MU-NLPC/Calc-aqua_rat huggingface dataset:
How many different subset of the set of the 12 Calendar Month will not have the Month of March.  Choose the correct option
A) 1951	B) 1948	C) 1953	D) 1947	E) 1949

Solution: This is a combination solution   Since we have 11 different Month other than the Month of March we can take any Month from the set of 11 Months to make a subset.   11C1 +11C2 + 11C3 + 11C4 + 11C5 + 11C6 + 11C7 + 11C8 + 11C9 + 11C10 + 11C11 = 1948   Plus the one set that is null that is the Set having no element in it which is 11C0 =1   = 1948 + 1= 
1948 + 1 = 1_949
1949   1949= 1949
Answer: E
In a mixture of 60 liters, the ratio of milk and water is 2:1. What amount of water must be added to make the ratio of milk and water as 1:2?
Pick:
A) 76 liters  B) 86 liters  C) 60 liters  D) 34 liters  E) 18 liters

Solution: 2:1 --- 60   1:2   2:4   ---------------   3   3 ----------- 60   3 ----------- ? => 60 liters   Answer:60 liters
Answer: C
Ajay’s age is 125% of what it was 10 years ago, but 831/3 % of what it will be after ten years. What is his present age?	Choose one:
A) 45 years B) 50 years C) 55 years D) 60 years E) 65 years

Solution: Let the present age be x years.   Then, 125% of (x - 10) = x   And 831/3% of (x + 10) = x   Therefore, 125% of (x - 10) = 831/3% of ( x + 10)   5x/12 = 250/12   x = 50 years   ANSWER:50 years
Answer: B
A cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?  Choose the correct choice from the following choices: A) 2.9 hrs B) 4.5 hrs C) 2.9 hrs D) 7.2 hrs E) 8.6 hrs

Solution: Net part filled in 1 hour = (1/3 - 1/9)   = 2/9   The cistern will be filled in 9/2 hrs i.e., 4.5 hrs.   Answer:4.5 hrs
Answer: B
Arnold and Danny are two twin brothers that are celebrating their birthday. The product of their ages today is smaller by 13 from the product of their ages a year from today. What is their age today?	Choose one:
A) 2. B) 6. C) 5. D) 7. E) 9.

Solution: ad = (a+1) (d+1) -13   0= a+d-12   a+d = 12   a=d (as they are twin brothers)   a=d=6   6. is the answer
Answer: B
P can complete a piece of work in 18 days & B can do the same piece of work in 15 days. They started working together but after 3 days P left & Q alone completed the remaining work. The whole work was completed in how many days?  Choose the correct choice from the following.
A) 12 days	B) 12.5 days	C) 13 days	D) 13.5 days	E) 15.5 days

Solution: Both together worked for 3 days.   In 3 days , P can do = 3 x   1   18   =   1   6   th work   In 3 days, Q can do = 3 x   1   15   =   1   5   th work   In 3 days , work finished =   1   6   +   1   5   =   11   30   12.5 daysalance work =   19   30   12.5 daysalance work finished by Q => Time taken by Q to finish the balance work =   19   30   x 15 = 9.5 days   The whole work was completed in  9.5 + 3= 
 9.5 + 3 = 12.5
12.5 days   12.5 days
Answer: B
If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is -.  Choose the correct choice from the following choices:	A) 2/10	B) 4/13	C) 3/5	D) 9/7	E) 1/4

Solution: Explanation:   P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.   P(SᴜK) = 13/52 + 4/52 - 1/52 = 4/13   Answer: 4/13
Answer: B
Mr X mixed 10 kg of variety A rice with 15 kg of variety B rice and sold the mixture at a price 40% more than that of A. He did not get any profit.What is the ratio of the cost price of variety A to that of B per kg?  Choose the correct choice from the following answers:
A) 2:5  B) 3:5  C) 4:5  D) 5:8  E) 8:5

Solution: Let Rs X, Rs Y be the cost price per kg of variety A and variety B of rice   By data 10X + 15Y = 25 (1.4) X.   Since sale price of the mixture is 40% more than the cost price or A.   Therefore 10X + 15Y 10  + 15= 
 10  + 15 = 25
25 (1.4) X.   Since sale price of the mixture is 40% more than the cost price or A.   Therefore 10X + 15Y= 35X   Thus,15Y = 25X.   Hence, X : Y = 15 : 25 = 3 : 5   ANSWER:3:5
Answer: B
What is the greatest prime factor of (11! × 10!  + 10! × 9!)/111? Choose the correct option:
A) 2	B) 3	C) 5	D) 7	E) 11

