MU-NLPC/Calc-aqua_rat huggingface dataset:
With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. If the second valve emits 50 cubic meters of water more than the first every minute, then what is the capacity T of the pool?  Choose the correct choice from the following answers.
A) 9000 cubic meters
B) 10500 cubic meters
C) 11750 cubic meters
D) 12000 cubic meters
E) 12500 cubic meters

Solution: D. 12000 cubic meters.   If both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in   (48*120)/(120-48)= 
  (48*120)/(120-48) = 80
80 minutes.   Now, if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120x and also 80 (x+50).   or, 120x= 80 (x + 50).   or x = 100.   Hence, the capacity of pool = 120x = 12000 cubic meters.
Answer: D
Can you find a six digit number under 5 lakh such that the sum of it's digits is 43 ? Choose the correct answer:  A) 588338  B) 499449  C) 399826  D) 788392  E) 622975

Solution: B   The required number is 499449.   The maximum sum of a number under 5 lakh will be of the number 499999 i.e. 49.   Thus the required number must be close to 499999.   The root of 499999 ~ 707.106   499449y calculating the square of 707, we get 499849 which is the answer.
Answer: B
In a certain deck of cards, each card has a positive integer written on it. In a multiplication game, a child draws a card and multiples the integer on the card by the next larger integer. If each possible product is between 26 and 200, then the least and greatest integers on the card could be Options.
A) 3 and 15 B) 3 and 20 C) 5 and 13 D) 4 and 14 E) 5 and 14

Solution: There child draws one number then multiplies that number by the number above it. The number must be more than 15 and less than 200.   x * (x+1)   Answer gives us choices of 3,4 and 5 (JUST ABOVE 26)   3*(3+1)= 
3*(3+1) = 12
12 <- WRONG   4*(4+1)= 
4*(4+1) = 20
20 <- WRONG   5*(5+1)= 
5*(5+1) = 30
30 <- CORRECT AS IT IS ABOVE 26   Answer gives us choices 13,14,15 and 20 (BELOW 200)   Immediately by knowing squares you should be able to rule out 15 (225) and 20 (400). And common sense dictates that as 14^2 is 196 that 14*(14+1) is above 200.   13*(13+1)= 
13*(13+1) = 182
182 <- 5 and 13ORRE5 and 13T   Answer is 5 and 13) 5 and 13
Answer: C
A and B undertake to do a piece of work for Rs. 1200. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. Find the share of C.	Choose the correct choice from the following choices:
A) 150
B) 450
C) 750
D) 800
E) None of them

Solution: C's 1 day's work = 1/3-(1/6+1/8)=24   A : B : C = Ratio of their 1 day's work = 1/6:1/8:1/24= 4 : 3 : 1.   A’s share = Rs. (1200 *4/8) = Rs.600, B's share = Rs. (1200 *3/8) = Rs. 450   C's share = Rs. [1200 - (300 + 225») = Rs. 150.   150nswer is 150
Answer: A
What is the present worth of Rs. 121 due in 2 years at 5% simple interest per annum	Choose the correct choice from the following: A) 110 B) 120 C) 130 D) 140 E) None of these

Solution: Explanation:   Let the present worth be Rs.x   Then,S.I.= Rs.(121 - x)   = (x*5*2/100) = 121 - x   = 10x = 12100 - 100x   = 110x = 12100   x= 110   110nswer:110
Answer: A
If |x-12| = 100, what is the sum of all the possible values of x? Options.
A) -12 B) -22 C) 24 D) 36 E) 42

Solution: There will be two cases   x-12 = 100 or x-12 = -100   => x = 112 or x= -88   sum of both the values will be  -88 + 112= 
 -88 + 112 = 24
24   Answer is 24
Answer: C
There are two positive numbers in the ratio 5:8. If the larger number exceeds the smaller by 45, then find the smaller number? Choose the most appropriate option
A) 25 B) 66 C) 77 D) 88 E) 75

Solution: Let the two positive numbers be 5x and 8x respectively.   8x - 5x = 45   3x = 45 => x = 15   => Smaller number = 5x = 75.   Answer: 75
Answer: E
A can be divided by 11 with no remainder. Which of the following expressions could be divided by 11 leaving a remainder of 1? Options
A) A-20.  B) A-12.  C) A-9.  D) A-10.  E) A-13.

