MU-NLPC/Calc-aqua_rat huggingface dataset:
Find the number of ways of arranging the letters of the word "MATERIAL" such that all the vowels in the word are to come together?
Choose one:
A) 1444
B) 1440
C) 1443
D) 1432
E) 1435

Solution: In the word, "MATERIAL" there are three vowels A, I, E.   If all the vowels are together, the arrangement is MTRL'AAEI'.   Consider AAEI as one unit. The arrangement is as follows.   M T R L A A E I   The above 5 items can be arranged in 5! ways and AAEI can be arranged among themselves in 4!/2! ways.   Number of required ways of arranging the above letters = 5! * 4!/2!   = (120 * 24)/2= 
(120 * 24)/2 = 1_440
1440 ways.   Answer:1440
Answer: B
12+6=792
10+2=110
1+9=9
2+7=16
11+4=??
Solve it?	Answers:
A) 100
B) 120
C) 190
D) 160
E) 154

Solution: x+y=x[y+(x-1)]=x^2+xy-x   12+6=12[6+(12-1)]=792   10+2=10[2+(10-1)]=110   1+9=1[9+(1-1)]=9   2+7=2[7+(2-1)]=16   11+4=11[4+(11-1)]=154   Answer :154
Answer: E
If 20 typists can type 50 letters in 30 minutes, then how many letters will 40 typists working at the same rate complete in 1 hour?	Choose one:	A) 400	B) 500	C) 350	D) 250	E) 200

Solution: No. of letters typing by 20 typists in 30 minutes = 50   No. of letters typing by 20 typists in 60 minutes = 50*2= 
50*2 = 100
100   No. of letters typing by 40 typists in 60 minutes= 100/10*40= 
100/10*40 = 400
400   400nswer : 400
Answer: A
Ages of two sisters differ by 9 years. If 5 years ago, the elder one was twice as old the younger one, find their present age	Choose the correct choice
A) 12,28  B) 14,23  C) 16,32  D) 18,34  E) 19,32

Solution: Explanation:   Let the age of younger sister be x,   Then elder sister's age is (x+9)   => 2(x-5) = (x+9-5) [5 years before]   => 2x-10 = x+4   => x = 14.   So older sister's age is x + 9 = 23   Answer: Option 14,23
Answer: B
Analyze the number square carefully and find out what number fits in place of question mark.
35	20	14
27	12	18
6	4	?	Choices.
A) 6
B) 12
C) 24
D) 36
E) 8

Solution: 20 fits in place of question mark.   This is because (number in first column) / (number in second column) * 8 = number in third column.   Here (left number / middle number) * 8 = right number   (6 / 4) * 8 = 6*2= 
6*2 = 12
12   12
Answer: B
If A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 18 days, then C alone can do it in? Choose the correct choice from the following.
A) 20	B) 22	C) 30	D) 10	E) 9

Solution: C = 1/4 - 1/12 â€“ 1/18 = 1/9 => 9 days   ANSW9R 9
Answer: E
To reach her destination, Jeanette must drive 90 miles. If she drives 5 miles every 6 minutes, how much time will it take her to reach her destination? Choose the most appropriate option
A) 2 hours and 2 minutes
B) 1 hours and 48 minutes
C) 2 hours and 10 minutes
D) 2 hours and 12 minutes
E) 2 hours and 15 minutes

Solution: 6 minute for 5 miles how much for 90? minutes for 1(6/5) mile multiplied by 90 miles.   6*90/5= 
6*90/5 = 108
108> 1 hours 48 min answer is 1 hours and 48 minutes
Answer: B
If the number of 194,n70, where n represents the hundreds digit, is a multiple of 9, then the value of n could be which of the following? Options.
A) 6  B) 5  C) 4  D) 2  E) 1

Solution: Divisibility rule of 9: The sum of the digits must be divisible by 9   i.e 1+9+4+n+7+0 = multiple of 9   or, 21 + n = multiple of 9.   If n=6, 21 + n =27,which is a multiple of 9.   Hence answer is 6.
Answer: A
How many two letter words are formed using the letters of the word BOOK?	Choose the correct answer:
A) 12
B) 10
C) 6
D) 3
E) 9

