MU-NLPC/Calc-aqua_rat huggingface dataset:
A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio W of milk and water in the resultant mixture?	Choose the correct choice from the following answers
A) 17 : 3  B) 9 : 1  C) 3 : 17  D) 5 : 3  E) 11: 2

Solution: he 20 litre mixture contains milk and water in the ratio of 3 : 2. Therefore, there will be 12 litres of milk in the mixture and 8 litres of water in the mixture.   Step 1.   When 10 litres of the mixture is removed, 6 litres of milk is removed and 4 litres of water is removed. Therefore, there will be 6 litres of milk and 4 litres of water left in the container. It is then replaced with pure milk of 10 litres. Now the container will have 16 litres of milk and 4 litres of water.   Step 2.   When 10 litres of the new mixture is removed, 8 litres of milk and 2 litres of water is removed. The container will have 8 litres of milk and 2 litres of water in it. Now 10 litres of pure milk is added. Therefore, the container will have 18 litres of milk and 2 litres of water in it at the end of the second step. Therefore, the ratio of milk and water is 18 : 2 or 9 : 1.   Shortcut.   We are essentially replacing water in the mixture with pure milk.   Let W_o be the amount of water in the mixture originally = 8 litres.   Let W_r be the amount of water in the mixture after the replacements have taken place.   Then,{W_r}/{W_o}= (1-R/M)^n   where R is the amount of the mixture replaced by milk in each of the steps, M is the total volume of the mixture and n is the number of times the cycle is repeated.   Hence, {W_r}/{W_o} =(1/2)^2  =1/4   Therefore W,W_r ={W_o}/4= 8/4= 
8/4 = 2
2 litres.9 : 1
Answer: B
A man purchases 8 pens for Rs.9 and sells 9 pens for Rs.8, how much profit or loss does he make?
Choose the correct choice from the following
A) 15 B) 66 C) 88 D) 1 E) 12

Solution: 90 * 10/60= 
90 * 10/60 = 15
15 kmph   15nswer: 15
Answer: A
A present value of a machine is $2500. Its value depletiation rate is 5% per annum then find the machine value after 2 years?  Choose one:	A) $2100	B) $2546	C) $2256	D) $2451	E) $2345

Solution: P= $2500   R = 5%   T = 2 years   Machine value after 2 years = P[(1-R/100)^T]   =2500*19/20 * 19/20   =$2256 approximately   Answer is $2256
Answer: C
Express the following as a fraction: 0.8% Pick one:	A) 1/8	B) 8/10	C) 8/100	D) 4/5	E) None of the Above

Solution: 0.8 =8/10 = 4/5   Answer is 4/5.
Answer: D
The side of a rhombus is 26 m and length of one of its diagonals is 20 m. The area of the rhombus is? Choose the correct answer
A) 287	B) 2878	C) 388	D) 480	E) 277

Solution: 262 – 102 = 242   d1 = 20 d2 = 48   1/2 * 20 * 48= 
1/2 * 20 * 48 = 480
480   Answer:480
Answer: D
A man bets on no. 16 on a roulette wheel 14 times and losses each time. On the 15th span he does a quick calculation and finds out that the no. 12 had appeared twice in the 14 spans and is therefore, unable to decide whether to bet on 16 or 12 in the 15th span. Which will give him the best chance and what are the odds of winning on the bet that he takes?  Select the correct option.
A) 23:2 B) 35:1 C) 37:13 D) 39:11 E) 41:11

Solution: Each of the span is an independent event and the outcome of the 15th span will not depend on the outcome of the earlier spans.   Either ;35:1   35:1)
Answer: B
For a certain art exhibit, a museum sold admission tickets to a group of 30 people every 6 minutes from 9:00 in the morning to 6:00 in the afternoon, inclusive. The price of a regular admission ticket was $10 and the price of a student ticket was $6. If on one day 2 times as many regular admission tickets were sold as student tickets, what was the total revenue from ticket sales that day? Choose the correct choice from the following choices: A) $23400 B) $25920 C) $28080 D) $28500 E) $29160

Solution: From 9:00 in the morning to 6:00 in the afternoon, inclusive there are 9*10= 
9*10 = 90
90 five-minute intervals, thus total of 54*30 tickets were sold.   Say x student and 2x regular tickets were sold, then x+2x=90*30 --> x=30*30 and 2x=2*(30*30)=30*60.   Therefore, the total revenue from ticket sales that day was 30*30*6+30*60*10=$23,400.   $23400nswer: $23400.
Answer: A
If a Bus is travelling at a speed of 45 kmph, crosses a pole in 1 sec, then the length of train is?  Pick
A) 12 m  B) 12.3 m  C) 12.5 m  D) 12.8 m  E) 13 m

