   Therefore x/y is (y*n)%   (y × n)%NSWER:(y × n)%
Answer: A
A “palindromic integer” is an integer that remains the same when its digits are reversed. So, for example, 43334 and 516615 are both examples of palindromic integers. How many 6-digit palindromic integers are both even and greater than 800,000?  Choose the correct answer:
A) 60	B) 100	C) 160	D) 240	E) 300

Solution: The first digit and last digit are the same so the only possibility is 8.   The second and third digits can be any number from 0 to 9.   The total number of palindromic integers is   1*10*10= 
  1*10*10 = 100
100   The answer is 100.
Answer: B
An amount of Rs.1560 was divided among A, B and C, in the ratio 1/2 : 1/3 : 1/4. Find the share of C?  Select the correct option: A) Rs.390 B) Rs.368 C) Rs.380 D) Rs.360 E) Rs.311

Solution: Let the shares of A, B and C be a, b and c respectively.   a : b : c = 1/2 : 1/3 : 1/4   Let us express each term with a common denominator which is the last number divisible by the denominators of each term i.e., 12.   a : b : c = 6/12 : 4/12 : 3/12 = 6 : 4 : 3.   Share of C = 3/13 * 1560 = Rs. 360.   Answer: Rs.360
Answer: D
There are some passengers riding on a bus. At the first stop, half the passengers get off and nobody gets on the bus. This pattern continues as the bus goes to the next stops. If only one passenger gets off at stop number 4, how many passengers were on the bus originally?  Pick one.
A) 128	B) 64	C) 32	D) 16	E) 8

Solution: Before stop 4, there were 2 passengers on the bus.   Before stop 3, there were 4 passengers on the bus.   Before stop 2, there were 8 passengers on the bus.   Before stop 1, there were 16 passengers on the bus.   The answer is 16.
Answer: D
In the Hillside summer camp there are 50 children. 90% of the children are boys and the rest are girls. The camp administrator decided to make the number of girls only 20% of the total number of children in the camp. How many more boys must she bring to make that happen?
Choose the correct option.
A) 35.  B) 45.  C) 40.  D) 30.  E) 25.

Solution: Given there are 50 students , 90% of 50 = 45 boys and remaining 5 girls.   Now here 90% are Boys and 10% are Girls.   Now question is asking about how many boys do we need to add, to make the girls percentage to or 20%..   If we add 35 to existing 45 then the count will be 80 and the girls number will be 20 as it.   Now boys are 80% and girls are 20%. ( out of 100 students = 80 boys + 20 girls ).   IMO option 35. is correct.
Answer: A
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability taht the ticket drawn has a number which is a multiple of 3 or 5? Choose the correct choice from the following options.
A) 1/2
B) 2/5
C) 8/15
D) 9/20
E) None

Solution: Solution   Here S=(1,2,3,4,5,...,19,20).   Let E=event of getting a multiple of 3 or 5   = (3,6,9,12,15,18,5,10,20)   P(E)= n(E) / n(S)   = 9/20.   Answer 9/20
Answer: D
A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.21000. A's share is?  Choices
A) 2999  B) 2778  C) 7000  D) 2889  E) 6612

Solution: x* 12 : 2x* 6: 3x* 4   1:1:1   1/3 * 21000= 
1/3 * 21000 = 7_000
7000   Answer:7000
Answer: C
The total cost of 100 paper plates and 200 paper cups is $4.50 At the same rates what is the total cost of 20 of the plates and 40 of the cups?  Choose the correct choice from the following answers
A) $.90
B) $1.00
C) $1.20
D) $1.50
E) $1.60

Solution: U dont need to go through all this   What u have with u is   100 P + 200 C = $4.50   Just divide the equation by 5 and you will get what u are looking for   20P + 40 C = $0.90   Therefore O$.90 is $.90
Answer: A
If two numbers are in the ratio 2:3. If 7 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
Choose the correct answer:
A) A)12
B) B)14
C) C)20
D) D)24
E) E)26