Solution: The number of letters in the given word is four.   The number of TWO letter words that can be formed using these four letters is 4P2 = 4 * 3= 
4 * 3 = 12
12.   12nswer:12
Answer: A
A gambler bought $4,000 worth of chips at a casino in denominations of $20 and $100. That evening, the gambler lost 16 chips, and then cashed in the remainder. If the number of $20 chips lost was 2 more or 2 less than the number of $100 chips lost, what is the largest amount of money that the gambler could have received back?  Choose the correct choice from the following options
A) $2,040  B) $2,120  C) $1,960  D) $3,120  E) $1,400

Solution: In order to maximize the amount of money that the gambler kept, we should maximize # of $20 chips lost and minimize # of $100 chips lost, which means that # of $20 chips lost must be 2 more than # of $100 chips lost.   So, if # of $20 chips lost is x then # of $100 chips lost should be x-2. Now, given that total # of chips lost is 16: x+x-2=16 --> x=9: 9 $20 chips were lost and 9-2= 
9-2 = 7
7 $100 chips were lost.   Total worth of chips lost is   9*20+7*100= 
  9*20+7*100 = 880
$880, so the gambler kept $4,000-$880=$3,120.   Answer: $3,120
Answer: D
A garrison of 400 men had a provision for 31 days. After 28 days 280 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?	Choose the correct choice from the following answers
A) 16 days	B) 34 days	C) 10 days	D) 16 days	E) 15 days

Solution: 400 --- 31   400 --- 3   120 --- ?   400*3 = 120*x => x   =10 days   Answer: 10 days
Answer: C
The temperature of a certain cup of coffee 2 minutes after it was poured was 120 degrees Fahrenheit. If the temperature F of the coffee t minutes after it was poured can be determined by the formula F = 120*2^(-at) + 60, where F is in degrees Fahrenheit and a is a constant. Then the temperature of the coffee 30 minutes after it was poured was how many degrees Fahrenheit?
Choose the correct answer.
A) 65  B) 60.003662  C) 80.2  D) 85  E) 90

Solution: First, we have to find a.   We know that after t=2 minutes the temperature F=120 degrees.   Hence:   120 = 120*(2^-2a)+60   60 = 120*(2^-2a)   60/120 = 2^-2a   1/2 = 2^-2a   2^-1 = 2^-2a   -1 = -2a   1/2 = a   Now we need to find F after t=30 minutes:   F = 120*(2^-1/2*30)+60   F = 120* (2^-15) +60   F = 120* (1/2^15) +60   F = 120*1/32768 +60   F = 0.003662+60= 
0.003662+60 = 60.003662
60.003662   Answer 60.003662!
Answer: B
Statement: Put thechild in school at the age of 5. Assumptions: At that age the child reaches appropriate level of development and is ready to learn. The schools do not admit children after 6years of age.
Answers
A) Only assumption I is implicit B) Only assumption II is implicit C) Either I or II is implicit D) Neither I nor II is implicit E) Both I and II are implicit

Solution: Since the statement talks of putting the child in school at the age of 5, it means that the child is mentally prepared for the same at this age. So, I is implicit. But nothing about admission after 6 years of age is mentioned in the statement. So, II is not implicit.   Only assumption I is implicit
Answer: A
A number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34. Such a least possible number M is
Choose the correct option.
A) 74  B) M=75  C) M=175  D) M=680  E) 690

Solution: I solved this question by plugging in numbers from the answer choices.   A.) 74   Starting with answer choice A, I immediately eliminated it because 74 is not even divisible by 5.   B.) 75   I divide 75/5 and get 15 as an answer. I divide 75/34 and get a remainder of 7.   15-7= 
15-7 = 8
8 so I know the correct answer isM=75
Answer: B
On what dates of April, 2001 did Wednesday fall?
Choose the correct choice from the following answers.
A) 1st, 8th, 15th, 22nd, 29th  B) 2nd, 9th, 16th, 23rd, 30th  C) 3rd, 10th, 17th, 24th  D) 4th, 11th, 18th, 25th  E) None of these

Solution: EXPLANATION   We shall find the day on 1st April, 2001.   1st April, 2001 = (2000 years + Period from 1.1.2001 to 1.4.2001)   Odd days in 1600 years = 0   Odd days in 400 years = 0   Jan. Feb. March April   (31 + 28 + 31 + 1)= 
(31 + 28 + 31 + 1) = 91
91 days 0 odd days.   Total number of odd days= (0 + 0 + 0)= 
(0 + 0 + 0) = 0
0   On 1st April, 2001 it was Sunday.   In April, 2001 Wednesday falls on 4th, 11th, 18th and 25th.   Answer 4th, 11th, 18th, 25th
Answer: D
At a supermarket, John spent 1/2 of his money on fresh fruits and vegetables, 1/3 on meat products, and 1/10 on bakery products. If he spent the remaining $8 on candy, how much did John spend at the supermarket?	Select:
A) $60	B) $80	C) $90	D) $120	E) $180