Solution: We could use the following logic:   since A is a multiple of 11, we could very well say A = 11K (where K is 1,2...n).   The condition here should now be   11K + 1 = <operation> such that it gives us an integer   11k +1 </operation>= A -20 => A = 11K + 21 Not divisible by 11   11K +1 = A -12 => A = 11K + 31 Not A-10.ivisible by 11   11K +1 = A -9 => A = 11K + 10 Not A-10.ivisible by 11   11K +1 = A -10 => A = 11K + 11A-10.ivisible by 11   11K +1 = A -13 => A = 11K + 14 Not A-10.ivisible by 11   Answer therefore is A -10 (A-10.)
Answer: D
Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?  Answers
A) 120  B) 720  C) 125  D) 729  E) None of these

Solution: Explanation :   The first ring can be worn in any of the 3 fingers   => There are 3 ways of wearing the first ring   Similarly each of the remaining 5 rings also can be worn in 3 ways   Hence total number of ways   =3×3×3×3×3×6=36=729. Answer : Option 729
Answer: D
The winning relay team in a high school sports competition clocked 48 minutes for a distance of 13.2 km. Its runners A, B, C and D maintained speeds of 17 kmph, 18 kmph, 19 kmph, and 20 kmph respectively. What is the ratio of the time taken by B to than taken by D?	Choose the correct choice from the following answers.
A) 5:16	B) 5:17	C) 9:8	D) 10:9	E) None of these

Solution: Explanation :   Since it is a relay race, all the runners ran the same distance.   Hence for a same distance, (ratio of times) = 1/(ratio of speeds).   Hence ratio of times taken by B t& D =20 : 18 = 10 : 9.   Answer : 10:9
Answer: D
A train of length 560 metres takes 90 seconds to cross a tunnel of length 340 metres. What is the speed of the train in km/hr?
Options:
A) 36 km/hr. B) 46 km/hr. C) 30 km/hr. D) 48 km/hr. E) None

Solution: Sol.   Speed = [560+340 / 90] m/sec = [900 / 90 * 18/5] km/hr = 36km/hr.   36 km/hr.nswer 36 km/hr.
Answer: A
In the coordinate plane, points (x, 5) and (9, y) are on line k. If line k passes through the origin and has slope 5/9, then x - y =	Choose the correct choice from the following options:
A) 4	B) 6	C) 5	D) 8	E) 7

Solution: Line k passes through the origin and has slope 1/4 means that its equation is y=5/9*x.   Thus: (x, 5)=(9, 5) and (9, y) = (9,5) --> x-y=9-5= 
9-5 = 4
4.   4nswer: 4
Answer: A
A bus can hold 120 passengers. If there are 12 rows of seats on the bus, how many seats are in each row? Answers.
A) 10 B) 12 C) 45 D) 8 E) 9

Solution: No. of seats = 120/12= 
120/12 = 10
10   There are 10 seats in each row   10nswer : 10
Answer: A
A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business?
Choose the correct choice from the following choices:  A) 2400  B) 2408  C) 2406  D) 2403  E) 2401

Solution: 1200 * 12: x * 9 = 2:3   x = 2400   2400nswer: 2400
Answer: A
A typist can type 120 words in 100 seconds. At that rate, how many seconds would it take her to type 258 words? Choose the correct choice from the following options.
A) 205  B) 210  C) 215  D) 220  E) 225