Solution: 2:3   2x + 7 : 3x + 7 = 3 : 4   4[2x + 7] = 3[3x + 7]   8x + 28 = 9x + 21   9x - 8x = 28 - 21= 
28 - 21 = 7
7   Then smallest number is= 2   2x = 14   Correct Option 14
Answer: B
What decimal of an hour is a second ? Choose the correct choice from the following options: A) 0.00027 B) 0.00029 C) 0.00031 D) 0.00025 E) 0.00023

Solution: Required decimal = 1/60x60 = 1/3600 = .00027   0.00027nswer is 0.00027.
Answer: A
When the price of an article was reduced by 35% its sale increased by 80%. What was the net effect on the sale? Select
A) 17% increase
B) 44% decrease
C) 60% increase
D) 66% increase
E) 66% decrease

Solution: if n items are sold for $p each, revenue is $np. If we reduce the price by 35%, the new price is 0.65p. If we increase the number sold by 80%, the new number sold is 1.8n. So the new revenue is (0.65p)(1.8n) = 1.17np, which is 1.17 times the old revenue, so is 17% greater.   17% increaseNSWER:17% increase
Answer: A
One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 7 robots altogether, if the robots build only one robot at a time?
Answers.
A) 70 1/7 min  B) 94 1/7 min  C) 110 1/7 min  D) 112 1/7 min  E) 131 1/7 min

Solution: First the 2 robots work at the rate of   1 + 1/2 = 3/2   so they complete one robot in 2/3 rd of an hour = 40 minutes - (1)   Now the 3 robots work together at the rate of   1 + 1/2 + 1/2 = 4/2= 
4/2 = 2
2/1   so they complete one robot in 1/2 an hour,i.e 30 minutes - (2)   Now the 4 robots work together at the rate of   1 + 1/2 + 1/2 + 1/2= 5/2   so they complete one robot in 2/5th of an hour - (3)   Now the 5 robots work together at the rate of   1 + 1/2 + 1/2 + 1/2+1/2= 
1 + 1/2 + 1/2 + 1/2+1/2 = 3
3   so they complete one robot in 1/3th of an hour - (4)   Now the 6 robots work together at the rate of   1 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2=7/2   so they complete one robot in 2/5th of an hour - (5)   And now we have 7 robots   So Total = (1) + (2) + (3)+(4)+(5) = 131 1/7minutes   Answer - 131 1/7 min
Answer: E
Teas worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs 152 per Kg , the price of the third variety per Kg will be?	Select.
A) Rs. 147.50  B) Rs. 785.50  C) Rs. 174.50  D) Rs. 258.50  E) None of these

Solution: Explanation :   Since first and second varieties are mixed in equal proportions.   So, their average price =Rs. (126+135)/2.   =>Rs. 130.50.   So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1.   We have to find x.   By the rule of alligation, we have:   Cost of 1 kg Cost of 1 kg   of 1st kind of 2nd kind   (Rs. 130.50) (Rs. x)   \ /   Mean Price   (Rs. 152)   / \   xâˆ’152 22.50   =>xâˆ’(152/22.50)=1.   =>xâˆ’152=22.50.   =>x= 174.50 Rs.   Answer : Rs. 174.50
Answer: C
One side of a triangle has length 5 and a second side has length 4. Which of the following could be the area of the triangle?
I. 15
II. 10
III. 5
Choose the most appropriate option:
A) I only  B) II only  C) III only  D) II and III only  E) I, II and III

Solution: The triangle will have a maximum area when it is a right angled triangle   The largest triangle will be formed when 5 and 4 are the base and height of triangle .   Area = 1/2 * 5 * 4= 
1/2 * 5 * 4 = 10
10   There is no lower limit on the area of any triangle whose only 2 sides are known.   Then 0 < Area <= 10   The answer is II and III only.
Answer: D
One card is drawn from a pack of 52 cards. What is the probability that the card drawn is a ten or a spade?
Choices.
A) 3/7
B) 4/13
C) 4/15
D) 7/19
E) 11/31

