MU-NLPC/Calc-aqua_rat huggingface dataset:
The probability that event A occurs is 0.4, and the probability that event B occurs is 0.45. If the probability that either event A or event B occurs is 0.6, what is the probability that event B and event B will occur?
Options:
A) 0.25
B) 0.15
C) 0.45
D) 0.5
E) 0.55

Solution: P(0.25 or B) = P (0.25) + P(B) - p(a n b)   0.6= 0.4 + p(a n b) + 0.45   P(B) = 0.25   0.25ns : 0.25
Answer: A
A 480 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 620 m in ?
Pick:
A) 41.1 sec
B) 72 sec
C) 31.8 sec
D) 50.4 sec
E) none of the above

Solution: Speed = 55 Km/hr   (to convert km/hr in to M/s)   = 55 x 5/18 M/s   Distance = 480 m + 620 m ( If questions is about train crossing a post you need to consider only the length of Train, )   = 1100 m   Time = Distance / Speed   = 1100 x 18 / (5 x 55)   = 72 sec   Ans is :72 sec
Answer: B
At a certain supplier, a machine of type A costs $20,000 and a machine of type B costs $60,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?  Choices: A) $10,000 B) $11,200 C) $12,000 D) $12,800 E) $26,400

Solution: Total Cost of 2 Machines of Type A   = 20% of (Cost of 2 machine A) + remainder + 40 % remainder   = 20% of 40000 + (40000 - 20% of 40000) + 40% of (40000 - 20% of 40000)   = 52800   Total Cost of 1 Machine of Type B   = 20% of (Cost of 1 machine B) + remainder + 40 % remainder   = 20% of 60000 + (60000 - 20% of 60000) + 40% of (60000 - 20% of 60000)   = 79200   Diff = 79200 - 52800= 
79200 - 52800 = 26_400
26400   Hence, $26,400.
Answer: E
A train is 360 meter long is running at a speed of 54 km/hour. In what time will it pass a bridge of 140 meter length? Choose the correct choice from the following choices:
A) 65 seconds  B) 33.33 seconds  C) 40 seconds  D) 97 seconds  E) 26 seconds

Solution: Speed = 54 Km/hr = 54*(5/18) m/sec = 15 m/sec   Total distance = 360+140= 
360+140 = 500
500 meter   Time= Distance/speed   = 500 * (1/15)   = 33.33 seconds   Answer:33.33 seconds
Answer: B
A and B together have $100. If 3/10 of A's amount is equal to 1/5 of B's amount, how much amount does B have?  Options:
A) $60  B) $55  C) $42  D) $31  E) $100

Solution: 3/10 $60 = 1/5 B   $60 = 1/5 * 10/3 B   $60 = 2/3 B   $60/B = 2/3   $60:B = 2:3   B's share = 100*3/5= 
100*3/5 = 60
$60   $60nswer is $60
Answer: A
Donovan took a math test and got 35 correct and 14 incorrect answers.
What was the percentage of correct answers? (Round to the nearest
hundredth)  Options
A) 57.78%
B) 67.78%
C) 71.43%
D) 47.78%
E) 97.78%

Solution: 35 correct our of 49 total (35+14)   35/49   correct answer 71.43%
Answer: C
In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together? Choose the correct option: A) 610 B) 720 C) 825 D) 920 E) 650

Solution: Explanation:   The word 'OPTICAL' has 7 letters. It has the vowels 'O','I','A' in it and these 3 vowels should always come together. Hence these three vowels can be grouped and considered as a single letter. That is, PTCL(OIA).   Hence we can assume total letters as 5 and all these letters are different.   Number of ways to arrange these letters   =5!=5Ã—4Ã—3Ã—2Ã—1=120=5!=5Ã—4Ã—3Ã—2Ã—1=120   All the 3 vowels (OIA) are different   Number of ways to arrange these vowels among themselves   =3!=3Ã—2Ã—1=6=3!=3Ã—2Ã—1=6   Hence, required number of ways   =120Ã—6=720   ANSWER IS 720
Answer: B
A deer runs k miles in n hours. How many miles will it run in x hours at the same rate?  Answers.
A) knx
B) k⁄n
C) kx⁄2n
D) kx⁄n
E) kn⁄x

Solution: Given Speed = k/n   To Find distance in x hours with same speed   kx⁄nistance = speed * time   kx⁄nistance = k/n*x = kx/n   Answer kx⁄n
Answer: D
The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/50 of the area of the field. What is the length of the field? Choose the correct choice from the following answers.
A) 73  B) 32  C) 34  D) 43  E) 80