Solution: (11!×10! +10!×9!)/111   In numerator take out 10!*9! as common term   10!∗9!(11×10 +1)/111   10!∗9!∗111/111   10!∗9!   10! has 7 as the greatest prime factor, so ans is 7   ANSWER:7
Answer: D
Two trains, each 100 meters long, moving in opposite directions, completely pass each other in 16 seconds. If one train is moving twice as fast the other, then what is the speed of the faster train (in km/hr)?	Choose the correct choice from the following choices:
A) 24 km/hr
B) 30 km/hr
C) 36 km/hr
D) 42 km/hr
E) 48 km/hr

Solution: Let the speed of the slower train be x m/s   Then, the speed of the faster train is 2x m/s   The relative speed is 3x m/s   (100 + 100)/16 = 3x   x = 25/6 m/s   So, the speed of the faster train is 50/6 = 50/6 * 18/5= 
50/6 * 18/5 = 30
30 km/hr   The answer is 30 km/hr.
Answer: B
Find the 10th term of the arithmetic progression 1, 3.5, 6, 8.5,...? Options
A) 20
B) 23.5
C) 22.5
D) 18.25
E) 19.5

Solution: common difference = d = 3.5 - 1= 
3.5 - 1 = 2.5
2.5 ,, n= 10, a = first term = 1----- 23.5y using arithmetic progression , t10 = a + (n-1)*d = 1 + (10-1)*2.5 = 1+22.5= 
1+22.5 = 23.5
23.5 Ans - 23.5
Answer: B
A candidate scoring 25% in an examination fails by 30 marks , while another candidate scores 50 % mark, gets 20 marks more than the minimum pass marks . Find the minimum pass marks. Find the minimum pass percentage.	Select the correct option:
A) 40%  B) 45%  C) 50%  D) 55%  E) 60%

Solution: Let x be the maximum marks,   Then (25% of x)+30 = (50% of x)-20   =>X/4 + 30 =X/2 - 20   =>X=200   Hence maximum marks = 200   Minimum pass marks = 200/4 + 30= 
200/4 + 30 = 80
80   Hence, minimum pass marks=80/200 X 100 =40%   40%NSWER IS 40%
Answer: A
A basketball team scored x points per game in its first n games of the season, and in all the following games it scored an average (arithmetic mean) of y points per game. What was the average number of points per game in its first n + 7 games?	Choose the correct choice from the following answers.
A) x + 3y/(n + 3)	B) x + y/(n + 3)	C) (x + 3y)/(n + 3)	D) (nx + 3y)/(n + 7)	E) (3x + ny)/(n + 3)

Solution: Total points in first n games = nx   Total marks in next 3 games is 3y   So, Average marks in n + 7 games = (nx+3y)/(n+7)   Hence, correct answer will be ((nx + 3y)/(n + 7))
Answer: D
The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $40,000?	Choose the most appropriate option:
A) $38,796.
B) $40,000.
C) $38,976.
D) $39,679.
E) $36,796.

Solution: 40,000 *1.16*.84= Unit and tens digit of the expression is 6 and 7 respectively.   Only option $38,976. fulfills the condition and hence is the answer
Answer: C
A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ? Pick:
A) 3 1/5min
B) 3 2/5min
C) 3 3/5min
D) 3 4/5min
E) 3 min

Solution: Explanation:   Do not be confused, Take this question same as that of work done question's. Like work done by 1st puncture in 1 minute and by second in 1 minute.   Lets Solve it:   1 minute work done by both the punctures =   (1/9+1/6)=(5/18)   So both punctures will make the type flat in   (18/5)mins=3 3/5mins   Option 3 3/5min
Answer: C
The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?	Choose the correct choice from the following
A) 77 m
B) 17 m
C) 82 m
D) 28 m
E) 26 m

Solution: Let the breadth of the plot be b m.   Length of the plot = 3 b m   (3b)(b) = 867   3b2 = 867   b2 = 289 = 172 (b > 0)   b = 17 m.   Answer: 17 m
Answer: B
A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
Select the correct option.
A) Rs. 4991 B) Rs. 5991 C) Rs. 6001 D) Rs. 6991 E) None