Solution: Explanation:   D = 45 * 5/18 * 1= 
45 * 5/18 * 1 = 25/2 = around 12.5
12.5 m   Answer: Option 12.5 m
Answer: C
The front wheels of a wagon are 2Π feet in circumference and the rear wheels are 3Π feet in circumference. When the front wheels have made 10 more revolutions than the rear wheels, how many feet has the wagon travelled?
Select the correct option:	A) 30Π	B) 45Π	C) 60Π	D) 90Π	E) None

Solution: Solution   Let the rear wheel make x revolutions. Then, the front wheel makes (x+10) revolutions.   (x+10) x 3Π = x×2Π   ‹=›3x + 30 = 2x   ‹=›x = 30.   Distance travelled by the wagon = (2Π x 30)ft   ‹=›(60Π) ft.   Answer 60Π
Answer: C
Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is? Select the correct option:
A) 17/26
B) 17/27
C) 17/22
D) 17/20
E) 17/98

Solution: n(S) = 20   n(Even no) = 10 = n(E)   n(Prime no) = 8 = n(P)   P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20   Answer: 17/20
Answer: D
If q = (x – 5)^2 + (x + 1)^2 – 6, then y is least when x = Choose the correct choice from the following choices.
A) -2  B) -1  C) 0  D) 2  E) None of the above

Solution: Let us transform the formula:   q = (x – 5)² + (x +1)² – 6 =   x² – 10x + 25 + x² + 2x + 1 – 6 =   2x² – 8x + 20 = 2 × (x² – 4x + 10) =   2 × ((x² – 4x + 4) + 6) =   2 × ((x – 2)² + 6)   Any square is greater or equal 0. Therefore the formula possess the least value when (x – 2)² = 0.   x – 2 = 0   x = 2   The correct answer is choice (2).
Answer: D
Look at this series: 201, 202, 204, 207, ... What number should come next?	Choose the correct choice from the following options.
A) 205	B) 208	C) 210	D) 211	E) None

Solution: Explanation: In this addition series, 1 is added to the first number; 2 is added to the second number; 3 is added to the third number; 4 is added to the fourth number; and go on.   Answer: Option 211
Answer: D
The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?	Options.
A) 1m B) 6m C) 9m D) 2m E) 8m

Solution: Let the sides of the rectangle be l and b respectively.   From the given data,   (√l2 + b2) = (1 + 108 1/3 %)lb   => l2 + b2 = (1 + 325/3 * 1/100)lb   = (1 + 13/12)lb   = 25/12 lb   => (l2 + b2)/lb = 25/12   12(l2 + b2) = 25lb   Adding 24lb on both sides   12l2 + 12b2 + 24lb = 49lb   12(l2 + b2 + 2lb) = 49lb   but 2(l + b) = 28 => l + b = 14   12(l + b)2 = 49lb   => 12(14)2 = 49lb   => lb = 48   Since l + b = 14, l = 8 and b = 6   l - b = 8 - 6= 
8 - 6 = 2
2m.   Answer: 2m
Answer: D
A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 13.69, the number of the member is the group is: Choices:
A) 57
B) 67
C) 37
D) 87
E) 97

Solution: Money collected =(13.69 x 100) paise = 1369 paise   numbers of members = 1369 squareroot = 37   Answer 37
Answer: C
A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio T of revenue from car sales in 1996 to revenue from truck sales in 1996?	Choose the correct choice from the following.
A) 1:2
B) 4:5
C) 1:1
D) 3:2
E) 5:3

Solution: A.. I have probably solved this question 3-4 times by now.. Remember the answer.. 1:2
Answer: A
If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x + y = ? Options:
A) 6 B) 4 C) 8 D) 8 E) None of these

Solution: 80 = 2 x 5 x 8   Since 653xy is divisible by 2 and 5 both, so y = 0.   Now, 653x is divisible by 8, so 13x should be divisible by 8.   This happens when x = 6.   x + y = (6 + 0)= 
(6 + 0) = 6
6.   6nswer: 6
Answer: A
What is the product of the prime numbers between 1 and 7?	Choices:
A) 10^1
B) 10^2
C) 10^3
D) 10^4
E) 10^5