Solution: 80xplanation:   A/50 = 8 * 8 => A = 8 * 8 * 50   x * 2x = 8 * 8 * 50   x = 40 => 2x = 80   Answer: Option 80
Answer: E
If the average of 8 digits is 20 and the average of 5 of them is 12, calculate the average of the remaining 3 numbers? Choose the correct choice from the following choices.
A) 13.3
B) 38.3
C) 35.3
D) 31.3
E) 33.3

Solution: 33.3xplanation:   Total of the 8 digits - 8*20 = 160   Total of the 5 digits - 5*12 = 60   Total of the remaining 3 digits - 160-60 = 100   average of the remaining 3 numbers = 100/3 = 33.3   ANSW33.3R: 33.3
Answer: E
The average weight of 10 men is increased by 1 ½ kg when one of the men who weighs 60 kg is replaced by a new man. What is the weight of the new man?
Choose the correct choice from the following answers:
A) 80 kg  B) 83 kg  C) 70 kg  D) 75 kg  E) 85 kg

Solution: Since the average has increased by 1.5 kg, the weight of the man who stepped in must be equal to 60+10x1.5   60+15= 
60+15 = 75
75 Kg   Ans: '75 kg'
Answer: D
Charlene's annual bonus is calculated in the following manner: Charlene receives 20 percent of her first $11,000 in sales and 30 percent of her sales in excess of $11,000. If Charlene received a bonus of $8,500, what were her annual sales? Choose the correct choice from the following answers
A) $ 20,000 B) $ 22,000 C) $ 24,666 D) $ 26,000 E) $ 28,000

Solution: Let x be the total sales in $.   For the 1st 11,000 you get 20% ---> 0.2*11000 = 2200$   For the remaining (x-11000) $, you get 30% ---> 0.3*(x-11000)   Thus, 0.3*(x-11000) + 2200 = 8500 ----> x= 24,666 $   $ 24,666 is thus the correct answer.
Answer: C
If four coins are tossed, the probability of getting two heads and two tails is?
Select.
A) 3/8  B) 3/6  C) 3/9  D) 3/1  E) 3/4

Solution: Since four coins are tossed, sample space = 24   Getting two heads and two tails can happen in six ways.   n(E) = six ways   p(E) = 6/24 = 3/8   3/8nswer:3/8
Answer: A
Three-fifth of a two digit number exceeds its one fifth by 6. What is the sum of the digits of the number? Choose the correct choice from the following answers:
A) 6  B) 9  C) 11  D) 12  E) 15

Solution: Explanation:   3x/5 – x/5 = 6 => x =15   1 + 5= 
1 + 5 = 6
6   6)
Answer: A
In a restaurant, the profit is 160% of the cost. If the cost increases by 12% but the selling price remains constant, approximately what percentage of the selling price is the profit?  Choose the correct answer:
A) 30% B) 57% C) 90% D) 100% E) None of these

Solution: Explanation :   Let C.P.= Rs. 100. Then, Profit = Rs. 160, S.P. = Rs. 260.   New C.P. = 112% of Rs. 100 = Rs. 112   New S.P. = Rs. 260.   Profit = Rs. (260 - 112) = Rs. 148.   Required percentage = (148 /260 *100) % = 57 % appox   Answer : 57%
Answer: B
An investor purchased 100 shares of stock X at 6 1/8 dollars per share and sold them all a year later at 30 dollars per share. If the investor paid a 2 percent brokerage fee on both the total purchase price and the total selling price, which of the following is closest to the investor's percent gain on this investment?  Select the correct option:
A) 92%
B) 240%
C) 280%
D) 395%
E) 380%

Solution: If the purchase price was 6$ per share then the investor would have made a profit of 400%.   Since the purchase price is slightly more than 6$ the profit would be slightly less than 400%.   Also a 2% brokerage is negligible and it brings down the profit percentage only by a small value. Approximation is very useful to solve these kind of problems as the answer choices are far apart.   Answer: 395%
Answer: D
A certain jacket was marked down 20% the first week and another 20% the next week. What percent of the regular price was the final cost of the jacket after the two markdowns? Choose one
A) 30%  B) 36%  C) 40%  D) 60%  E) 64%

Solution: This is a case of successive discounts.   64%ffective discount = -a -b + ab/100   64%ffective Discount = -20 - 20 + 400/100 = -36%   Final cost = 100 - 36= 
100 - 36 = 64
64% of the initial cost   ANSW64%R:64%
Answer: E
A dishonest dealer professes to sell his goods at Cost Price but still gets 20% profit by using a false weight. What weight does he substitute for a kilogram?	Choose the correct choice.
A) 223 1/3 grams.
B) 833 1/3 grams.
C) 2873 1/3 grams.
D) 273 1/3 grams.
E) 832 1/3 grams.

