MU-NLPC/Calc-aqua_rat huggingface dataset:
A started a business with Rs.25000 and is joined afterwards by B with Rs.30,000. After how many months did B join, if profit per annum is divieded equally?	Choose the most appropriate option:
A) 2 months B) 4 months C) 5 months D) 7 months E) 9 months

Solution: Given their profits are equal per annum so   25000*12=30000*x   x=10 months    12-10= 
 12-10 = 2
2 months   2 monthsNSWER:2 months
Answer: A
If k is a non-negative integer and 15^k is a divisor of 759,325 then 3^k - k^3 = Choose the correct choice from the following options
A) 0	B) 1	C) 37	D) 118	E) 513

Solution: At first we should understand whether 759325 divisible by 15.   15 is equal to 3 * 5 so 759325 should be divisible on these integers   759325 is divisible by 5 because of last digit 5   but not divisible by 3 because sum of its digits doesn't divisible by 3: 7 + 5 + 9 + 3 + 2 + 5 = 31 and 31 doesn't divisible by 3   so 759325 can be divisible by 15^k only if k = 0 and 15^k = 1   so 3^k - k^3 = 1 - 0= 
1 - 0 = 1
1   Answer is 1
Answer: B
Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 10 hours and 8 hours respectively. The ratio of their speeds is	Choose the correct choice from the following:
A) 4 : 9	B) 4 : 3	C) 4 : 12	D) 4 : 8	E) 4 : 5

Solution: Let us name the trains as A and B. Then, (A's speed) : (B's speed) = b : a = 8 : 10 = 4 : 5.Answer: 4 : 5
Answer: E
J and M were each paid x dollars in advance to do a certain job together. J worked on the job for 12 hours and M worked for 2 hours less than J. If M gave J y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that J was paid in advance?
Choose the correct choice from the following answers:	A) a)4y	B) b)5y	C) c)6y	D) d)11y	E) e)10y

Solution: J and M were both paid x dollars   If M gave Y dollars from her X to J then at the end   J will have X+Y dollars   M will have X- Y dollars   Now since the hourly wages have to be same then   Hourly wage of J = (X+Y) / 12 (Since J worked for 12 hrs)   Hourly wage of M = (X-y) /10 (Since M worked 2 hrs less than J)   Equating both   (X+Y)/12=(X-Y)/10   on simplifying X=11y   Answer d)11y
Answer: D
A bowl contains pecans, cashews, and almonds in a ratio of 7 : 12 : 18, respectively. If some of the nuts of one of the three types are removed, which of the following could be the ratio of pecans to cashews to almonds remaining in the bowl? i. 1 : 2 : 3 ii. 2 : 3 : 4 iii. 4 : 7 : 10  Pick one
A) I only	B) III only	C) I,II only	D) II only	E) II,III only

Solution: i. The ratio 2 : 3 is the same as the given ratio 12 : 18. If one pecan were removed, the new ratio would be 6 : 12 : 18, or 1 : 2 : 3.   ii. None of the nuts currently have a ratio of 3 : 4. The cashews and almonds do have a ratio of 2 : 3, but there are not enough pecans in the bowl to complete the ratio.   iii. The ratio 4 : 10 is the same as the given ratio 6 : 15. To see this, multiply the ratio by 3/2 . The new ratio is 6 : 10.5 : 15. Unfortunately, this means that there are fewer cashews that this ratio would require. Removing cashews won’t create the desired ratio.   I onlynswer : I only
Answer: A
Current ages of Rahim and Thomas are in the ratio of 5 : 4 correspondingly. 0.2 decades hence, the ratio of their ages will become 11 : 9 correspondingly, What is Thomasâ€™s current age in years?  Choose the correct choice from the following options:
A) 24 years B) 44 years C) 34 years D) 64 years E) 16 years

Solution: 16 years   If current ages of Rahim and Thomas be 5A years and 4A years correspondingly   Then, 5A + 2 = 11   4A + 2 = 9   9(5A + 2)=11(4A + 2)   A = 4   Thomasâ€™s current age = 4A   = 16 years.   16 years
Answer: E
Four milkmen rented a pasture. A grazed 24 cows for 3 months; B 10 for 5 months; C 35 cows for 4 months and D 21 cows for 3 months. If A's share of rent is Rs. 2160, find the total rent of the field. Select.
A) 3750 B) 3550 C) 4250 D) 9750 E) 3250