Solution: 120/100=258/n   120* n=258*100   120n	=25800   n=215   Answer:215
Answer: C
A bag contains 12 red jellybeans and 12 blue jellybeans. If 3 jellybeans are removed one at a time, at random and are not replaced, what is the probability that all 3 jellybeans removed from the bag are blue? Choose the correct choice from the following answers.
A) 9/100 B) 2/19 C) 1/8 D) 3/20 E) 3/10

Solution: Method-1   10 red jellybeans and 10 blue jellybeans   Total Outcomes = No. of ways to choose 3 Jelly bean at random out of a total 20 jellybeans = 20C3 = 1140   Favourable Outcomes = No. of ways to choose 3 Jelly bean such that they are all Blue out of 10 Blue = 10C3 = 120   Probability = Favourable Outcomes / Total Outcomes = 10C3 / 20C3   Probability = 120 / 1140 = 2/19   Answer: option B   Method-2   Probability of First jelly bean to be Blue = 10/20 [Total 10 Blue out of total 20 jellybeans]   Probability of Second jelly bean to be Blue = 9/19 [Total 9 Blue remaining out of total 19 jellybeans remaining]   Probability of Third jelly bean to be Blue = 8/18 [Total 8 Blue remaining out of total 18 jellybeans remaining]   Required Probability = (10/20)*(9/19)*(8/18) = 3/10   Answer: option 3/10
Answer: E
If A lends Rs.3150 to B at 8% per annum and B lends the same sum to C at 12.5% per annum then the gain of B in a period of 2 years is? Choose the correct answer:
A) 280
B) 295
C) 283.5
D) 245
E) 200

Solution: (3150*4.5*2)/100= 
(3150*4.5*2)/100 = 283.5
> 283.5   Answer: 283.5
Answer: C
In how many ways can the digit of the number 2233558888 be arranged so that the odd digits are placed in the even positions?  Choose the correct answer:
A) 380  B) 400  C) 430  D) 450  E) 480

Solution: odd place combination = 5!/2!*2!=30   even place combination= 6!/2!*4!=15   to total=30*15= 
30*15 = 450
450   ANSWER:450
Answer: D
A solution of X pounds of water and sugar is boiled until 20% of the water content evaporates. Originally s% of sugar was present in the solution. After evaporation, what percentage of the solution is sugar?  Options:
A) 100s/(1-s) B) 80s/(1-s) C) 75s/(1-s) D) 100s/(80-0.2s) E) 100s/(80+0.2s)

Solution: We'll go for the ALTERNATIVE approach since there are variables in all the answers (which means that any number could work). Since the question deals with percents, the easiest number to use is X = 100. Now let's say that s = 10. Before the evaporation we had 10 pound of sugar and 90 pounds of water. Since only water evaporated, after the evaporation the 10 pounds of sugar remained the same, but the water reduced by 20% of 90 (18 pounds), so we have only 72 pounds of water. 10 out of 82 is the fraction of sugar, so if we multiply it by 100 we get the percents. The correct answer is 100s/(80+0.2s): 100s/(80+0.2s) >>> 100x10 / 82
Answer: E
On a certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 20% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?
Choose one:
A) 10.5%
B) 12.5%
C) 15%
D) 22%
E) 30%

Solution: Say there are 100 motorists.   {# of motorists who exceed speed & receive tickets} + {# of motorists who exceed speed & don't receive tickets} = {Total # of motorist who exceed speed};   Given: {# of motorists who exceed speed & receive tickets}=10;   Also, if {Total # of motorist who exceed speed}=x, then 0.2x={# of motorists who exceed speed & don't receive tickets};   10+0.2x=x --> x=12.5   Answer: 12.5%.
Answer: B
At the opening of a trading day at a certain stock exchange, the price per share of stock M was $25. If the price per share of stock M was $28 at the closing of the day, what was the percent increase in the price per share of stock M for that day?
Answers
A) 1.4%	B) 5.9%	C) 12%	D) 12.5%	E) 23.6%