Solution: Explanation:   If the cost price is Rs.100, then to get a profit of 20%, the selling price should be Rs.120.   If 120kg are to be sold, and the dealer gives only 100kg, to get a profit of 20%.   How many grams he has to give instead of one kilogram(1000 gm).   120 gm ------ 100 gm   1000 gm ------ ?   (1000 * 100)/120 = 2500/3 = 833 1/3 grams.   Answer:833 1/3 grams.
Answer: B
Of 100 apples in a tree, 30 percent are green. How many red apples must be picked in order to bring the number of green apples up to 50 percent of the apples in the tree?
Pick:	A) 40	B) 50	C) 30	D) 70	E) 20

Solution: Now, there are 30 green apples (30% of 100) and   100-30= 
  100-30 = 70
70 red apples in the tree. We need there to be 30 green apples and 30 red apples, in this case there will be 50% green apples and 50% red apples.   Therefore  70-30= 
 70-30 = 40
40 red apples must be picked.   40nswer: 40.
Answer: A
A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
Options:	A) 33	B) 77	C) 72	D) 55	E) 88

Solution: Length = Speed * time   Speed = L/T   S = 400/20= 
400/20 = 20
20 M/Sec   Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 72 Kmph   Answer:72
Answer: C
The time it took car P to travel 300 miles was 2 hours less than the time it took car R to travel the same distance. If car P’s average speed was 10 miles per hour greater than that of car R, what was car R’s average speed, in miles per hour?
Choose the correct choice from the following answers: A) 34 B) 50 C) 60 D) 70 E) 80

Solution: Let speed of car R be=x   Then speed of car P= x+10   A/Q,   (300/x)-(300/(x+10))=2   Solving for x=34 miles\hr.   34
Answer: A
A student can select one of 8 different math book, one of 3 different chemistry book & one of 4 different science book.In how many different ways students can select book of math, chemistry & science.  Pick one:	A) 22	B) 72	C) 96	D) 37	E) 01

Solution: 8961×3961×4961 = 8x3x4=96 ways   Answer:96
Answer: C
In how many ways can the letters of the word APPEAR be rearranged such that the vowels always appear together? Choose the correct answer:
A) 6!/2!
B) 3!*3!
C) 4!/2!
D) 4! *3!/(2!*2!)
E) 3!*3!/2

Solution: In the word ABACUS , there are 3 vowels - 2 A's and U   Number of ways the letters of word APPEAR be rearranged such that the vowels always appear together   = (4! * 3! )/2!*2!   We can consider the the 3 vowels as a single unit and there are 3 ways to arrange them . But since 2 elements of vowel group AND 2 elements of consonant group are identical we divide by 2! 2! .   The entire vowel group is considered as a single group .   Answer 4! *3!/(2!*2!)
Answer: D
A die is thrown twice and the sum of the numbers appearing is observed to be 6.
find the conditional probability that the number 4 has appeared at least once?  Choices:
A) 2/5 B) 3/5 C) 4 D) 4/11 E) 5

Solution: Let E be the event that ‘number 4 appears at least once’ and F be   the event   that ‘the sum of the numbers appearing is 6’.   Then, E = {(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4),   (5,4), (6,4)}   and F = {(1,5), (2,4), (3,3), (4,2), (5,1)}   We have P(E) = 11/36   and P (F) = 5/36   2/5lso EnF = {(2,4), (4,2)}   Therefore P(EnF) = 2/36   the required probability   P(E|F) = P(EnF)/P(F) = (2/36)/(5/36) = 2/5   Option is 2/5
Answer: A
How many numbers between 100 and 798 are divisible by 2, 3, and 7 together?
Choose the most appropriate option:	A) 112	B) 77	C) 267	D) 17	E) 99