Solution: Ratio of shares of A, B, C, D = (24 x 3) : (10 x 5) : (35 x 4) : (21 x 3) = 72 : 50 : 140 : 63.   Let total rent be Rs. x. Then, A’s share = Rs. (72x)/325   (72x)/325=2160 = x=(2160 x 325)/72 = 9750   Hence, total rent of the field is Rs. 9750.   Answer is 9750.
Answer: D
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 answer.
A) 45 kmph  B) 25 kmph  C) 30 kmph  D) 50 kmph  E) None of these

Solution: Explanation:   Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec.   [(25/2) x (18/5)] km/hr = 45 km/hr.   Let the speed of the train be 'S' km/hr.   Then, relative speed = (S - 5) km/hr.   S - 5 = 45 => S = 50 km/hr.   ANSWER IS 50 kmph
Answer: D
Sreedhar and Sravan together can do a work in 25 days. With the help of Pavan, they completed the work in 8 days and earned Rs. 225. What is the share of Sravan, if Sreedhar alone can do the work in 75 days?	Choose the correct choice from the following choices:	A) 22	B) 26	C) 48	D) 77	E) 12

Solution: Sravan's one day's work = 1/25 - 1/75 = 2/75   Sravan worked for 8 days. So, his 8 days work = 8 * 2/75 = 16/75   Sravan completed 16/75th of total work.   So, his share is 16/75 * 225 = Rs. 48.   Answer:48
Answer: C
An examiner rejects 0.16% of the meters as defective. How many will be examine to reject 4?	Choose the correct choice from the following answers
A) 500	B) 4000	C) 2500	D) 5500	E) None of these

Solution: Explanation :   Solution: let the number of meters to be examined be x. then, 0.16% of x = 4   =>(16/100 * 1/100 * x) = 4   =>x = (4*100*100)/16= 
(4*100*100)/16 = 2_500
2500.   Answer : 2500
Answer: C
An object thrown directly upward is at a height of h feet after t seconds, where h = -14 (t-3)^2 + 150. At what height, in feet, is the object 2 seconds after it reaches its maximum height?  Choose the correct choice from the following answers.
A) 80 B) 88 C) 94 D) 112 E) 124

Solution: We see that h will be a maximum h=150 when t-3=0, that is when t=3.   At t=5, h = -14(5-3)^2 + 150 = -14(4) + 150 = 94   The answer is 94.
Answer: C
In a forest 150 deer were caught, tagged with electronic markers, then released. A week later, 50 deer were captured in the same forest. Of these 50 deer, it was found that 10 had been tagged with the electronic markers. If the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest, and if no deer had either left or entered the forest over the preceding week, what is the approximate number of deer in the forest?
Choose the correct choice
A) 150	B) 750	C) 3,000	D) 1,500	E) 2,500

Solution: The percentage of tagged deer in the second sample = 10/50*100= 
10/50*100 = 20
20%.   So, 150 tagged deers comprise 10% of total # of deers --> total # of deers= 150*20 = 3,500.   Answer: 3,000
Answer: C
There are 15 points in a given plane, no three of which are on the same line. If one of the points is represented as 'Y', then how many triangles can be determined with the 15 points that contain the point Y?
Choose the correct choice from the following choices:
A) 91
B) 105
C) 182
D) 210
E) 455

Solution: Fist point is A which is fixed so can be selected in 1 way   Second point can be selected in 14 ways   Third point can be selected in 13 ways   so total ways = 1x14x13 = 182   but answer is 91 which is 182/2=182
Answer: C
if 70% of (x-y) = 30% of (x+y) then what percent of x is y? Choose the correct choice from the following answers:
A) 2.5%  B) 40%  C) 5%  D) 15%  E) 25%

Solution: 70% of (x-y)=30% of(x+y)   (70/100)(x-y)=(30/100)(x+y)   7(x-y)=3(x+y)   4x=10y   x=5/2y   therefore required percentage   =((y/x) X 100)% = ((y/(5/2)y) X 100) =40%   Answer is 40%.
Answer: B
A and B can do a work in 8 hours and 12 hours respectively. A starts the work at 6AM and they work alternately for one hour each. When will the work be completed?	Select the correct option:
A) 9.6 days
B) 7.6 days
C) 4 days
D) 8.6 days
E) 6.6 days