Solution: Opening = 25   12%losing = 28   Rise in price = 3   So, percent increase = 3/25*100= 
3/25*100 = 12
12   Answer : 12%
Answer: C
From the integer n, if n*n*n*n is even, then what is true from below options?	Options:
A) n is odd	B) n*n is even	C) n is odd and n*n is even	D) n is even	E) None

Solution: n is even   Option n is even
Answer: D
What is the sum of the greatest common factor and the lowest common multiple of 16 and 36?
Choose the most appropriate option:
A) 124	B) 152	C) 148	D) 123	E) 412

Solution: Prime factorization of 16 = 2 x 2 x 2 x 2   Prime factorization of 36 = 2 x 2 x 3 x 3   G148F=4   L148M=144   Sum=148   Option: 148
Answer: C
John and Mary were each paid x dollars in advance to do a certain job together. John worked on the job for 10 hours and Mary worked 4 hours less than John. If Mary gave John 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 John was paid in advance?	Choose the correct choice from the following options: A) 4y B) 5y C) 6y D) 8y E) 9y

Solution: Let $x be the advance that both receive = 4x   Amount earned per hour by John and Mary = x/10 and x/6   Mary gives $y to John to make the wages earned equal   Hence John wage per hr = (x+y)10 which is now equal to Mary's wage (x-y)/6   Solve (x+y)10 = (x-y)/6   6x + 6y = 10x -10y   4x = 16y   x = 4y   Ans. 4y
Answer: A
For one toss of a certain coin, the probability that the outcome is heads is 0.6. If this coin is tossed 5 times, which of the following is the probability that the outcome will be heads at least 4 times? Pick one:
A) (0.6)^5
B) 2(0.6)^4
C) 3(0.6)^4
D) 4(0.6)^4(0.4) + (0.6)^5
E) 5(0.6)^4(0.4) + (0.6)^5

Solution: P(h)=0.6P(h)=0.6, so P(t)=0.4P(t)=0.4. We want to determine the probability of at least 4 heads in 5 tries.   At least 4 heads means 4 or 5. Let's calculate each one:   5 heads: P(h=5)=0.6^5;   4h and 1t: P(h=4)=5!/4!∗0.6^4∗0.4=5∗0.6^4∗0.4, multiplying by 5 as 4h and 1t may occur in 5 different ways:   hhhht   hhhth   hhthh   hthhh   thhhh   So, P(h≥4)=0.6^5+5∗0.6^4∗0.4   Answer: 5(0.6)^4(0.4) + (0.6)^5.
Answer: E
Three numbers are in the ratio 5 : 4 : 3 and their average is 360. The largest number is :  Options.
A) 30  B) 450  C) 27  D) 21  E) 22

Solution: Explanation:   Let the numbers be 5x, 4x and 3x, Then, (5x + 4x + 3x ) / 3 =360   => 12x = 360*3   => x = 90   Largest number 5x = 5*90= 
5*90 = 450
450   Answer: 450
Answer: B
A radio station has to choose 6 days of the seven in a week to broadcast a certain program, and that set will repeat each week. The program can be broadcast equally on any of the seven weekdays —- weekdays vs. weekends don’t matter at all —- nor does it matter whether the days the program airs are adjacent or not. Absolutely any 6 of the seven weekdays can be chosen. How many different 6-day combinations of the seven weekdays can be constructed?  Select the correct option
A) 7
B) 15
C) 21
D) 35
E) 56

Solution: Pick 6 days out of 7.. 7C6 = 7   7nswer : 7
Answer: A
The positive numbers w, x, y, and z are such that x is 20 percent greater than y, y is 20 percent greater than z, and w is 20 percent less than x. What percent greater than z is w ?  Options
A) 15.2%  B) 16.0%  C) 20.0%  D) 23.2%  E) 24.8%