Solution: Explanation:   As the division is by 2, 3, 7 together, the numbers are to be divisible by:  2*3*7= 
 2*3*7 = 42
42   The limits are 100 and 798   The first number divisible is 42*3= 
42*3 = 126
126   To find out the last number divisible by 42 within 798:    798/42= 
 798/42 = 19
19   Hence, 42*19= 798 is the last number divisible by 42 within 798   Hence, total numbers divisible by 2, 3, 7 together are (19 â€“ 2) = 17   ANSWER: 17
Answer: D
A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?	Choose the correct choice from the following
A) 221  B) 287  C) 288  D) 280  E) 271

Solution: 80* 7: x* 3 = 1:1 1/2   560: 3x = 2: 3   x = 280   Answer: 280
Answer: D
Tough and Tricky questions: Absolute Values.
If |a| = 1/5 and |b| = 2/3, which of the following CANNOT be the result of a + b?	Pick one:
A) 13/15 B) -13/15 C) -7/15 D) 7/15 E) 7/5

Solution: |a| = 1/5   Absolute value of 'a' can have two values = 1/5 and -(1/5)   |b| = 2/3   Absolute value of 'b' can have two values = 2/3 and -(2/3)   Now different combinations of a + b are as follows:   a + b = (1/5) + (2/3) = 13/15   - a - b = -(1/5) - (2/3) = -13/15   a - b = (1/5) - (2/3) = -(7/15)   -a + b = -(1/5) + (2/3) = 7/15   Cross verifying with the given options, left over option is 7/5.
Answer: E
A sum is divided among C, D and E in such a way that for each rupee C gets, D gets 75 paisa and E gets 50 paisa. If the share of E is RS. 80, what is the total amount? Pick.
A) 360	B) 350	C) 340	D) 330	E) 320

Solution: c:d:e = 100:75:50   20:15:10   10 --- 80   45 --- ? => 360   360nswer:360
Answer: A
How many times will the hands of a clock coincide in a day?	Choose the correct answer:
A) 24	B) 22	C) 23	D) 44	E) 42

Solution: solution   The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock). The hands overlap about every 65 minutes, not every 60 minutes. Thus the minute hand and the hour hand coincide 22 times in a day   so Answer is 22
Answer: B
The sector of a circle has radius of 14 cm and central angle 144o. Find its perimeter? Pick.
A) 60cm  B) 63.2cm  C) 70cm  D) 80cm  E) 90cm

Solution: Perimeter of the sector = length of the arc + 2(radius)   = (144/360 * 2 * 22/7 * 14) + 2(14)   = 35.2 + 28= 
35.2 + 28 = 63.2
63.2 cm   Answer:63.2cm
Answer: B
The area of a square is equal to 2 times the area of a rectangle of dimensions 8 cm * 64 cm. What is the perimeter of the square? Choose the correct option:	A) 482	B) 268	C) 800	D) 128	E) 632

Solution: Area of the square = s * s = 2(8 * 64)   => s = 4 * 8= 
4 * 8 = 32
32 cm   Perimeter of the square= 4 * 32= 
4 * 32 = 128
128 cm.   Answer: 128
Answer: D
In how many ways can a committee consisting of 4 men and 5 women be formed from a group of 7 men and 8 women? Choices
A) 7C4 8C5
B) 4C7 5C8
C) 7C5 8C4
D) 9C4 7C5
E) NONE

Solution: Group consisting of 7 men and 8 women   4 men can be selected from 7 men in 7C4 ways   5 women can be selected from 8 women in 8C5 ways   Therefore, Total number of ways= 7C4 8C5   7C4 8C5NSWER:7C4 8C5
Answer: A
If p and q are integers and p divided by q is 16.15, then which of the following integers is a possible value for the remainder when p is divided by q?
I. 15
II. 5
III. 3 Choose the correct choice from the following answers:	A) I only	B) II only	C) III only	D) I,III only	E) II,III only

Solution: p=16.15q from which p = 16q + 15q/100 or p = 16q + 3q/20.   Since p and q are integers, 3q/20 must also be an integer. 3 is not divisible by 20, then q must be divisible by 20, and therefore, q/20 is an integer and 3q/20 is an integer which is a multiple of 3. From the given answers, only 15 and 3 are divisible by 3.   Answer I,III only
Answer: D
If, 7 years ago, Jamie was half as old as he is now, how old will he be in x years?  Choose the correct choice from the following answers:
A) x + 10  B) x + 14  C) x + 2  D) x – 5  E) 2x