Solution: Out of 52 cards there will be 13 spades including 1 ten and there are 3 more tens. Total 16   probability= 16/52 = 4/13   Answer is 4/13
Answer: B
According to the directions on a packet of smoothie mix, 1 3-ounce packet of smoothie mix is to be combined with 19 ounces of water to make a smoothie. How many 3-ounce packets of smoothie mix are required to prepare 150 12-ounce smoothies?	Choices
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?   600
Answer: E
There are m cities. What is the number of airlines that connected 2 different cities (airline from city A to city B is different with airline from city B to city A)?	Choose one
A) n(n-1) B) m(m-1) C) n(n-1)/2 D) n(n+1)/2 E) n2

Solution: First of all, the possible number of airlines is m. Then, the possible number of airlines departing from one city to another becomes (m-1). Hence, the answer is m(m-1), which makes A an answer choice.   m(m-1)
Answer: B
In how many ways can the integer 800 be expressed as a product of two different positive integers?
Select
A) 10	B) 7	C) 5	D) 4	E) 2

Solution: 800=(2^5)*(5^2)   Since 800 is not a perfect square, no of ways=7   Answer 7
Answer: B
One day, Connie plays a game with a fair 6-sided die. Connie rolls the die until she rolls a 6, at
which point the game ends. If she rolls a 6 on her first turn, Connie wins 6 dollars. For each
subsequent turn, Connie wins 1
6 of the amount she would have won the previous turn. What is
Connie's expected earnings from the game? Choose the correct answer.
A) 32/31 B) 33/31 C) 34/31 D) 36/31 E) 0/31

Solution: Connie has a 1   6 chance of winning 6 dollars her first turn. She has a 5/6   1/6 chance of   winning 1 dollar her second turn. Next, she has a 25   36   1/6 chance of winning 1/6 dollars her third turn.   Generalizing, Connie's expected earnings form a geometric series with initial term  1/6 *6= 
 1/6 *6 = 1
1 and   common ratio 5/6* 1/6= 5/36 . Hence, Connie's expected earnings are   1/1- 5/36   =   36/31   correct answer 36/31
Answer: D
Visitors to show were charged Rs.15 each on the first day. Rs.7.50 on the second day, Rs.2.50 on the third day and total attendance on the three days were in ratio 2:5:13 respectively. The average charge per person for the whole show is?
Options
A) Rs.6.00  B) Rs.5.50  C) Rs.5.00  D) Rs.7.00  E) Rs.8.00

Solution: Answer: Option Rs.5.00   2: 5: 13   2x 5x 13x   15 7.5 2.5   30x + 37.5x + 32.5x = 100x/20x   average 30  + 37.5  + 32.5= 
30  + 37.5  + 32.5 = 100
100x/20x   average = 5100 /20= 
100 /20 = 5
5
Answer: C
In the first round of the elections, the only two candidates got exactly the same number of votes. During the second round, 20,000 votes switched from the first candidate to the second one. The total number of votes remained the same in both rounds, and no other votes switched sides. If, in the second round, the winning candidate got five times as many votes as the other candidate, how many people have voted in each round?  Choose the correct choice from the following
A) 15,000	B) 30,000	C) 40,000	D) 50,000	E) 60,000

Solution: Let A be the first candidate and B be the second one.   Given x+20000 = 5(x-20000)   4x = 120000=>x=30000   2x=60000   IMO option 60,000.
Answer: E
The average weight of a group of boys is 30 kg. After a boy of weight 37 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?	Choose the correct choice from the following answers:
A) A)4  B) B)8  C) C)6  D) D)2  E) E)1

Solution: Let the number off boys in the group originally be x.   Total weight of the boys = 30x   After the boy weighing 37 kg joins the group, total weight of boys = 30x + 37   So 30x + 37 = 31(x + 1) = > x = 6.   Answer:6
Answer: C
6x – 5y + 3z = 23
4x + 8y – 11z = 7
5x – 6y + 2z = 11
Given the equations above, x + y + z = ?
Choose one.
A) 11  B) 12  C) 13  D) 14  E) 15

Solution: (6x – 5y + 3z) - (5x – 6y + 2z ) = 23-11   or, x+y+z = 12   Option 12 is the ans
Answer: B
Three coins are tossed. Find the probability of at least 2 tails ?  Answers.
A) 1/2  B) 2/3  C) 1/4  D) 1/8  E) 3/8