Solution: Let's let T = total number of dollars spent at the supermarket. With this variable we can set up an equation and determine T.   We are given that John spent 1/2 of his money on fresh fruits and vegetables, or (1/2)T, 1/3 on meat products, or (1/3)T, and 1/10 on bakery products, or (1/10)T. We are also given that he spent the remaining $8 on candy. Since we know where all his money was allocated, we can sum these values together and set the sum to T. So we have:   (1/2)T + (1/3)T + (1/10)T + 8 = T   To get rid of the fractions we can multiply the entire equation by 30, and we obtain:   15T + 10T + 3T + 240 = 30T   28T + 240 = 30T   240 = 2T   T = 120   John spent $90 at the supermarket.   Answer: $120
Answer: D
The table below shows the enrollment in various classes at a certain college.
Class | Number of Students
Biology | 58
Physics | 35
Calculus | 40
Although no student is enrolled in all three classes, 15 are enrolled in both Biology and Physics, 10 are enrolled in both Biology and Calculus, and 12 are enrolled in both Physics and Calculus. How many different students are in the three classes?  Choose the correct answer:	A) 51	B) 88	C) 90	D) 96	E) 162

Solution: No. of total students = no of students of biology + no of students of physics but not biology + no of students of calculus but not biology and physics   No. of total students = 58 + (35-15) + (40-10-12) = 58+20+18= 
58+20+18 = 96
96   Hence, Answer will be 96.
Answer: D
How many words can be formed by using all the letters of the word “DAUGHTER” so that vowels always come together & vowels are never together?
Choose the correct choice from the following answers
A) 2310  B) 4510  C) 5231  D) 2351  E) 4320

Solution: Given word contains 8 different letters   When the vowels AU4320 are always together we may suppose   them to form an entity ,treated as one letter   then the letter to be arranged are DAHTR(AU4320)   these 6 letters can be arranged in 6p6 = 6!   = 720 ways   The vowels in the group (AU4320) may be arranged in 3! = 6 ways   Required number of words = 760 * 6 =4320   Ans: 4320
Answer: E
How many possible ways are there to select 3 stocks at random from 7 stocks?
Choose the correct choice from the following answers:
A) 26
B) 29
C) 32
D) 35
E) 38

Solution: 7C3 = 35   The answer is 35.
Answer: D
If Raj walks at 12.5 km/hr instead of 10 km/hr, he would have walked 6 km more. The actual distance traveled by him during this period is? Choose the most appropriate option:
A) 10
B) 11
C) 12
D) 13
E) 24

Solution: Let the actual distance traveled is 'x' km   Then by given conditions, we have   x/10 = (x+6)/12.5   12.5x = 10x + 60   x = 24 km   Ans- 24
Answer: E
If the population of a certain country increases at the rate of one person every 30 seconds, by how many persons does the population increase in 10 minutes?  Choose the correct choice from the following choices
A) 20
B) 30
C) 15
D) 10
E) 80

Solution: 20nswer = 2 * 10= 
2 * 10 = 20
20   20nswer= 20
Answer: A
Length of a rectangular plot is 20 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:	A) 45 m	B) 60 m	C) 57 m	D) 69 m	E) 78 m

Solution: Let breadth = x metres.   Then, length = (x + 20) metres.   Perimeter = 5300 m = 200 m.   26.50   2[(x + 20) + x] = 200   2x + 20 = 100   2x = 80   x = 40.   Hence, length = x + 20 = 60 m   60 m
Answer: B
The maximum number of students among them 1230 pens and 920 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is:  Choose the correct option: A) 91 B) 10 C) 1001 D) 1911 E) None of these

Solution: Explanation:   Required number of students = H.C.F of 1230 and 920 = 10. Answer: 10
Answer: B
A train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 85 seconds. What is the length of the train in meters?	Choose the most appropriate option.
A) 400 meters
B) 1111 meters
C) 160 meters
D) 850 meters
E) None of these