Solution: let his age be a. a-7=a/2 hence a=14. 14 years hence, a =x+14   Answer x + 14
Answer: B
Suresh and Ramesh started a business investing Rs. 24,000 and Rs. 40,000 respectively. Out of total profit of Rs. 20,000, what is Ramesh's share?  Choices: A) s. 8375 B) s. 9379 C) s. 10376 D) s. 11372 E) s. 12500

Solution: Explanation:   Ratio of Suresh and Ramesh's share = 24,000 : 40,000 = 3 : 5   Ramesh's share = Rs. (20000 x 5 / 8) = Rs. 12500   ANSWs. 12500R: s. 12500
Answer: E
The number of even factors of 21600 is  Select:	A) 32	B) 42	C) 60	D) 25	E) 52

Solution: Make a prime factorization of the number: 21,600=25∗33∗52   According to the above the number of factors is (5+1)(3+1)(2+1)=72   Now, get rid of powers of 2 as they give even factors --> you'll have 33∗52 which has (3+1)(2+1)=12 factors. All the remaining factors will be odd, therefore 21,600 has   72-12= 
  72-12 = 60
60 even factors.   Answer: 60.
Answer: C
C and D walk around a circular track. They start at 11 a.m from the same point in the opposite directions. C and D walk at a speed of 7 rounds per hour and 8 rounds per hour respectively. How many times shall they cross each other before 5 p.m Select:
A) 90 B) 95 C) 100 D) 105 E) 110

Solution: Explanation:   Relative speed = (7+8)= 
(7+8) = 15
15 rounds per hour   So, they cross each other 15 times in an hour hence, they cross 90 times before 5 p.m   90nswer: Option 90
Answer: A
Fred and Sam are standing 100 miles apart and they start walking in a straight line toward each other at the same time. If Fred walks at a constant speed of 5 miles per hour and Sam walks at a constant speed of 5 miles per hour, how many miles has Sam walked when they meet? Choose one: A) 5 B) 9 C) 25 D) 30 E) 75

Solution: relative distance =100 miles   relative speed =5+5= 
5+5 = 10
10 miles per hour   time taken=100/10=15 hours   distance travelled by sam =15*5= 
15*5 = 75
75 miles=75
Answer: E
In how many ways can the letters {U, U, U, R} be arranged? Choose the correct choice from the following answers:
A) 4
B) 20
C) 120
D) 720
E) 840

Solution: My answer : 4   There is 4! ways to arrange those letters in total, however letter U repeats 3! times and letter R repeats 1! times   => the way to arrange without repeating = 4!/ [3!x1!] = 4
Answer: A
Find the value of X, Y by solving the below equations
X + Y = 12
X - Y = 4	Choices:
A) 5, 7  B) 8, 4  C) 6, 6  D) 7, 5  E) 9, 3

Solution: X + Y = 12 ---(I)   X - Y = 4 -----(II) by adding (I) and (II)   ------------   2X = 16 ==> X = 16/2= 
16/2 = 8
8   By Replacing the value of X in (I) we get 8 + Y= 12 ==> Y = 12-8= 
12-8 = 4
4.   So, X= 8, Y = 4   Answer 8, 4) 8, 4
Answer: B
One hour after Adrienne started walking the 60 miles from X to Y, William started walking from X to Y as well. Adrienne walks 3 miles per hour and William walks 1 mile per hour faster than Adrienne. How far from X will William be when he catches up to Adrienne?
Choose the correct choice from the following options:	A) 8 miles	B) 9 miles	C) 10 miles	D) 11 miles	E) 12 miles

Solution: First, determine how far Adrienne has walked in the one hour. She has walked three miles which means she is three miles ahead of William when he sets off. William walks at four miles/hour which means that every hour, William will get one mile closer to Adrienne. If he gets one mile closer every hour, it will take him three hours to catch up to her which means he travels 3hours * 4 miles/hour = 12 miles and she travels 4 hours * 3 miles/hour = 12 miles. He will be 12 miles from X when he catches up to her.   A slightly different way to solve...   We don't know how long they will walk before they catch up to one another but we do know that A walks for one hour more than J. J = T and A = T+1. We are looking for the distance at which they meet up which means the distance will be the same. 11 miles=r*t so,   r*t (William ) = r*t (adrienne)   r*(t) = r*(t+1)   4t = 3t+3   t=3   d=r*t   d=4*3= 
4*3 = 12
12   11 miles) 12 miles
Answer: D
If -12 < x < 14, Then which of the following must be true ?
Choose the correct choice.
A) x = -11
B) x <= 13
C) x > 12
D) x > -43
E) x >= 11