Solution: y = 100 (start with yy, it makes getting x easier).   x = y*1.2 = 120   z = y/1.2 = 83.33   w = x*0.8 = 96   Then for the answer:   (w-z)/z = (96 - 83.33)/83.33   = 15.2%   15.2%NSWER:15.2%
Answer: A
A seller sells his apple at CP but uses a weight of 800 gm instead of kg weight. What is his profit %?
Choices.
A) 20%	B) 23%	C) 25%	D) 30%	E) 32%

Solution: If a trader professes to sell his goods at cost price, but uses false weights, then   Gain%=[Error(True Value−Error)×100]%So here profit percentage=[200(1000−200)×100]%=[200800×100]%=25%   25%
Answer: C
Today is Thursday. The day after 59 days will be?
Choose the most appropriate option:	A) Monday	B) Tuesday	C) Saturday	D) Sunday	E) wednesday

Solution: Explanation:   59 days = 8 weeks 3 days = 3 odd days   Hence if today is Thursday, After 59 days, it will be = (Thursday + 3 odd days)   = Sunday   Answer: Option Sunday
Answer: D
M and B are integers. The expression (M+1)(B+1) is even. What can be said about M and B?
Answers:	A) They are both even numbers.	B) At least one of them is even.	C) At least one of them is odd.	D) They are both odd.	E) Nothing can be said surly on M and B

Solution: Odd x Odd = Odd   Odd x Even = Even   Even x Even = Even   To fulfill condition Either (M+1) or (B+1) needs to be Even   So either M or B needs to be odd   Or At least one of them is odd.   At least one of them is odd=At least one of them is odd.
Answer: C
A shirt goes on sale for 80% of its original price. One week later, the sale price is marked down 10%. The final price is what percent of the original price?  Choose the correct option:
A) 72%
B) 70%
C) 52%
D) 50%
E) 28%

Solution: Just assume original price is 100.   Sale price = 80   Then it is marked down by 10% = 80-8= 
80-8 = 72
72.   Hence it is 72% of the original price. Hence answer is 72%
Answer: A
Sakshi can do a piece of work in 12 days. Tanya is 20% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is? Choose the correct choice from the following answers.
A) 10
B) 12
C) 14
D) 16
E) 18

Solution: Ratio of times taken by Sakshi and Tanys = 120:100 = 6:5   Suppose Tanya takes x days to do the work.   6:5 :: 12:x => x= 10 days.   Hence, Tanya takes 10 days to complete the work.   10nswer: 10
Answer: A
The LCM and HCF of two numbers are 100000 and 10000 respectively. Find the larger of the two numbers if their sum is 110000.  Choose one.
A) 100000  B) 46  C) 577  D) 577  E) 767

Solution: There are 2 approaches in solving this.   Methode 1.   HCF * LCM = The Actual Number.   100000* 10000= 
100000* 10000 = 1_000_000_000
1000000000   So the answer which we are looking for has to be a factor of 1000000000.   So among the options shortlist the answers by eliminating those numbers which is not divisible by 1000000000. and then take the highest number as the answer as the question asks abt the highest number.   answer is 100000
Answer: A
How many words can be formed by using all letters of the word ‘PENCIL’ ? Choose the correct answer.
A) 480	B) 600	C) 720	D) 900	E) 1060

Solution: The word contains 6 different letters.   The number of permutations is 6! = 720   The answer is 720.
Answer: C
if log 2 = 0.30103 and log 3 = 0.4771, find the number of digits in (648)5  Choose one:
A) 14.05
B) 14.02
C) 277
D) 288
E) 222