Solution: 10^3)
Answer: C
A train 320 m long passed a pole in 28 sec. How long will it take to pass a platform 700 m long? Pick one: A) 12 sec B) 59 sec C) 93 sec D) 89 sec E) 46 sec

Solution: Speed = 320/28   = 11 m/sec.   Required time = (320 + 700)/11   = 92.7 sec.   Answer: 93 sec
Answer: C
What is the dividend? Divisor is 0, the Quotient is 69, the remainder is 1. Choices:
A) 2
B) 69
C) 0
D) 4
E) 1

Solution: Dividend= Divisor * Quotient + Remainder   D= 0 * 69 + 1   D= 0 + 1= 
0 + 1 = 1
1   (e.g. Answer: 1)
Answer: E
A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent? Options:  A) 98%  B) 20%  C) 80%  D) 90%  E) 23%

Solution: 900 ---- 180   100 ---- ? => 20%   Answer: 20%
Answer: B
m and n are the x and y coordinates, respectively, of a point in the coordinate plane. If the points (m, n) and (m + p, n + 18) both lie on the line defined by the equation x = (y/6) - (2/5), what is the value of p? Options:
A) 1	B) 2	C) 3	D) 4	E) 5

Solution: x = (y/6) - (2/5), and so y = 6x + 12/5. The slope is 6.   (n+18-n) / (m+p-m) = 6   p = 3   The answer is 3.
Answer: C
Three candidates contested an election and received 500, 7632 and 11628 votes respectively. What percentage of the total votes did the winning candidate get? Choose one: A) 57% B) 60% C) 58.8% D) 90% E) 80%

Solution: total votes are 19760 ( sum of votes obtained by 3 candidates)   percentage of the total votes recd by the winning candidate = 100*11628/19760 = 58.8%   ANSWER:58.8%
Answer: C
There 3 kinds of books in the library physics, chemistry and biology. Ratio of physics to chemistry is 3 to 2; ratio of chemistry to biology is 4 to 3, and the total of the books is more than 3000. Which one of following can be the total T of the book? Choose the correct choice from the following options:
A) 3003	B) 3027	C) 3024	D) 3021	E) 3018

Solution: First, you have to find the common ratio for all 3 books. You have:   P:C:B   3:2 --> multiply by 2 (gives you row 3)   4:6   6:4:3   Hence:   P:C:B:T(Total)T   6:4:3:13 ----> This means, the Total Number must be a multiple of 13.   3003nswer 3003 is correct since 299 is divisible by 13, hence is 2990 and so is 3003 (2990+13).
Answer: A
Ben likes long bike rides. On one ride, he goes biking for six hours. For the rst hour, he bikes
at a speed of 15 miles per hour. For the next two hours, he bikes at a speed of 12 miles per
hour. He remembers biking 90 miles over the six hours. Compute the average speed, in miles
per hour, Ben biked during the last three hours of his trip.  Pick
A) 20
B) 35
C) 17
D) 51
E) 46

Solution: Ben biked 90-15- 2 * 12= 
90-15- 2 * 12 = 51
51 miles over the last three hours, averaging a speed of   51/3= 
51/3 = 17
17 miles per hour.   correct answer 17
Answer: C
The Guests at a football banquet consumed a total of 411 pounds of food. if no individual guest consumed more than 2.5 pounds of food, What is the minimum number of guests that could have attended the banquet?
Choose the correct choice from the following
A) 165 B) 161 C) 162 D) 163 E) 164

Solution: To minimize one quantity maximize other.   164*2.5 (max possible amount of food a guest could consume) = 410 pounds, so there must be more than 164 guests, next integer is 165.   165nswer: 165.
Answer: A
The daily high temperatures were recorded at an Antarctic weather station. If a temperature of -38.2 degrees Celsius is 2 units of standard deviation below the mean temperature, and a temperature of -22.6 degrees Celsius is 4 units of standard deviation above the mean, which of the following temperatures is 3 unit of standard deviation above the mean?  Pick:
A) -35.6 degrees Celsius  B) -33.0 degrees Celsius  C) -30.4 degrees Celsius  D) -27.8 degrees Celsius  E) -25.2 degrees Celsius