Solution: SOLUTION:   A. x = -11 --> Not always true. x can be any value between -12 and 14   B. x <= 13 --> Not always true. If x = 13.5 then x > 13.   C. x > 12 --> Not always true. x can be a value less than 12.   D. x > -43 --> Always true. x can take a minimum value of -12 (approx.). Hence x is always greater than -43.   E. x >= 11 -->Not always true. x can be a value less than 11.   Answer: x > -43
Answer: D
The R train leaves station A moving at a constant speed, and passes by stations B and C, in this order. It takes the R train 7 hours to reach station B, and 5 additional hours to reach station C. The distance between stations A and B is m kilometers longer than the distance between stations B and C. What is the distance between stations A and C in terms of m?
Choose the correct choice from the following answers:	A) 1.8m	B) 6m	C) 7m	D) 9m	E) 12m

Solution: The reason it is failing for you is that you chose incorrect numbers. If the question says R it took 7 hrs to reach from A to B and 5 hrs to reach from B to C at a constant speed. It shows that distance AB and BC should be in ratio of 7/5.   If you take such numbers you can solve problem.   A6m = 7, 6mC=5   Therefore   A6m-6mC = 2   6mut from question, A6m-6mC =m   => m=2   Now total distance = A6m+6mC= 12   Substitute 12 to get answer in terms of m   Total distance 6 +6= 
6 +6 = 12
12   Substitute 12 to get answer in terms of m   Total distance=12 =6m   Ans 6m
Answer: B
A towel, when bleached, lost 20% of its length and 20% of its breadth. What is the percentage decrease in area?  Options.
A) 24%
B) 36 %
C) 32%
D) 54%
E) 64%

Solution: percentage change in area   =(−20−20+(20×20)/100)%=−36%   i.e., area is decreased by 36%   ANSWER:36 %
Answer: B
A class has a ratio of 3:6:7 of children with red hair, blonde hair and black hair respectively. If the class has 9 kids with red hair, how many kids are there with black hair?	Choose the correct choice from the following answers:
A) 7
B) 6
C) 9
D) 21
E) 63

Solution: Since there is a 3:7 ratio between red haired children and black-haired children, if there are 9 children with red hair, then there must be 3 times the amount of black-haired children. Therefore, are 21 children with black hair.   Answer: 21)
Answer: D
What is the probability that out of the combinations that can be made using all the letters of the word EXCESS, Jerome will randomly pick a combination in which the first letter is a vowel and the last letter is a consonant? Select
A) 96/320	B) 24/180	C) 33/100	D) 48/180	E) 96/180

Solution: lets see the possiblilties with the given restrictions..   lets put the starting letter as vowel E..   then remaining 5 places can be filled in 5!/2!= 60..   but this consists of second E as the last letter and we will have to subtract these ways from 60..   so when first and last places are occupied by E, the remaining 4 places can be filled by 4!/2!=12 ways..   so ways with the restrictions= 60-12= 48..   so prob= 48/180   ANSWER :48/180
Answer: D
A, B and C are inner angles in a triangle. If A= B+ C, what can't be the size of B?
Choose one: A) 90 DEGREES B) 70 DEGREES C) 760 DEGREES D) 940 DEGREES E) 940 DEGREES

Solution: Given A= B+ C, and A, Band Care inner angles in a triangle. Thus A+ B+ C= 180   B+ C+ B+ C= 180 => 2(B+ C) = 180 => B+ C= 90. Thus beta will be less than 90.   Hence the answer is 90 DEGREES.
Answer: A
Length of a rectangular plot is 24 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr? Choose the correct choice from the following choices.
A) 52 m B) 62 m C) 72 m D) 82 m E) 92 m

Solution: Let breadth = x metres.   Then, length = (x + 24) metres.   Perimeter = 5300 m = 200 m.   26.50   2[(x + 24) + x] = 200   2x + 24 = 100   2x = 76   x = 38.   Hence, length = x + 24 = 62 m   62 m
Answer: B
8 machines can do a work in 10days. How many machines are needed to complete the work in 40days? Choose the correct choice from the following answers:
A) 2
B) 6
C) 4
D) 7
E) 5

Solution: Required number of machines = 8*10/40= 
8*10/40 = 2
2   2nswer is 2
Answer: A