Solution: log(648)5   = 5 log(648)   = 5 log(81 × 8)   = 5[log(81) + log(8)]   =5 [log(34) + log(23)]   =5[4log(3) + 3log(2)]   = 5[4 × 0.4771 + 3 × 0.30103]   = 5(1.9084 + 0.90309)   = 5 × 2.81149   ≈ 14.05   14.05nswer: 14.05
Answer: A
In an university college, the ratio of the number of boys and girls is 5 : 9. If the percentage increase in the number of boys and girls be 20% and 40% respectively. What will be the new ratio ?
Options
A) 21 : 10 B) 12 : 17 C) 15 : 23 D) 10 : 21 E) None of these

Solution: Explanation :   Solution: Originally, let the number of boys and girls in the university college be 5x and 9x respectively.   Their increased number is (20% of 5x) : (40% of 9x)   => (120*5x/100) : (140*9x/100) = 60x : 126x   => x : y = 10 : 21.   Answer : 10 : 21
Answer: D
John was thrice as old as Tom 6 years ago. John will be 3/2 times as old as Tom in 6 years. How old is Tom today? Choices
A) 6  B) 8  C) 10  D) 12  E) 14

Solution: J-6 = 3(T-6), so J = 3T-12   J+6 = 3/2 * (T+6)   2J + 12 = 3T + 18   2(3T-12) + 12 = 3T + 18   3T = 30   T = 10   The answer is 10.
Answer: C
A sum of money amounts to Rs 9800 after 5 years and Rs 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is Answers:
A) 9%	B) 10%	C) 11%	D) 12%	E) 13%

Solution: Explanation:   We can get SI of 3 years = 12005 - 9800= 
12005 - 9800 = 2_205
2205   SI for 5 years= (2205/3)*5= 
(2205/3)*5 = 3_675
3675 [so that we can get principal amount after deducting SI]   Principal= 12005 - 3675 = 6125   So Rate = (100*3675)/(6125*5)= 
(100*3675)/(6125*5) = 12
12%   Option 12%
Answer: D
The sum of the first 30 positive even integers is 930. What is the sum of the first 30 odd integers? Choose the correct choice from the following options.
A) 930 B) 900 C) 960 D) 975 E) 980

Solution: Sum of first n even numbers = n(n+1) =930   Sum of first n odd numbers = n^2 = 30*30= 
30*30 = 900
900 (here n=30)   Answer : 900
Answer: B
If a(a + 7) = 60 and b(b + 7) = 60, where a ≠ b, then a + b =  Select the correct option:	A) −7	B) −2	C) 2	D) 46	E) 48

Solution: i.e. if a = 5 then b = -12   or if a = -12 then b = 5   But in each case a+b = -12+5 = -7   −7nswer: option −7
Answer: A
There is a 50% chance Jen will visit Chile this year, while there is a 50% chance that she will visit Madagascar this year. What is the probability that Jen will visit either Chile or Madagascar this year, but NOT both? Choose one.
A) 25.0%  B) 50.0%  C) 62.5%  D) 75.0%  E) 80.0%

Solution: P(Chile and not Madagascar) = 0.5*0.5= 
0.5*0.5 = 0.25
0.25   P(Madagascar and not Chile)= 0.5*0.5= 
0.5*0.5 = 0.25
0.25   Total probability= 0.25 + 0.25= 
0.25 + 0.25 = 0.5
0.5= 50%   The answer is 50.0%.
Answer: B
Find the remainder when the polynomial x4 - 3x2 + 7x - 10 is divided by (x - 2).  Pick
A) 8 B) -20 C) 18 D) 0 E) None

Solution: Explanatory Answer   By remainder theorem: If a polynomial in one variable 'x' is divided by (x - a), where 'a' is any real number, then the remainder is the value of the polynomial at x = a.   Therefore, remainder = (2)4 - 3(2)2 + 7(2) - 10 = 8   8nswer 8
Answer: A
Robert invests $120,000 in an account that pays 12% annual interest: the interest is paid once, at the end of the year. Jody invests $120,000 in an account that pays 12% annual interest, compounding monthly at the end of each month. At the end of one full year, compared to Robert's account, approximately how much more does Jody’s account have? Choose the correct choice: A) Zero B) $81.90 C) $819.00 D) $8190.03 E) $81900.30