Solution: Work done by A and B in the first two hours, working alternately = First hour A + Second hour B = 1/8+ 1/12 = 5/24.   Total time required to complete the work = 2 * 24/5= 
2 * 24/5 = 48/5 = around 9.6
9.6 days.   9.6 daysNSWER:9.6 days
Answer: A
If KING is coded as 17 and DON is coded as 18 Then MASS is coded as
Answers.
A) 21  B) 20  C) 19  D) 29  E) None

Solution: KING = 11+9+14+7= 
11+9+14+7 = 41
41 i.e (4*4)+(1*1)=17   MASS = 13+1+19+19= 
13+1+19+19 = 52
52 i.e (5*5)+(2*2)=29   29ON = 4+14+15= 
4+14+15 = 33
33 i.e(3*3)+(3*3)=18   ANSWER:29
Answer: D
Judges will select 5 finalists from the 7 contestants entered in a singing competition. The judges will then rank the contestants and award prizes to the 3 highest ranked contestants: a blue ribbon for first place, a red ribbon for second place, and a yellow ribbon for third place. How many different arrangements of prize-winners are possible?  Choose one:	A) 10	B) 21	C) 210	D) 420	E) 1,260

Solution: First Select 5 from 7 contestants and then select top 3 from those 5 =   72105*52103 = 42 * 5= 
42 * 5 = 210
210   ANS:210
Answer: C
A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 40% marks is Choose the correct choice from the following options.
A) 5  B) 4  C) 3  D) 2  E) 1

Solution: Here we can assume that one subject is of 100 marks so total there are 5 subjects => 100*5= 
100*5 = 500
500.   Now according to the question he secured 60 % of those which is 60%of 500= 300 marks in total.   The ratio between the marks is given as 6 : 7 : 8 : 9 : 10 , so now we can distribute 300 marks according to the ratio.   Total ratio = 40   For 6 : (300/40)*6= 
(300/40)*6 = 45
45   Similarly , we will get for others as 52.5 , 60 , 62.5 , 75.   Hence , there are 4 subject where he secured more that 40 %.   The answer is 5.   5
Answer: A
If 7^w is a factor of the product of the integers from 1 to 100, inclusive, what is the largest value of w? Choose one:  A) 12  B) 13  C) 14  D) 15  E) 16

Solution: So the question just means that we have to find all the multiples w of 7 between 1 to 100   So there are 14 multiples of 7 ( 7 - 98)   But 49 and 98 contain two 7's as factors   so we have to add  14 + 2= 
 14 + 2 = 16
16   16
Answer: E
24 oz of juice P and 25 oz of juice V are mixed to make smothies A and Y . The ratio of p to V in smothie A is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie A? Choose the correct choice from the following options:	A) 5	B) 10	C) 15	D) 20	E) 25

Solution: The ratio of p to V in smothie X is 4 is to 1 and that in Y is 1is to 5. p1 + p2 = 24   v1 + v2 = 25   p1 = 4v1   p2 = v2/5   4v1 + v2/5 = 24   v1 + v2 = 25   4v2 - v2/5 = 76   19v2/5 = 76 => v2 = 20   => v1 = 5   => p1 = 20   Answer - 20
Answer: D
Lucy bought a 1-year,10000 certificate of deposit that paid interest at an annual rate of 8 percent compunded semiannually. What was the total amount of interest paid on this certificate at maturity ? Select: A) 10464 B) 864 C) 816 D) 800 E) 480

Solution: Solution:   It says, 8 percent per annum per compounded semi annually.   Therefore r = 8/2= 
8/2 = 4
4% .   So, P= 10000   r = 4   n = 2   Net Amount A = 10816, I = 800.   ANSWER:800
Answer: D
A shop owner sells 30mtr of cloth and gains SP of 10 mtrs. Find the gain %?	Choices:
A) 30%	B) 40%	C) 50%	D) 60%	E) 70%

Solution: Here, selling price of 10 m cloth is obtained as profit.   Profit of 10 m cloth = (S.P. of 30 m cloth) – (C.P. of 30 m cloth)   Selling price of 20 m cloth = Selling Price of 30 m of cloth   Let cost of each metre be Rs. 100.   Therefore, cost price of 20 m cloth = Rs. 2000 and S.P. of 20 m cloth = Rs. Rs. 3000   Profit% = 10 × 100 = 50%   20   Profit of 50% was made by the merchant.   50%
Answer: C
For some integer x, x^2 - 5 is divisible by all of the following EXCEPT  Choose the correct choice from the following.
A) 41  B) 38  C) 29  D) 31  E) 30