Solution: n(s) = 2^3 = 8   let E is the event of getting at least 2 tails   n(E) = TTT, TTH , HTT, THT = 4   P(E) = n(E) / n(s)   = 4/8   = 1/2   1/2ns- 1/2
Answer: A
The amount of water (in ml) that should be added to reduce 12 ml. Lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is?  Choose the correct choice from the following:
A) 8 ml
B) 5 ml
C) 4 ml
D) 6 ml
E) 1 ml

Solution: 6 6   30% 70%   30% ----- 6   70% ------? => 14 - 6= 
14 - 6 = 8
8 ml   8 mlnswer:8 ml
Answer: A
Mary and Mike enter into a partnership by investing $550 and $450 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Mary received $1000 more than Mike did, what was the profit made by their business in that year?	Choose the correct option:
A) $8000  B) $10000  C) $15000  D) $12000  E) $12500

Solution: Explanatory Answer   Let the profit made during the year be $3x   Therefore, $x would have been shared equally and the remaining $2x would have been shared in the ratio 5.5 : 4.5   i.e., 55% of 2x would go to Mary and 45% of 2x would go to Mike.   Hence, Mary would get (55 - 45)% of 2x more than Mike   Or10% of 2x = $1000   i.e.,(60/100)*2x = 1000   or 2x = 10000.   Hence, the profit made by the company during the year $3x = $15000.   Answer : $15000
Answer: C
In an election, candidate A got 79% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favour of candidate.  Choose the correct choice from the following answers.
A) 357003	B) 357090	C) 37667	D) 379888	E) 287761

Solution: Total number of invalid votes = 15 % of 560000   = 15/100 × 560000   = 8400000/100= 
8400000/100 = 84_000
84000   Total number of valid votes 560000 – 84000= 476000   Percentage of votes polled in favour of candidate A = 75 %   Therefore, the number of valid votes polled in favour of candidate A = 75 % of 476000   = 75/100 × 476000   = 35700000/100   = 357090   Answer:357090
Answer: B
A plane flies 660 km with the wind and 570 km against the wind in the same length of time. If the speed of the wind is 15 km/h, what is the speed of the plane in still air? Choose one:
A) 185 km/h B) 195 km/h C) 205 km/h D) 215 km/h E) 225 km/h

Solution: The speed of the plane in still air = x km/h   The speed of the wind is 15 km/h   Speed with the wind = (x + 15) km/h   Speed against the wind = (x â€“ 15) km/h   Time = Distance/ Speed   660 / (x+15) = 570 / (x-15)   660(x-15) = 570(x+15)   66x - 990 = 57x + 855   9x = 1845   x = 205   Therefore, the speed of the plane in still air is 205 km/h.   The answer is 205 km/h.
Answer: C
Quentin's income is 60% less than Rex's income, and Sam's income is 25% less than Quentin's income. If Rex gave 60% of his income to Sam and 40% of his income to Quentin, Quentin's new income would be what fraction of Sam's new income?  Select the correct option:
A) 8/9  B) 11/12  C) 8/13  D) 11/13  E) 12/13

Solution: We can take some easy numbers and make calculations simpler.   Let R ( Rex's income) = 100   Q (Quentin's income) = 40%R = 40   S (Sam's income) = 75% Q = (3/4)*40= 
(3/4)*40 = 30
30   Now, if Rex gives 40% to Quentin --> Q= 40 + 40= 
40 + 40 = 80
80   60% given to Sam --> S= 30+60= 
30+60 = 90
90   The ratio is : Q/S= 80/90 = 8/9   8/9NSWER:8/9
Answer: A
What is the principal sum?
I. The sum amounts to Rs. 660 in 3 years at S.I.
II. The sum amounts to Rs. 700 at S.I.
III. The rate of interest is 6% p.a.	Choose the correct choice from the following answers:
A) I and III only	B) II and III only	C) I and II only	D) Any two of the three	E) None of these