Solution: EXPLANATION   Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.   Required sale = Rs. [ (6500 x 6) – 34009 ]   = Rs. (39000 – 34009)   = Rs. 4991.   Rs. 4991nswer Rs. 4991
Answer: A
Two machines, Y and Z, work at constant rates producing identical items. Machine Y produces 30 items in the same time Machine Z produces 24 items. If machine Y takes 36 minutes to produce a batch of items, how many minutes does it take for machine Z to produce the same number of items?  Answers
A) 60  B) 90  C) 9 1/2  D) 45  E) 13 1/2

Solution: rate z/rate y=24/30   time z/time y=30/24   30/24*36= 
30/24*36 = 45
45 minutes   45
Answer: D
A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?  Answers:
A) Rs.250 B) Rs.257 C) Rs.228 D) Rs.229 E) Rs.226

Solution: CP1 = 100 SP1 = 90   CP2 = 80 SP2 = 80 * (140/100)= 
80 * (140/100) = 112
112   22 ----- 100   55 ----- ?=> Rs.250   Rs.250nswer: Rs.250
Answer: A
On a certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 10% 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 the correct choice from the following answers:
A) 10.5%	B) 18%	C) 15%	D) 22%	E) 11.11%

Solution: 0.1 M = 0.90 E   => E/M = 1/9 * 100 = 11.11%=E.   M - # of Motorists   11.11% - # of Motorists exceeding speed
Answer: E
What is the are of an equilateral triangle of side 6 cm?  Choose the correct choice from the following answers
A) 8√3  B) 9√3  C) 7√3  D) 4√3  E) 3√3

Solution: Area of an equilateral triangle = √3/4 S2   If S = 6, Area of triangle = √3/4 * 6 * 6   = 9√3 cm2;   Answer:9√3
Answer: B
John left home and drove at the rate of 50 mph for 2 hours. He stopped for lunch then drove for another 3 hours at the rate of 55 mph to reach his destination. How many miles did John drive? Choose the correct choice from the following options
A) 235 miles. B) 245 miles. C) 255 miles. D) 265 miles. E) 275 miles.

Solution: The total distance D traveled by John is given by   D = 50 * 2 + 3 * 55= 
50 * 2 + 3 * 55 = 265
265 miles.   Answer 265 miles.
Answer: D
If a large pizza has a radius that is 10% larger that that of a medium pizza, what is the percent increase in area between a medium and a large pizza?  Choose the correct choice from the following.
A) 15%	B) 21%	C) 25%	D) 30%	E) 36%

Solution: Let the radius of medium pizza be r. Then the radius of large pizza is 1.1r.   The area of the medium pizza is pi*r^2   The area of the large pizza is pi*(1.1*r)^2 = 1.21*pi*r^2, an increase of 21%.   The answer is 21%.
Answer: B
When you multiply a number by 4 and
then subtract 6, the result is the same as
if you first subtracted 6 from the same
number and then multiplied by 10. What
is the number?
Choose the correct option.
A) A)23  B) B)9  C) C)19  D) D)31  E) E)10

Solution: Let x equal the number and then change the words into an equation and solve for x:   4x – 6 = 10(x – 6)   4x – 6 = 10x – 60   54 = 6x   9 = x   correct answer 9)9
Answer: B
The ages of two persons differ by 16 years. 4 years ago, the elder one was 3 times as old as the younger
one. What are their present ages of the elder person	Choose the correct choice from the following answers:	A) 15	B) 20	C) 28	D) 30	E) 35

Solution: Explanation:   Let's take the present age of the elder person = x   and the present age of the younger person = x � 16   (x � 4) = 3 (x-16-4)   => x � 4 = 3x � 60   => 2x = 56   => x = 60/2 = 28   Answer: Option 28
Answer: C
There is 60% increase in an amount in 6 years at S.I. What will be the C.I. of Rs. 12,000 after 3 years at the same rate?  Pick
A) 2160
B) 3120
C) 3972
D) 6240
E) 5240

Solution: Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.   R = (100 * 60)/(100 * 6)= 
(100 * 60)/(100 * 6) = 10
10% p.a.   Now, P= Rs. 12000, T = 3 years and R = 10% p.a.   C.I. = [12000 * {(1 + 10/100)3 - 1}]   = 12000 * 331/1000 = Rs. 3972   ANSWER:3972
Answer: C
How many numbers with 3 different digits can be formed using only the even-numbered digit?
Choose the correct choice from the following
A) 12	B) 20	C) 40	D) 60	E) 120