Solution: Train overtakes a bike means that we are talking about total length of the train. (train's head is close to bike when it started and its tail crosses the bike when it overtakes the bike)   Relative speed= 100-64= 
100-64 = 36
36Km/h= 36000 m/h   time= 85 seconds   Distance= speed*time    36000* 85/3600= 
 36000* 85/3600 = 850
850 meters.   850 meters is the answer.
Answer: D
The ratio of the incomes of Lakshmi and Latha is 5:4 and the ratio of their expenditure is 4:3. If at the end of the year, each saves $6000 then the income of Lakshmi is?
Choose the most appropriate option
A) $26000	B) $20000	C) $23000	D) $25000	E) $22000

Solution: Let the income of Lakshmi and Latha be $5x and $4x   Let their expenditures be $4y and $3y   5x-4y = 6000-------1)   4x-3y = 6000-------2)   From 1) and 2)   x = 6000   Lakshmi's income = 5x = 5*5000= 
5*5000 = 25_000
$25000   Answer is $25000
Answer: D
If daily wages of a man is four times to that of a woman, how many men should work for 20 days to earn Rs.14400? Given that wages for 40 women for 30 days are Rs.21600.  Choose the correct choice.
A) 10 B) 14 C) 16 D) 18 E) 20

Solution: Explanation :   Wages of 1 woman for 1 day = 21600/40Ã—30   Wages of 1 man for 1 day = 21600Ã—4/40Ã—30   Wages of 1 man for 20 days = 21600Ã—4Ã—20/40Ã—30   Number of men = 14400/(21600Ã—4Ã—20/40Ã—30)=144/(216Ã—80/40Ã—30)=10   10nswer : Option 10
Answer: A
One half of a two digit number exceeds its one third by 7. What is the sum of the digits of the number?	Choose the correct choice from the following answers:	A) A)3	B) B)5	C) C)7	D) D)9	E) E)10

Solution: x/2 – x/3 = 7 => x =46   4 + 6= 
4 + 6 = 10
10   ANSW10R:10
Answer: E
Doug, who runs track for his high school,
was challenged to a race by his younger
brother, Matt. Matt started running first,
and Doug didn’t start running until Matt
had finished a quarter-mile lap on the
school track. Doug passed Matt as they
both finished their sixth lap. If both boys
ran at a constant speed, with Doug running
2 miles an hour faster than Matt, what was
Matt’s speed?
Choices:
A) 10.5 miles per hour
B) 10 miles per hour
C) 9 miles per hour
D) 8 miles per hour
E) 7.5 miles per hour

Solution: Doug runs 2 miles an hour faster than Matt, so let Matt’s speed equal x miles per hour.   Then Doug’s speed equals x + 2 miles per hour. Each lap is one-quarter of a mile, so Doug   runs 1.5 miles in the time it takes Matt to run 1.25 miles. Place this information in a chart:   DOUGH RATE:x-2 TIME:1.5/1 DISTANCE:1.5   MATT RATE:X TIME:1.25/X DISTANCE:1.25   The two boys took the same amount of time from the time Doug started, so make an   equation by setting the two times in the chart equal to each other, and then solve for x:   1.5/X+2=1.25/X   1.5X=1.25(X+2)   1.5X=1.25X+2.5   0.25X=2.5   X=10   So Matt ran at 10 miles per hour.   correct answer 10 miles per hour)10 miles per hour
Answer: B
A person plans to start a business with x% of a list of 10,000 products in his inventory. Next year after a business loss, the person wants to reduce the list by (x − 4)%. In terms of x, how many products will be in the inventory?	Select the correct option.
A) x*x – 4x
B) (x)(104 – x)
C) (100)(104 – x)
D) (100)(96 – x)
E) (x-4)/100

Solution: Based on the answer choices and the question, this question begs the use of x=4 as a sample number.   Initial = 4%*10000 = 400   Reduction = 4-4= 
4-4 = 0
0%, so no math required here to calculate the reduction; just make sure that you can calculate 400 in your answer.   A. x*x – 4x= 0; No   B. (x)(104 – x) = 400; Winner!   C. (100)(104 – x) > 400; No   D. (100)(96 – x) > 400; No   E. (x-4)/100 = 0; No   (x)(104 – x)
Answer: B
A grocer has 400 pounds of coffee in stock, 20 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated?  Choose the correct choice from the following choices:
A) 28%
B) 30%
C) 32%
D) 34%
E) 40%