Solution: Let us suppose mean = M and SD = d.   So, we are given M - 2d = -38.2   and M + 4d = -22.6   solving both the equations, we will get M = -33 an d = 2.6   So, we need to find out M + 3d = -33 +3* 2.6 = -25.2. Hence, -25.2 degrees Celsius
Answer: E
If the price has fallen by 10% what percent of its consumption be: increased so that the expenditure may be the same as before?	Pick one: A) 15 1/9% B) 11 8/9% C) 11 1/9% D) 16 1/9% E) 11 1/2%

Solution: 100 – 10 = 90   90------10   100------? => 11 1/9%   Answer:11 1/9%
Answer: C
What is the principal sum?
I. The sum amounts to Rs. 720 in 4 years at S.I.
II. The sum amounts to Rs. 810 in 7 years at S.I.
III. The rate of interest is 10% p.a.  Options:	A) I and III only	B) II and III only	C) I and II only	D) Any one of the three	E) Any two of the above

Solution: Any two of the abovexplanation:   Clearly, any of the three will give us the answer   Answer: Any two of the above
Answer: E
Exactly 3/7 of the people in the room are under the age of 21, and exactly 5/10 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21? Choose the correct choice from the following: A) 21 B) 35 C) 39 D) 30 E) 65

Solution: The total number of the people in the room must be a multiple of both 7 and 10 (in order 3/7 and 5/10 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 7 and 10, which is 70.   Since, the total number of the people in the room is greater than 50 and less than 100, then there are 70 people in the room.   Therefore there are   3/7*70= 
  3/7*70 = 30
30 people in the room under the age of 21.   Answer: 30.
Answer: D
What is 121 times 11?	Choose one: A) 1331 B) 1313 C) 1133 D) 3131 E) 3311

Solution: 1331 1331
Answer: A
A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 5 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is? Choose the correct choice from the following answers:
A) 5729  B) 5760  C) 7200  D) 2870  E) 2799

Solution: 1/x - 1/6 = -1/8   x = 24 hrs    24 * 60 * 5= 
 24 * 60 * 5 = 7_200
7200.Answer: 7200
Answer: C
44Ã—98Ã—101=?  Choose the correct option.
A) 435512	B) 434431	C) 548654	D) 543286	E) 546543

Solution: 44Ã—(100-2)Ã—(100+1)   (4400-88)Ã—(100+1)   4312Ã—(100+1)   431200+4312= 
431200+4312 = 435_512
435512   answer 435512
Answer: A
A man performs 3/5 of the total journey by rail, 17/20 by bus and the remaining 6.5 km on foot. His total journey is : Choose the correct choice from the following choices:
A) 125 km  B) 130 km  C) 135 km  D) 140 km  E) None

Solution: Sol.   Let the total journey be x km. Then   3x/5 + 7x/20 + 6.5 = x   ⇔ 12x + 7x + 20 * 6.5 = 20x   ⇔ x = 130 km.   Answer 130 km
Answer: B
If k^3 is divisible by 120, what is the least possible value of integer k?
Choose the correct choice from the following answers:
A) 15	B) 30	C) 60	D) 90	E) 120

Solution: k^3 = 120*x = 2^3*3*5*x   The factors of k must at minimum include 2*3*5= 
2*3*5 = 30
30.   The answer is 30.
Answer: B
The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210? Choices
A) 3	B) 14	C) 30	D) 42	E) 70

Solution: Let's try the Prime Box Approach   Prime Box is simply a collection of all prime factors of a given number!   (1) Prime Box of 16 = |2, 2, 2, 2|   (2) Prime Box of 45 = |3, 3, 5|   (3) Prime Box of n = |2, 2, 3....|   (4) Prime Box of 210 = |2, 5, 3, 7|   From 3 and 4:   The GCF of n and 210 must be a multiple of 6.   So we can eliminate A, B and E!   From 2 and 3:   n is not a multiple of 5. If it were, the GCF of n and 45 would have been 15!   So we can eliminate C   The only remaining choice is '42'
Answer: D
Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 15 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?  Choose the most appropriate option
A) 477
B) 432
C) 279
D) 276
E) 291

Solution: 1h ----- 5   ? ------ 60   12 h   RS = 15 + 21= 
15 + 21 = 36
36   T= 12   D = 36 * 12= 
36 * 12 = 432
432.Answer: 432
Answer: B
Solomon taken a loan Rs.15000/- from Co-operative Society with an interest @ 11.5% per month. At the same time he deposited Rs. 10000/- as Fixed Deposit with an interest @ 9.5% per month. After one week sam asked the manager to calculate the interest to be paid. What is the interest amount for 7 days?	Pick one.
A) A)165  B) B)220  C) C)310  D) D)185  E) E)181