Solution: Odd digits are 2, 4, 6, 8.   We want 2 different digits.   First digit can be chosen in 4 ways.   Second digit can be chosen in 3 ways.   Total ways = 4*3= 
4*3 = 12
12   Hence option (12).
Answer: A
An electric motor makes 2,800 revolutions per minutes. How many degrees does it rotate in one second?  Choose the correct choice from the following:  A) 16.800 d/sec  B) 28.000 d/sec  C) 38.000 d/sec  D) 26.000 d/sec  E) 35.000 d/sec

Solution: 2800 revolutions / minute   = 2800*360 degrees / 60 seconds   = 16,800 degrees / second   16.800 d/sec
Answer: A
In how many ways can the letters of the word ARRANGED be arranged?	Pick one:
A) 20160	B) 20180	C) 20120	D) 21021	E) 20170

Solution: ARRANGED has 8 words, but r is repeated two times. Thus ways = 8! / 2! = 20160 ways   20160
Answer: A
Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 49 years. What will be the age of the B ten years hence? Choose the correct choice from the following options.
A) 39  B) 23  C) 28  D) 98  E) 26

Solution: Let the present ages of A, B and C be a, b and c respectively.   Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)   (b + c)/2 = 49 => b + c = 98 --- (2)   Answer: 98
Answer: D
Find compound interest on $ 4000 at 15% per annum for 2 years 4 months, compounded annually.	Choose the correct choice:
A) 1554.5
B) 1509.5
C) 1108.5
D) 1107.5
E) 1100.5

Solution: Time = 2 years 4 months = 2(4/12) years = 2(1/3) years.   Amount = $ [4000 X (1+­(15/100))2 X (1+((1/3)*15)/100)]   =$ [4000 * (23/20) * (23/20) * (21/20)= 
4000 * (23/20) * (23/20) * (21/20) = 11_109/2 = around 5_554.5
$ 5554.50	.   :. C.I.= Rs. (5554.50 - 4000) = $ 1554.50   1554.5nswer 1554.5.
Answer: A
A sum of money becomes double itself in 8 years at simple interest. How many times will it become 10 years at the same rate?  Choose the correct choice from the following choices.
A) 2 1/4
B) 2 1/9
C) 2 1/6
D) 2 1/5
E) 2 1/2

Solution: P ---- 2P ---- 8 years   2 1/4 P ---- 10 years   2 1/4nswer: 2 1/4
Answer: A
A train 400 m long passes a man, running at 7 km/hr in the same direction in which the train is going, in 30 sec. The speed of the train is?	Pick.
A) 39 km/hr
B) 40 km/hr
C) 41 km/hr
D) 42 km/hr
E) 43 km/hr

Solution: Speed of the train relative to man = 400/30 = 40/3 m/sec.   = 40/3 * 18/5= 
40/3 * 18/5 = 48
48 km/hr   Let the speed of the train be x km/hr. Then, relative speed= (x - 5) km/hr.   x - 7 = 48 => x = 41 km/hr.   Answer: 41 km/hr
Answer: C
A positive number x is multiplied by 4, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ?  Answers.
A) 9/4  B) 3/2  C) 4/3  D) 2/3  E) 1/2

Solution: sq rt(4x/3) = x   => 4x/3 = x^2   => x = 4/3   Ans - 4/3
Answer: C
In a family 16 people eat only vegetarian, 9 people eat only non veg., 12 people eat both veg and non veg.. How many people eat veg in the family? Options:
A) 28	B) 26	C) 22	D) 31	E) 21

Solution: Total people eat veg = only veg + both veg and non veg   Total= 16+12= 
16+12 = 28
28   28nswer= 28
Answer: A
A house seller can deduct 5 percent from the total sales value. If he has sold 5 houses, and the price of two houses is between $150,000 and $250,000, one of them is $350,000 house, two houses are between $500,000 and 750,000, what is the range of his revenue?	Choose the correct choice from the following choices
A) 782.5
B) 785
C) 780
D) 790
E) 800