Solution: 1. 20% of 400=80 pounds of decaffeinated coffee   2. 60% of 100=60 pounds of decaffeinated coffee   3. Wt have 140 pounds of decaffeinated out of 500 pounds, that means 140/500*100= 
140/500*100 = 28
28%.   The correct answer is 28%.
Answer: A
A father was as old as his son's present at the time of your birth. If the father's age is 38 years now, the son's age 5years back was? Answers:	A) 10 years	B) 12 years	C) 14 years	D) 15 years	E) 16 years

Solution: Let the son's present age be x years. Then, (38 - x) = x   2x = 38.   x = 19.   Son's age 5 years back (19 - 5)= 
(19 - 5) = 14
14 years.   14 years
Answer: C
If n is an integer and n^4 is divisible by 32, which of the following could be the remainder when n is divided by 32?
Answers:
A) 2
B) 4
C) 5
D) 6
E) 10

Solution: Given:   n^4/32 = int   n^4/2^5 = int   1/2(n/2)^4 = int   try n= int = 2,4,6,8... because n/2 must be an integer   n=2 wont work because 1/2(n/2)^4 needs to be an integer.   n=4, result = 1/2 (2)^4 = 8, so the remainder of n/32 = remainder of 8/32 = 8 (not an option)   n=8, result = 1/2(8/2)^4 = 1/2(4)^4 = 1/2x16x16= 16x8, so the remainder of n/32 = remainder of 16x8/32 = 4 (option 4)
Answer: B
The average monthly salary of 20 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary?
Select.
A) 2000  B) 3000  C) 3600  D) 4800  E) 4000

Solution: Manager's monthly salary   = Rs. (1600 * 21 - 1500 * 20) = Rs. 3600   ANSWER 3600
Answer: C
n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4 ? Choose the most appropriate option:
A) 2	B) 4	C) 7	D) 9	E) 11

Solution: Let n = 4q + 3. Then 2n = 8q + 6 = 4(2q + 1 ) + 2.   Thus, when 2n is divided by 4, the remainder is 2.   Option 2
Answer: A
In what time will a train 300 m long cross an electric pole, it its speed be 144 km/hr?  Choose the correct choice from the following:
A) 2.5 sec  B) 9.7 sec  C) 3.5 sec  D) 2.9 sec  E) 7.5 sec

Solution: Speed = 144 * 5/18= 
144 * 5/18 = 40
40 m/sec   Time taken= 300/40= 
300/40 = 15/2 = around 7.5
7.5 sec.   Answer: 7.5 sec
Answer: E
24 = 3a + 5b
3 > |–a|
If ‘a’ and ‘b’ are both integers, then what is the highest possible values of ‘b’ that can be used to solve the above equation.  Choose the correct choice from the following answers:
A) 2	B) 3	C) 4	D) 5	E) 6

Solution: Let us understand the meaning of 5 > |-a|   1) when we write |-x| this means the same as |x|.   2) Mod is very easy concept if you solve mod question by considering as a distance. when a mod is written as |x-(a)| = b, this means the distance from point 'a' (both side left and right of 'a' on number line) is b. |x-(a)| < b means the distance is between the two extreme distance(left and right side of 'a' on number line, considering the max distance is 'b' from 'a' - as per this scenario.....hence the value of 'a' must be between these two extremes. |x-(a)| > b means the distance is greater than the distance of 'b'..i.e the value of a could be anywhere more than 'b'.   Now come to the question. First its given|-a| < 3 ==> |a| < 3 ===> |a-0| < 3 ==> the distance from zero is less than 3. So the point ‘a’ will be -2,-1,0,1,2 as distance from 0 to these values is less than 3.   Now, lets move to equation 3a + 5b = 24 ==> b = (24 – (3 * a))/5. According to question, b is an integer, hence to make ‘b’ integer (24 – (3*a)) must be divisible by 5. Now remove the value which can’t make (24-(3*a)) divisible by 5 from the possible values of a. It will remain is -2. With only one value of ‘a’ we can have only one value of ‘b’ and that is b = (24 – 3 *(-2))/5 ==> b = (24 + 6)/5 ==> b = 6. Hence the highest value that b can take is 6 and the answer is 6 (value 6).
Answer: E
Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 15 minutes. The waste pipe can empty the full cistern in? Choose the correct choice from the following answers.
A) 10 min
B) 7 min
C) 5 min
D) 9 min
E) 4 min