Solution: Hint: x^2-5 (x is an integer) is never multiple of 3 (try to prove this), hence 30 is out.   Answer: 30
Answer: E
The number x of cars sold each week varies with the price y in dollars according to the equation x = 800,000 – 50y. What would be the total weekly revenue W, in dollars, from the sale of cars priced at $ 15,000?
Choose the correct choice from the following options.
A) 50,000  B) 750,000  C) 850,000  D) 7,500,000  E) W=750,000,000

Solution: number of cars sold = x=800000-50y   y=15000   x=800000-750000= 
800000-750000 = 50_000
50000   revenue from 50000 cars=15000*50000= 
15000*50000 = 750_000_000
750000000 W=750,000,000
Answer: E
In an election between two candidates, 75% of the voters cast thierthier votes, out of which 2% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election.	Choose the correct choice from the following answers:  A) 1600  B) 16000  C) 16800  D) 1680  E) 16870

Solution: Let the number of votes enrolled be x. Then ,   Number of votes cast =75% of x. Valid votes = 98% of (75% of x).   75% of (98% of (75%of x)) =9261.   [(75/100)*(98/100)*(75/100)*x] =9261.   X = [(9261*100*100*100)/(75*98*75)= 
(9261*100*100*100)/(75*98*75) = 16_800
16800.   ANSWER 16800 16800
Answer: C
KODAK bank offers an interest of 5% per annum compounded annually on all its deposits. If $10,000 is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year? Choices:
A) 1:5  B) 625:3125  C) 100:105  D) 100^4:105^4  E) 725:3225

Solution: Hi Bunuel,   Here is my approach: is this correct?   KODAK bank offers an interest of 5% per annum compounded annually on all its deposits.   Interest earned in 4 year= 10000(1+0.05)^4   Interest earned in 5 year= 10000(1+0.05)^5   Ratio= {10000(1.05)^4}/{10000(1.05^5)} =>1.05^4/1.05^5 =>1/1.05 Multiplied by 100 in both numerator and denominator gives 100:105   Hence Ans:100:105
Answer: C
Virat buys an old car for Rs. 60000 and spends Rs. 4000 on its repairs. If he sells the scooter for Rs. 65000, his gain percent is:  Choose one
A) 3 (4/7) % B) 11 (1/9) % C) 12 (2/3) % D) 1.6% E) None of these

Solution: Explanation:   C.P. = Rs. (60000 + 4000) = Rs. 64000   S.P. = Rs. 65000.   Gain% = ( (1000 / 64000) * 100 ) % = 1.6%   ANSWER 1.6%
Answer: D
Of the 800 employees of Company X, 30 percent have been with the company for at least ten years. If y of theselong-termmembers were to retire and no other employee changes were to occur, what value of y would reduce the percent oflong-termemployees in the company to 20 percent ?  Choices:
A) 200 B) 160 C) 112 D) 80 E) 100

Solution: The # oflong-termemployees is 30%*800=240.   After y of them retire new # oflong-termemployees would become 240-y.   Total # of employees would become 800-y.   We want 240-y to be 20% of 800-y --> 240-y=(800 -y)*20% --> y = 100.   Answer: 100.
Answer: E
A solution of 90 litres contains milk and water in the ratio 7:x. If ten litres of water is added to the solution, the ratio becomes 3:2, find the value of x? Pick one: A) 2 B) 1.5 C) 3.5 D) 2.5 E) 3

Solution: Exp. Total new quantity = original sol + water =90+10= 
90+10 = 100
100   New ratio= 3:2, New quantity of milk =3/5*100= 
3/5*100 = 60
60 Lit,   New quantity of water= 2/5*100= 
2/5*100 = 40
40 Lit   Water present initially= (40-10)= 
(40-10) = 30
30 Lit   Ratio= 60/30 =7/x There for x = 3.5   Answer: 3.5
Answer: C
A rectangular-shaped carpet remnant that measures x feet by y feet is priced at $70. What is the cost of the carpet, in dollars per square yard? (9 square feet = 1 square yard) Select the correct option
A) 70xy
B) 630xy
C) xy/9
D) xy/70
E) 630/(xy)