Solution: taking away '000 thousand sfor easy calculation   (1) 2(150)+350+2(500) = 1650   1600*0.95=1567.5 (Revenue considering the minimum values with the discount)   (2) 2(250)+350+2(750) = 2350 (Revenue considering the maximum values without the discount)   So, the the revenue range could be = 2350 - 1567.5= 
2350 - 1567.5 = 782.5
782.5   782.5
Answer: A
According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 15 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice? Choose the correct choice from the following answers:	A) 20	B) 34	C) 50	D) 67	E) 100

Solution: Orange juice concentrate: water::1:3   total quantity of orange juice = 200*6= 
200*6 = 1_200
1200 oz   so Orange juice concentrate: water :: 300 oz:900 oz   no. of 15 oz can= 300 oz/15 oz = 20   20nswer 20, 20 cans
Answer: A
If 9^y = 3^12, what is y?  Select.
A) 1 B) 3 C) 4 D) 5 E) 6

Solution: 3^2y = 3^12   2y=12, therefore y=6   6
Answer: E
What is the sum of the digits of integer k, if k = (10^30- 54) Choices.
A) 251	B) 261	C) 262	D) 269	E) 278

Solution: There are 31 digits in 10^30   When we subtract 54 from it, there will be 30 digits left.   10^30 can be written as 9999999....(30 times) + 1   So,   10^30 - 54 = 9999999....(30 times) + 1 - 54 = 9999999....(30 times) - 53   Consider the last 2 digits,   99-53= 
99-53 = 46
46   The last 2 digits will be 46.   And our number would be 99999......99946 with 2 less 9s after subtraction.   Number of 9s left are 28 and the last two digits are 46   The sum of the digits will be     (28*9) + 4 + 6= 
  (28*9) + 4 + 6 = 262
262   Answer:- 262
Answer: C
A person buys an article at Rs.350. At what price should he sell the article so as to make a profit of 30%? Choose the correct answer.
A) 455  B) 277  C) 269  D) 261  E) 281

Solution: Cost price = Rs.350   profit = 30% of 350 = Rs.105   Selling price = Cost price + Profit   = 350 + 105= 
350 + 105 = 455
455   455nswer: 455
Answer: A
If q and r are both odd numbers Z, which of the following must also be odd?
Choose the correct choice from the following choices.
A) q – r B) (q + r)^2 C) q(q + r) D) (qr)^2 E) q/r

Solution: We're told that q and r are both ODD numbers Z. We're asked which of the following must also be odd.   IF...   q = 1   r = 3   Answer A) q – r = 1-3 = -2 NOT odd   Answer B) (q + r)^2 = (1+3)^2 = 16 NOT odd   Answer C) q(q + r) = (1)(4) = 4 NOT odd   Answer (qr)^2) (qr)^2 = (3)^2 = 9 This IS O(qr)^2(qr)^2   Answer E) q/r = 1/3 NOT odd   Final Answer:   (qr)^2
Answer: D
Find the numbers which are in the ratio 3 : 2 : 4 such that the sum of the first and the second added to the difference of the third and the second is 21 ?  Choose the correct choice from the following
A) 9, 6, 16 B) 9, 6, 11 C) 9, 6, 17 D) 9, 6, 12 E) 9, 6, 19

Solution: Let the numbers be a, b and c.   Given that a, b and c are in the ratio 3 : 2 : 4.   let, a = 3x, b = 2x and c = 4x   Given, (a+b) + (c - b) = 21   = > a + b + c - b = 21 = > a + c = 21   = > 3x + 4x = 21 = >7x = 21 = > x = 3   a , b , c are 3x, 2x, 4x.   Answer:9, 6, 12   a, b, c are 9 , 6 , 12.
Answer: D
Given that E and F are events such that P(E) = 25, P(F) = 75 and P(E n F) = 75,
find P (E|F) and P(F|E)
Choose the correct choice from the following answers.
A) 5	B) 46	C) 52	D) 12	E) 3

Solution: Here, E and F are events   P(E|F) = P(EnF)/P(F) = 75/25= 
75/25 = 3
3   P(F|E)= P(EnF)/P(E) = 75/75= 
75/75 = 1
1.   3)
Answer: E
In Arun’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother does not agree with Arun and he thinks that Arun’s weight is greater than 60 kg but less than 70 kg. His mother’s view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of different probable weights of Arun?  Choose the most appropriate option:
A) 67 kg
B) 68 kg
C) 69 kg
D) 66.5 kg
E) None of the above