Solution: Explanation:   Clearly, I and III is needed to solve this question where as II is not needed   I and III onlynswer: I and III only
Answer: A
The side of a rhombus is 26 m and length of one of its diagonals is 20 m. The area of the rhombus is?
Choose the correct choice from the following answers
A) 388 B) 267 C) 298 D) 480 E) 281

Solution: 262 – 102 = 242   d1 = 20 d2 = 48   1/2 * 20 * 48= 
1/2 * 20 * 48 = 480
480.Answer:480
Answer: D
A shopkeeper wishes to give 5% commission on the marked price of an article but also wants to earn a profit of 10%. If his cost price is Rs. 95, then marked price is: Choose the correct answer
A) Rs. 100	B) Rs.110	C) Rs. 120	D) Rs. 130	E) None

Solution: Solution: CP = Rs. 95.   Then SP = 95 + 10% of 95 = Rs. 104.5.   Let MP = X. He gives 5% commission on MP.   So,   SP = X - 5% of X   SP = 0.95X.   104.5 = 0.95X.   X = 104.5/0.95= 
104.5/0.95 = 110
110.   Thus, MP= Rs. 110.   Short-cut   95===10%(gain)===>104.5===5%(Commission)===>109.72( = 110)   Answer: Option Rs.110
Answer: B
A and B together can do a work in 9 days. If A alone can do it in 18 days. In how many days can B alone do it?	Pick one.
A) 10 B) 99 C) 18 D) 55 E) 21

Solution: 1/9 – 1/18 = 1/18   => 18   Answer: 18
Answer: C
There are some pigeons and hares in a zoo. If heads are counted, there are 250. If legs are counted, there are 580. The number of hares in the zoo is?	Choose the correct answer.
A) 40	B) 50	C) 60	D) 70	E) 80

Solution: 250*2= 
250*2 = 500
500   580   -----   80   1----2   ?----80= 40   40NSWER:40
Answer: A
The average age of 30 students in a class is 14 years. If the age of teacher is also included, the average becomes 15 years, find the age of the teacher.  Choose the correct option.
A) 43 B) 44 C) 45 D) 47 E) 48

Solution: Explanation:   If teacher's age is 14 years, there is no change in the average. But teacher has contributed 1 year to all the students along with maintaining his age at 15.   Age of teacher = Average age of all + Total increase in age   = 15 + (1 x 30 ) = 45 years   Answer:45
Answer: C
There are 3 red paints and 1 white paint that can be mixed to make new red paint colors. The paints are labeled A for Red78/Red23, B for Red23/Red17, C for Red17/White001. When mixing the paint for the new paint Firehouse Red, the formula calls for 4A:1D. How many of each paint is in Firehouse Red?  Choose the correct choice from the following options:
A) none of the below options
B) one part White001 : four parts Red23
C) four parts Red78 : one part Red17
D) four parts Red23 : one part Red17
E) one part White001 : four parts Red78

Solution: Solution   A : B = Red78 : Red23, B : C = Red23 : Red17, C : D = Red17 : White1   âˆ´Aâˆ¶Bâˆ¶Câˆ¶D= Red78 : Red23 : Red17 : White001.   Thus, A : D = Red78 : White001   4A:1D = Red78, Red78, Red78, Red 78 : White001   Correct Option one part White001 : four parts Red78
Answer: E
A man can row 7.2 kmph in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of stream. Choose one.
A) 2.4 km/hr
B) 12.5 km/hr
C) 1 2.6 km/hr
D) 22.5 km/hr
E) 22.6 km/hr

Solution: Given that, time taken to travel upstream = 2 × time taken to travel downstream   When distance is constant, speed is inversely proportional to the time   Hence, 2 × speed upstream = speed downstream   Let speed upstream = x   Then speed downstream = 2x   we have, 1/2(x+2x) = speed in still water   ⇒1/2(3x)=7.2   3x = 14.4   x = 4.8   i.e., speed upstream = 4.8 km/hr   Rate of stream = 1/2(2x−x)=x/2=4.8/2= 
4.8/2 = 2.4
2.4 km/hr   2.4 km/hrnswer is 2.4 km/hr
Answer: A
Two pipes A and B can fill a cistern in 75/2 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:	Select:
A) 5 min.
B) 9 min.
C) 10 min.
D) 15 min
E) 18 min