Solution: Loan amount : Rs.15000/- @ 11.5%   Interest per month = 15000/- * 11.5% =Rs.1725   Interest for one day = 1725/30= 
1725/30 = 115/2 = around 57.5
57.50   Interest for 7 days is= 57.50*7 =403   FD amount is = Rs.10000/- @ 9.5%   Interest per month = 10000 * 9.5% = 950/-   Interest for 7 days = 950/30*7 = 222   Interest amount to be paid by Solomon = 403-222= 
403-222 = 181
181/- for 7 days   Answer is 181
Answer: E
Five bells begin to toll together at 12:00 noon and toll respectively at intervals of 3, 4, 5, 6, and 7 seconds. Not including the toll at 12:00 noon, how many more times will all five bells toll together before 1:00 pm (i.e. one hour later)?  Choose the correct choice from the following answers:
A) 6 B) 8 C) 10 D) 12 E) 14

Solution: The least common multiple is 2*2*3*5*7= 
2*2*3*5*7 = 420
420.   3600 seconds / 420= 8 + remainder.   The answer is 8.
Answer: B
A number is divided by 406 leaves remainder 115,what will be the remainder when it will be divided by 29?  Choose the correct choice from the following choices.
A) 26	B) 30	C) 27	D) 28	E) 29

Solution: Let the Number be N.   So N=406x+115.   Now divide this number by 29   As 406 is exactly divisible by 29,we have to divide 115 by 29 and find the remainder.   So Remainder is 28   Option 28 is answer
Answer: D
Find the amount on Rs.5000 in 2 years, the rate of interest being 4% per first year and 5% for the second year?	Options.
A) 2288	B) 277	C) 9888	D) 5460	E) 2777

Solution: 5000 * 104/100 * 105/100= 
5000 * 104/100 * 105/100 = 5_460
> 5460,Answer: 9888
Answer: C
A car travels from point A to point B. The average speed of the car is 60 km/hr and it travels the first half of the trip at a speed of 75 km/hr. What is the speed of the car in the second half of the trip?	Choose the correct answer
A) 40
B) 45
C) 48
D) 50
E) 55

Solution: Let D be the distance and let V be the speed in the second half.   The total time = T1 + T2   50/60 = 50/150 + (50/2) / V   50/100 = 50/2V and so V = 50 km/hr   The answer is 50.
Answer: D
There is one four-digit whole number n, such that the last four digits of n2 are in fact the original number n
Select the correct option:
A) 8476
B) 7376
C) 9376
D) 7378
E) 9466

Solution: C   9376   Looking at the last digit, the last digit must be either 0, 1, 5 or 6.   Then looking at the last two digits, the last two digits must be either 00, 01, 25 or 76.   Then looking at the last three digits, the last three digits must be either 000, 001, 625 or 376.   Then looking at the last four digits, the last four digits must be either 0000, 0001, 0625 or 9376.   Out of those, only 9376 is a 4 digit number
Answer: C
A train 600 m long can cross an over brdge of 100m long in 70 sec and then find the speed of the train? Answers.
A) 79
B) 30
C) 36
D) 66
E) 12

Solution: Length = Speed * time   Speed = L/T   S = 700/70= 
700/70 = 10
10 M/Sec   Speed= 10*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 36Kmph.Answer:36
Answer: C
The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 5830, what is the length of the plot in metres?  Choose the correct option
A) 333  B) 200  C) 288  D) 276  E) 220

Solution: Let length of plot = L meters, then breadth = L - 20 meters   and perimeter = 2[L + L - 20] = [4L - 40] meters   [4L - 40] * 26.50 = 5830   [4L - 40] = 5830 / 26.50= 
5830 / 26.50 = 220
220   4L= 260   L = 260/4= 
260/4 = 65
65 meters.   Answer: 220
Answer: E
A man engaged a servant on a condition that he'll pay Rs 90 and also give him a bag at the end of the yr. He served for 9 months and was given a turban and Rs 65. So the price of turban is Select the correct option.
A) Rs 10
B) Rs 9
C) Rs 0
D) Rs 55
E) Rs 8