Solution: xy sq ft = $70   1 sq ft = $70/xy   multiplying by 9 on both side   9 sq ft = $630/xy   or 1 sq yard = $630/xy   Hence 630/(xy).
Answer: E
A man in a train notices that he can count 41 telephone posts in one minute. If they are known to be 50 metres apart, then at what speed is the train travelling?
Pick.
A) 620 km/hr  B) 220 km/hr  C) 220 km/hr  D) 120 km/hr  E) 203 km/hr

Solution: Explanation:   Number of gaps between 41 poles = 40   So total distance between 41 poles = 40*50= 
40*50 = 2_000
2000 meter= 2 km   In 1 minute train is moving 2 km/minute.   Speed in hour = 2*60= 
2*60 = 120
120 km/hour   Answer: 120 km/hr
Answer: D
An investor deposited $10,000 to open a new savings account that earned 8 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in the account 6 months after the account was opened?
Choices:  A) $10,200  B) $10,202  C) $10,400  D) $10,404  E) $10,800

Solution: The amount in the account after 6 months is 1.02*1.02($10,000) = $10,404.   The answer is $10,404.
Answer: D
Find the odd man out. 30, -5, -45, -90, -145, -195, -255	Choose the correct choice from the following choices
A) -145
B) -195
C) -30
D) -90
E) -5

Solution: 30   30 - 35 = -5   -5 - 40 = -45   -45 - 45 = -90   -90 - 50 = -140   -140 - 55 = -195   -195 - 60 = -255   Hence, -145 is wrong. -140 should have come in place of -145   -145nswer is -145
Answer: A
How many positive integers less than 8,000 are there in which the sum of the digits equals 5?	Pick:
A) 57
B) 56
C) 55
D) 54
E) 53

Solution: Basically, the question asks how many 4 digit numbers (including those in the form 0XXX, 00XX, and 000X) have digits which add up to 5. Think about the question this way: we know that there is a total of 5 to be spread among the 4 digits, we just have to determine the number of ways it can be spread.   Let X represent a sum of 1, and | represent a seperator between two digits. As a result, we will have 5 X's (digits add up to the 5), and 3 |'s (3 digit seperators).   So, for example:   XX|X|X|X = 2111   ||XXX|XX = 0032   etc.   There are 8C3 ways to determine where to place the separators. Hence, the answer is 8C3 = 56.   56
Answer: B
In a deck of cards there are 50 cards numbered from 1 to 13. There are 4 cards of each number in the deck. If you insert 12 more cards with the number 10 on them and you shuffle the deck really good, what is the probability to pull out a card with a number 10 on it? Pick one:	A) 1/4.	B) 4/17.	C) 5/29.	D) 8/31.	E) 1/3.

Solution: 4+12 tens/50+12 total cards=16/62=8/31   8/31.
Answer: D
If x is a whole number, then x²(x² - 1) is always divisible by	Choose one:
A) 12-x  B) Multiple of 12  C) 12  D) 24  E) 48

Solution: Putting x = 2,we get 2²(2² - 1) = 12.   checking with other integers, the above equation always gives a value which is a multiple of 12,   So, x²(x² - 1) is always divisible by 12.   ANSWER:12
Answer: C
The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? Choices.
A) 2.3	B) 2.5	C) 3.5	D) 3.6	E) 4.6

Solution: Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)]   = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20.   Required average = (9.2 / 2) = 4.6.   4.6
Answer: E
AB
+BA
___
121
In the addition problem above, A and B represent digits in two different two-digit numbers. What is the sum of A and B?  Choose the most appropriate option.
A) 6
B) 8
C) 9
D) 11
E) 14

Solution: two ways to do it..   1) straight logic..   we can see that ones digit is 1 when units digit B and A are added..   answer has to be 1 in the units digit..   only 11 fits in..   2) BA=10B+A, and   AB=10A+B..   it is given that BA+AB=121..   or 10B+A +10A+B=121..   11(A+B)=121..   so A+B=11..   ANSWER:11
Answer: D
Calculate the average mark scored by Adam if he had the following scores in an examination: 86, 75, 72, 63 and 65 marks (out of 100) in French Language, Geography, Art and design, History and Physical Education respectively?	Pick:
A) 39.2
B) 79.2
C) 72.2
D) 71.2
E) 76.2