Solution: If 9 min. is closed after x mins, then   30*2/75 + x/45 = 1   x/45 = 1 - 4/5 = 1/5   x= 45/5= 
45/5 = 9
9 mins   ANSWER:9 min.
Answer: B
During the months May through October, Teddy the bear sextuples his weight, and during the months November through April, Teddy loses 100 pounds. If at the beginning of November 1973, Teddy's weight was m pounds, what was Teddy's weight in pounds by the end of April 1976?	Answers:
A) 36m - 1300  B) 36m - 1200  C) 6m - 1300  D) 6m - 1200  E) 6m

Solution: Nov ' 73 = m   36m - 1300pril ' 74 = m - 100   Oct ' 74 = 6m - 300   36m - 1300pril' 75 = 6m - 400   Oct' 75 = 36m - 1200   36m - 1300pril'76 = 36m - 1300   Hence answer will be (36m - 1300) 36m - 1300
Answer: A
A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 24m/h. what is the speedof the person while he was going to his office?  Choose the correct choice from the following options.
A) 8km/h B) 10km/h C) 12km/h D) 16km/h E) 14km/h

Solution: u = k , v= 3k   \inline \therefore \frac{2uv}{u+v}\: \: \Rightarrow \frac{2\times k\times 3k}{(k+3k)}=24   \inline \Rightarrow 1.5k = 24   \inline \Rightarrow k=16km/h   16km/h
Answer: D
A car travels uphill at 30 km/hr and downhill at 80 km/hr. It goes 100 km uphill and 50 km downhill. Find the average speed of the car? Options:
A) 38kmph
B) 33kmph
C) 34kmph
D) 35kmph
E) 36kmph

Solution: avg speed=total distance/total time.   total distance traveled=100+50= 
100+50 = 150
150km;   time taken for uphill journey=100/30=10/3;   time taken for down hill journey=50/80=5/8;   avg speed=150/(10/3+5/8)=38kmph   38kmphNSWER:38kmph
Answer: A
The number of arrangements that can be made with the letters of the word WORDS so that the vowels occupy the even places? Choose the correct choice from the following answers.
A) 14 B) 32 C) 777 D) 24 E) 221

Solution: The word MEADOWS has 7 letters of which 3 are vowels.   -V-V-V-   As the vowels have to occupy even places, they can be arranged in the 1 even places in 1! i.e., 1 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.   Hence the total ways are  24 * 1= 
 24 * 1 = 24
24.   Answer:24
Answer: D
There are 50 students in a class. If 14% are absent on a particular day, find the number of students present in the class.  Choose the correct choice from the following answers: A) 43 B) 36 C) 28 D) 129 E) 11

Solution: Number of students absent on a particular day = 14 % of 50   i.e., 14/100 × 50 = 7   Therefore, the number of students present = 50 - 7= 
50 - 7 = 43
43 students.   43nswer:43
Answer: A
A train running at the speed of 27 km/hr crosses a post in 20 seconds. What is the length of the train?
Choose the correct choice from the following:  A) 200  B) 150  C) 300  D) 175  E) 250

Solution: Speed=(27x5/18)=7.5 m/sec.   Length of the train=(Speed x Time).   Length of the train=7.5 x20	m = 150 m.   Answer: 150
Answer: B
The inverse ratio of 3: 2: 1 is?
Choose the correct answer:
A) 2:3:7
B) 2:3:9
C) 2:3:2
D) 2:3:6
E) 2:3:1

Solution: 1/3: 1/2: 1/1 = 2:3:6   Answer:2:3:6
Answer: D
Luke travelled 12 2/3 miles in 1 hours and 40 minutes. What was his average rate of speed in miles per hour?  Choose the correct choice from the following options
A) 7  B) 7 3/5  C) 8 1/5  D) 9  E) 9 2/5

Solution: D = 12(2/3) = 38/3   T = 1(2/3) = 5/3   S = D/T = 7 3/5   Answer = 7 3/5
Answer: B