Solution: 1/10 + 1/15 - 1/x   = 1/10   x = 10   10 minnswer: 10 min
Answer: A
A trader purchased two colour televisions for a total of Rs. 35000. He sold one colour television at 30% profit and the other 40% profit. Find the difference in the cost prices of the two televisions if he made an overall profit of 32%?	Choose the correct choice from the following answers:	A) Rs.21000	B) Rs.21028	C) Rs.21098	D) Rs.21021	E) Rs.21007

Solution: Let the cost prices of the colour television sold at 30% profit and 40% profit be Rs. x and Rs. (35000 - x) respectively.   Total selling price of televisions = x + 30/100 x + (35000 - x) + 40/100 (35000 - x)   => 130/100 x + 140/100 (35000 - x) = 35000 + 32/100 (35000)   x = 28000   35000 - x = 7000   Difference in the cost prices of televisions = Rs.21000   Rs.21000nswer:Rs.21000
Answer: A
In August,a cricket team that played 120 matches won 28% of the games it played.After a continuous winning streak,this team raised its average to 52%.How many matches did the team win to attain this average?
Choose one
A) 40 B) 52 C) 60 D) 80 E) 98

Solution: let the no of matches played more=x   so,   (120+x)*52/100=33.6+x   by solving we get x=60   ANSWER:60
Answer: C
If 13 lions can kill 13 deers in 13 minutes how long will it take 100 lions to kill 100 deers?  Choose the correct choice from the following.
A) 1 minutes	B) 13 minute	C) 100 minutes	D) 10000 minutes	E) 1000 minutes

Solution: we can try the logic of time and work,our work is to kill the deers so 13(lions)*13(min)/13(deers)=100(lions)*x(min)/100(deers)hence answer is x=13   ANSWER:13 minute
Answer: B
In a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class?	Pick
A) 12 Years B) 12.3 Years C) 12.6 Years D) 13 Years E) 15 Years

Solution: Total age of 50 students   (30X 13+20 X 12) = 630   Average = 630/50= 
630/50 = 63/5 = around 12.6
12.6 Years   12.6 Years
Answer: C
How many positive three-digit integers are divisible by both 3 and 5?	Answers: A) 50 B) 60 C) 65 D) 70 E) 80

Solution: A number to be divisible by both 3 and 5 should be divisible by the least common multiple of 3 and 5 so by 15.   Multiples of 15 between 100 and 999, inclusive is   (last-first)/multiple+1=(990-105)/15+1=59+1= 
59+1 = 60
60   Answer: 60.
Answer: B
Abel can complete a work in 10 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but Abel had to leave after 3 days and Ben 4 days before the completion of the work. How long did the work last? Choose the correct option: A) 6 8/9 B) 7 C) 8 D) 9 E) 10

Solution: Abel in the 3 days that he worked completed 3/10 of the job = 7/10 remains   Then if Ben had to leave 4 days before the completion, this means that Carla had to work alone for these 4 days in which she completed 4/15 of the job.   Now together, Ben and Carla completed the job in (1/12 + 1/15)(t) = 13/30   3/20 (t) = 13/30 ---> t = 26/9=2 8/9   Therefore, these 2 8/9 days worked plus the 4 days that Carla had to work by herself add to 6 8/9 days   6 8/9nswer: 6 8/9
Answer: A
How many times are the hands of a clock at right angle in a day?	Pick one
A) 22	B) 24	C) 44	D) 34	E) 38

Solution: In 12 hours, they are at right angles 22 times.   In 24 hours, they are at right angles 44 times.   Answer: Option 44
Answer: C
Townville has 100 residents, and 20 of them are females. If half of Townville’s male residents are smokers, and 1/2 of the female residents are smokers, which of the following represents the total number of Townville’s residents who are NOT smokers?	Pick one:
A) 40
B) 45
C) 50
D) 55
E) 60

Solution: Number of people =100   Females = 20   men = 100-20= 
100-20 = 80
80   Half of the men are smoker  80/2= 
  80/2 = 40
40, that means the remaining men 80-40= 
80-40 = 40
40 are non smokers.   1/2 females are smoker. i.e 1/2*20= 10   20-10= 
20-10 = 10
10 females are non smokers   So, total number of non smokers in the town are 40+10= 
40+10 = 50
50   Answer : 50
Answer: C