Solution: Let the value of turban =Rs x   For 1 year=90+x   For 9 months(i,e 3/4 year)=65+x   i,e   1:(90+x)::3/4:(65+x)   i,e   (90+x)/(65+x)=1/(3/4)   270+3x=260+4x   Thus x=10   Rs 10NSWER:Rs 10
Answer: A
A train covers a distance of 100km in 1 hour. If its speed is decreased by 15km/hr, the time taken by the car to cover the same distance will be? Choose the correct choice from the following options.
A) 1hr
B) 1hr 10min
C) 50min
D) 1hr 30min
E) 1hr 45min

Solution: Speed = 100/1= 
100/1 = 100
100km/hr   New speed= 100-15= 
100-15 = 85
85 km/hr   Time taken= 100/85 = 1hr 10min   Answer is 1hr 10min
Answer: B
Each week a restaurant serving Mexican food uses the same volume of chili paste, which comes in either 55-ounce cans or 15-ounce cans of chili paste. If the restaurant must order 30 more of the smaller cans than the larger cans to fulfill its weekly needs, then how many larger cans are required to fulfill its weekly needs?  Select.
A) 15 B) 28 C) 18 D) 24 E) 21

Solution: let x be the number of 55 ounce cans. Therefore (x+30) is the number of 15 ounce cans.   Total volume is same, therefore   55x=15(x+30)   30x=450   x=15   15ns - 15
Answer: A
Find the value of (1/(2*3))+(1/(3*4))+(1/(4*5))+(1/(5*6))+…..+ ((1/(9*10)).	Pick.
A) 2/5 B) 1/5 C) 4/5 D) 3/5 E) None of them

Solution: Given expression=((1/2)-(1/3))+((1/3)-(1/4))+((1/4)-(1/5))+   ((1/5)-(1/6))+….+ ((1/9)-(1/10))   =((1/2)-(1/10))=4/10 = 2/5.   2/5nswer is 2/5.
Answer: A
If the average (arithmetic mean) of the four numbers K, 2K + 3, 3K – 5 and 5K + 1 is 85, what is the value of K?
Pick: A) 11 B) 15 3/4 C) 31 D) 23 E) 25 3/10

Solution: K + 2K +3 + 3K - 5 + 5K +1 = 11K -1   (11K -1)/4 = 85   11K = 85 * 4 +1 = 340 +1= 
340 +1 = 341
341   K= 253 / 11 = 31.   Answer 31.
Answer: C
If (1+f)g=g, which of the following must be true?  Choose the correct choice from the following.
A) f=-1 or g=0
B) f=0 or g=0
C) f=1 or g=1
D) f=-1 or g=-1
E) f=0 or g=1

Solution: By only having fg=0, we cannot say answer is B as A and E options also satisfy the condition fg=0. ans f=0 or g=0
Answer: B
The area of a rhombus is equal to the area of a square whose side length is 8cm. If one of the diagonals is 16cm what is the length of other diagonal? Choose the correct choice from the following answers.
A) 4
B) 8
C) 12
D) 16
E) 20

Solution: Area of the square=8x8=64   Let 'l' be the unknown diagonal   0.5 x 16 x 'l' = 64 which gives 'l'=8cm   Answer: 8
Answer: B
If p and q are integers, such that p < 6 < q, and s is a nonnegative integer, which of the following must be true?
Choose the correct answer:
A) p^2 < q^2	B) p + q = 0	C) sp < sq	D) sp ≠ sq	E) p/q < s

Solution: We're told that P < 0 < Q and that S is a NON-NEGATIVE INTEGER. We're asked which of the following MUST be true.   P = -2   Q = 1   S = 0   Answer A: P^2 < Q^2.... 4 < 1 NOT TRUE   Answer B: P+Q=0... -2+1 = -1 NOT TRUE   Answer C: SP < SQ... 0 < 0 is TRUE   Answer D: SP ≠ SQ... 0 = 0 NOT TRUE   Answer E: P/Q < S... -2/1 < 0 not TRUE   sp < sq
Answer: C
Five years ago, the average age of A, B, C and D was 45 yr. with E joining them now, the average of all the five is 50 yr. How old is E?  Choose one:
A) 50 yr  B) 40 yr  C) 45yr  D) 64 yr  E) NOne

Solution: Solution:   Total present age of A, B, C and D,   = (45*4)+(4*5)= 
(45*4)+(4*5) = 200
200 yr;   Total age present age of A, B, C, D and E,= 50*5= 
50*5 = 250
250 yr.   So, age of E= 50 yr.   50 yrnswer: Option 50 yr
Answer: A