Solution: Let Arun’s weight be X kg.   According to Arun, 65 < X < 72.   According to Arun’s brother, 60 < X < 70.   According to Arun’s mother, X < 68.   The values satisfying all the above conditions are 66 and 67.   ∴ Required average = (66+67/2)=(133/2)= 
(133/2) = 133/2 = around 66.5
66.5kg.   Answer 66.5 kg
Answer: D
Find the area of a parallelogram with base 24 cm and height 16 cm.
Choose the correct answer.
A) 345 cm2	B) 384 cm2	C) 156 cm2	D) 657 cm2	E) 887 cm2

Solution: Area of a parallelogram   = base * height = 24 * 16= 
24 * 16 = 384
384 cm2   Answer: 384 cm2
Answer: B
Two men starting from the same place walk at the rate of 5 kmph and 5.5 kmph respectively. What time will they take to be 7.5 km apart, if they walk in the same direction? Choices
A) 12 hrs B) 14 hrs C) 15 hrs D) 17 hrs E) None

Solution: Sol.   to be 0.5 km apart, they take 1 hour.   To be 7.5 km apart, they take [1/0.5 * 7.5= 
1/0.5 * 7.5 = 15
15 hrs.   Answer 15 hrs
Answer: C
A man sells a horse for Rs.420 and loses something, if he had sold it for Rs.620, his gain would have been double the former loss. Find the cost price of the horse?
Choose the correct choice from the following:
A) 27
B) 66.6
C) 55.2
D) 60.6
E) 71

Solution: CP = SP + 1CP = SP - g   420 + x = 620 - 2x   3x = 200 => x = 66.6   Answer:66.6
Answer: B
The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is?	Choose the correct choice from the following answers
A) 35 years  B) 40 years  C) 50 years  D) 55 years  E) none of these

Solution: Explanation:   Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.   Sum of the present ages of wife and child = (20 x 2 + 5 x 2) years = 50 years.   Husband's present age = (90 - 50)= 
(90 - 50) = 40
40 years.   ANSWER: 40 years
Answer: B
A and B complete a job in 6 days. A alone can do the job in 8 days. If B works alone, how many days will it take to complete the job?	Choose the correct choice from the following answers:
A) 12
B) 16
C) 20
D) 24
E) 28

Solution: The rate of A and B is 1/6   A's rate is 1/8   B's rate is 1/6 - 1/8 = 1/24   B can complete the job in 24 days.   The answer is 24.
Answer: D
Two buses and a van were employed to transport a class of students on a field trip. 3/5 of the class boarded the first bus. 1/3 of the remaining students boarded the second bus, and the rest of the students boarded the van. When the second bus broke down, 1/2 of the students on the second bus boarded the first bus. What fraction of the class was on board the first bus?  Choose the correct choice from the following options
A) a) 7/10	B) b) 2/3	C) c) 11/15	D) d) 23/30	E) e) 4/5

Solution: This is a pure ratio question (we aren't given any numbers for anything), so you can just choose any starting number you like, and use it to solve the problem. The best number to pick is almost always the product of all the denominators of your fractions, so here we could start with 30 students. Then we have:   • 3/5 of these, or 18 students, board the first bus   • there are 12 students left. 1/3 of these, or 6 students, board the second bus   • this bus breaks down, and 1/2 of the 6 students, or 3 students, board the first bus   • the first bus now contains 21 out of the original 30 students, so the answer is 21/30 = 7/10   a) 7/10nswer a) 7/10
Answer: A
n how many different ways can a group of 8 people be divided into 4 teams of 2 people each?	Pick one: A) 90 B) 105 C) 168 D) 420 E) 2520

Solution: How many ways can you arrange the following:   T1 T1 T2 T2 T3 T3 T4 T4   That would be: 8!/(2!*2!*2!*2!)   Then also recall that we don't care about the differences between the teams, therefore   8!/(2!*2!*2!*2!*4!) = 105 ANS:105
Answer: B
A rectangular-shaped carpet that measures x feet by y feet is priced at $55. What is the cost of the carpet, in dollars per square yard? (1 square yard = 3 square feet)	Choose the correct option:
A) xy/297
B) 11xy/3
C) 3xy/11
D) 165/(xy)
E) 297xy

Solution: The area of the carpet in feet is xy.   The area in square yards is xy / 3.   The price per square yard is 55 / (xy/3) = 165/(xy).   The answer is 165/(xy).
Answer: D