Solution: Robert's interest= $120,000*0.12 = $14400 or $1,200 each month.   Jody’s interest, 12%/12 = 1% each month:   For the 1st month = $120,000*0.01 = $1,200;   For the 2nd month = $1,200 + 1% of 1,200 = $1,212, so we would have interest earned on interest (very small amount);   For the 3rd month = $1,212 + 1% of 1,212 = ~$1,224;   For the 4th month = $1,224 + 1% of 1,224 = ~$1,236;   ...   For the 12th month = $1,320 + 1% of 1,320 = ~$1,332.   The difference between Robert's interest and Jody's interest = ~(12 + 24 + ... + 132) = $792.   Answer: $819.00.
Answer: C
What two-digit number is less than the sum of the square of its digits by 15 and exceeds their doubled product by 5?
Choose the most appropriate option.
A) 95	B) 99	C) 26	D) 73	E) None of the Above

Solution: Let the digits be x and y. The number would be 10x + y.   We are given that 2xy + 5 = 10x +y = x^2 y^2 -15   Thus 2xy +5 = x^2 + y^2 - 15   x^2 + y^2 -2xy = 16   (x-y)^2 = 16   (x-y) = 4 or -4   Substituting the values of (x-y) in the equation 2xy +5 = 10x + y   x comes out to be 1 or 9... thus the two numbers can be 15 or 73   Thus the answer is 73
Answer: D
The wages of 24 men and 16 women amount to 11600 per day. Half the number of men and 37 women has same money. The daily wages paid to each man is	Choose the correct choice from the following options:
A) 223  B) 350  C) 31887  D) 2797  E) 911

Solution: 24m + 16w = 11600   12m + 37 w = 11600   Solving we get 12 m = 21w   Substituting in the first equation we get, 42w + 16 w = 11600 ⇒⇒ w = 200   M = 350   Answer:350
Answer: B
If x/4 years ago Roger was 14 years old and x/4 years from now he will be 4x years old, how old will he be 3x years from now?
Choose the most appropriate option
A) 32 B) 35 C) 30 D) 40 E) 27

Solution: Assume the current age = a   a - x/4 = 14 (i)   a + x/4 = 4x   Or a = 15x/4 (ii)   Putting the value of a from (ii) in (i)   15x/4 - x/4 = 14   Or 14x/4 = 14 Therefore x = 4 and a = 15   3x years from now, age will be  15 + 3*4= 
 15 + 3*4 = 27
27   Option 27
Answer: E
1397 x 1397 = ?  Choose the correct option:	A) 1951000	B) 1951500	C) 1951509	D) 1951511	E) 1951609

Solution: 1397 x 1397	= (1397)^2   = (1400 - 3)^2   = (1400)2 + (3)2 - (2 x 1400 x 3)   = 1960000 + 9 - 8400   = 1960009 - 8400= 
1960009 - 8400 = 1_951_609
1951609.   1951609)
Answer: E
If n is an integer from 1 to 96 (inclusive), what is the probability for n*(n+1)*(n+2) being divisible by 8?  Choose the correct choice from the following options:
A) 25%	B) 50%	C) 62.5%	D) 72.5%	E) 75%

Solution: (A) 25% , to be divisible by 8 the number needs to have 3 2s in it. Only a multiple of 4 can provide that. Number of numbers divisible by 4 = 96/4= 
96/4 = 24
24. So P(8)= 24/96 = 25% .
Answer: A
36 workers can reap a field in 6 days. If the work is to be completed in 4 days, the extra workers required are Options.
A) 10
B) 25
C) 18
D) 15
E) 16

Solution: Explanation:   M1D1 = M2D2   36(6)=X(4)   =54   Extra required workers are 54-36= 
54-36 = 18
18   Answer: Option 18
Answer: C