Solution: Explanation:   Average mark = 86+75+72+63+65/5=72.2   Answer: Option 72.2
Answer: C
Light glows for every 15 seconds . How many max. times did it glow between 1:57:58 and 3:20:47 am.
Choose the correct option: A) 380 times B) 381 times C) 382 times D) 392 times E) 331 times

Solution: Time difference is 1hr,22min,49sec=4969sec. So, light glows floor(4969/15)=331 times.   ANSW331 timesR:331 times
Answer: E
If both 5^3 and 3^4 are factors of n x (2^5) x (12^2) x (7^3) x (10^2), what is the smallest possible positive value of n?	Choose the correct choice from the following answers:
A) 15
B) 45
C) 75
D) 125
E) 150

Solution: (2^5) x (12^2) x (7^3) x (10) has two appearances of 3 (in 12^2) and two appearances of 5 (in 10^2).   Thus n must include at least 3^2 * 5 = 45   The answer is 45.
Answer: B
In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 46, the dividend is?
Choose the most appropriate option
A) 5320
B) 5325
C) 5330
D) 5334
E) 5336

Solution: Divisor = (5 * 46)= 
(5 * 46) = 230
230= 10 * Quotient = Divisor   => Quotient = 230/10= 
230/10 = 23
23   Dividend= (Divisor * Quotient) + Remainder   Dividend = (230 * 23) + 46= 
(230 * 23) + 46 = 5_336
5336   5336)
Answer: E
Suppose, the speed of any positive integer n is defined as follows:
seed(n) = n, if n < 10
= seed(s(n)), otherwise,
where s(n) indicates the sum of digits of n.For example, seed(7) = 7, seed(248) = seed(2 + 4 + 8) = seed(14) = seed(1 + 4) = seed(5) = 5 etc. How many positive integers n, such that n < 500, will have seed (n) = 9?	Options:
A) 39
B) 72
C) 81
D) 108
E) 55

Solution: Explanation :   We need to find out numbers less than 500, with sum of digits as 9.   We know that a number will be divisible by 9, if the sum of its digits is divisible by 9.   For eg : 18 has sum of digits 9.   198 has sum of digits 18, which has its sum of digits 9.   So, we need to find numbers less than 500 which are divisible by 9, or are multiples of 9 i.e 500/9 is 55.5555.   Hence, there are 55 numbers which are multiples of 9 less than 500.   Answer : 55
Answer: E
What is the smallest integer that satisfies the inequality ((x - 3)/ (x^2 - 8x - 20)) > 0?
Choose the most appropriate option
A) -2
B) 10
C) -1
D) 3
E) 0

Solution: Let us factorize the denominator and rewrite the expression as (xâˆ’3)/((xâˆ’10)(x+2))> 0   Equate each of the terms of the expression to zero to identify the values of x that are relevant to test whether the inequality holds good.   The values that are relevant to us are x = 3, x = 10 and x = -2.   Let us arrange these values in ascending order: -2, 3 and 10.   The quickest way to solve inequalities questions after arriving at these values is verifying whether the inequality holds good at the following intervals.   Interval 1: x < -2.   Pick a value in that range and check whether the inequality holds good.   Let us take x = -10. When x = -10, (xâˆ’3)/((xâˆ’10)(x+2))< 0; the inequality DOES NOT hold good in this interval.   Interval 2: -2 < x < 3.   Let us take x = 0. When x = 0, (xâˆ’3)/((xâˆ’10)(x+2)) = (0âˆ’3)/((0âˆ’10)(0+2)) > 0; the inequality holds good in this interval.   The least integer value that x can take if x > -2 is x = -1.   ANSWER : -1.
Answer: C
Eight children — A, B, C, D, E, F, G and H — are going to sit in eight chairs in a row. The children C & F have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children?	Options.
A) 600  B) 720  C) 10080  D) 14320  E) 14800

Solution: for such questions , we can treat both as one then total person=7..   these 7 can be arranged in 7! ways.. but within these 7 , one consists of two people who can be arranged in 2 ways CF or FC.. so ans =7!*2=10080   ans 10080
Answer: C
Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 184 cms. What was the ratio D of men to women?	Options.
A) 5:2 B) 5:1 C) 4:3 D) 4:1 E) 3:1

Solution: (5:2) D=184 x 5 + 170 x 2 = 1260.5:2
Answer: A