MU-NLPC/Calc-aqua_rat huggingface dataset:
A graph may be defined as a set of points connected by lines called edges. Every edge connects a pair of points. Thus, a triangle is a graph of 3 edges and 3 points. The degree of a point is the number of edges connected to it. For, example, a triangle is a graph with 3 points of degree 2 each. Consider a graph with 12 points. It is possible to reach any point from any through sequence of edges. The number of edges 'e' in the graph must satisfy the condition	Answers:
A) 11 ≤ e ≤ 66	B) 10 ≤ e ≤ 66	C) 11 ≤ e ≤ 65	D) 0 ≤ e ≤ 11	E) None

Solution: Explanation :   The least number of edges will be when one point is connected to each of the other 11 points, giving a total of 11 lines. One can move from any point to any other point via the common point.   The maximum edges will be when a line exists between any two points. Two points can be selected from 12 points in 12C2 i.e. 66 lines.   11 ≤ e ≤ 66nswer : 11 ≤ e ≤ 66
Answer: A
A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Select the correct option:	A) 177 m	B) 176 m	C) 240 m	D) 187 m	E) 186 m

Solution: Speed = [54 * 5/18] m/sec = 15 m/sec.   Length of the train = (15 * 20)= 
(15 * 20) = 300
300 m.   Let the length of the platform be x meters.   Then, x + 300 / 36= 15   x + 300 = 540   x = 240 m.   Answer: 240 m
Answer: C
If m and n are positive integers such that m is a factor of n, how many positive multiples of m are less than or equal to 2n ?  Choose the correct choice.
A) 2m/n + 1	B) 2n/m + 1	C) 2n/(m+1)	D) 2m/n	E) 2n/m

Solution: Lets say N=10, M=5   2N=20. so the answer should be 4 (20/5)   lets try to plug in the answers:   A-not an integer   B-not an integer   C-not an integer   D-1 (not the answer)   E-4 - the answer. (the only one).   I would choose E.   Method 2   N=M*A (A is an integer)   So - A=N/M   therefore in 2N A will be 2N/M   Again - Answer is 2n/m.
Answer: E
Jake remembers only the last three letters of his four-letter Klingon name. If he is sure that the first letter is neither "N" nor "X", and assuming that there are only 12 letters in the Klingon alphabet, what is the probability that he will give the correct name when asked for it by the space attendant? Choose the most appropriate option:
A) A)8/100 B) B)9/100 C) C)1/8 D) D)4/5 E) E)1/10

Solution: Total letters 12, out of which the first letter is anything of 10 but N or X...   So there are 10 possible letters for first place..   And only one of them is correct..   So 1/10.   Answer: 1/10
Answer: E
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue? Choices:
A) 1/455  B) 1/458  C) 1/453  D) 1/456  E) 1/454

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.   Probability that all the three marbles picked at random are blue   = ³C₃/¹⁵C₃ = (1 * 3 * 2 * 1)/(15 * 14 * 13)   = 1/455   1/455nswer: 1/455
Answer: A
For any real number x, the operatoris defined as:
(x) = x(5 − x)
If p + 1 =(p + 1), then p =
Choose the correct choice from the following answers
A) −2
B) 0
C) 1
D) 2
E) 4

Solution: (x) = x(5 − x)   (p + 1) = (p + 1)(5 - p - 1) = (4-p)(p+1)   We are given that p + 1 =(p + 1)   Therefore (4-p)(p+1) = (p + 1)   Or (p + 1) + (p-4)(p+1) = 0   (p + 1)(p-4) = 0   p = -1,p=4   Option 4
Answer: E
Last year Elaine spent 20% of her annual earnings on rent. This year she earned 20% more than last year and she spent 30% of her annual earnings on rent. The amount she spent on rent this year is what percent of the amount spent on rent last year? Choose the correct choice from the following.
A) 185.5 B) 180.0 C) 167.5 D) 172.5 E) 177.5

Solution: For this it is easiest to use simple numbers. Let's assume that Elaine's annual earnings last year were $100.   She would've spent $20 of this on rent.   This year she earned 20% more, or $120   She would've spent 30% of this on rent, or $36   Do $36/$20   This will give you 180%   180.0 is the correct answer.
Answer: B
A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train? Choose the correct option: A) 150m B) 157m C) 750m D) 850m E) 350m

Solution: Length of the train be ‘X’   X + 150/15 = X + 250/20   4X + 600 = 3X + 750   X = 150m   150mnswer:150m:
Answer: A
Calculate the average of all the numbers between 10 and 86 which are divisible by 9.	Choose the most appropriate option.
A) 49.5  B) 41.5  C) 45.5  D) 40.5  E) 47.5

Solution: Explanation:   numbers divisible by 9 are 18,27,36,45,54,63,72,81,   49.5verage = (18+27+36+45+54+63+72+81,) / 8 = 396/8= 
396/8 = 99/2 = around 49.5
49.5   49.5NSWER: 49.5
Answer: A
Two stations P and Q are 200 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?
Choices
A) 10 am  B) 12 noon  C) 10.30 am  D) 12.30 am  E) 11 am

Solution: Assume both trains meet after x hours after 7 am   Distance covered by train starting from P in x hours = 20x km   Distance covered by train starting from Q in (x-1) hours = 25(x-1)   Total distance = 200   => 20x + 25(x-1) = 200   => 45x = 225   => x= 5   Means, they meet after 5 hours after 7 am, ie, they meet at 12 noon   Answer is 12 noon.
Answer: B
A tank is 25m long 12m wide and 6m deep. The cost of plastering its walls and bottom at 55 paise per sq m is	Choose the correct option.
A) Rs. 209.20	B) Rs. 309.20	C) Rs. 409.20	D) Rs. 509.20	E) None of these

Solution: Explanation:   Area to be plastered = [2(l + b) Ã— h] + (l Ã— b)   = [2(25 + 12) Ã— 6] + (25 Ã— 12) = 744 sq m   Cost of plastering = 744 Ã— (55/100) = Rs. 409.20 Answer: Rs. 409.20
Answer: C
Working at a constant rate, P can finish a job in 3 hours. Q, also working at a constant rate, can finish the same job in 15 hours. If they work together for 2 hours, how many more minutes will it take P to finish the job, working alone at his constant rate? Select:
A) 30
B) 36
C) 40
D) 45
E) 48

Solution: Each hour they complete 1/3 + 1/15 = 2/5 of the job.   In 2 hours, they complete 2(2/5) = 4/5 of the job.   The time for P to finish is (1/5) / (1/3) = (3/5) hour = 36 minutes   The answer is 36.
Answer: B
A money lender lends Rs.2000 for six months at 20% p.a. rate. It the interest is reckoned quarterly than find the amount given after time limit?	Choose the most appropriate option:
A) 2205
B) 2229
C) 2205
D) 2984
E) 2223

Solution: 2205 = 2000(21/20)2   = 2205   2205nswer:2205
Answer: A
Find the least number of five digits which is exactly divisible by 12 and 18?	Choose the correct option
A) A)1080	B) B)10080	C) C)10025	D) D)11080	E) E)12080

Solution: The smallest five digit numbers are   10025,10080,11080   10025 is not divisible by 12   10080 is divisible by both 12 and 18   ANSWER:10080
Answer: B
A, B and C invest in a partnership in the ratio: 7/2, 4/3, 6/5. After 4 months, A increases his share 50%. If the total profit at the end of one year be Rs. 22,140, then what is B's share in the profit?	Options: A) Rs. 2000 B) Rs. 3100 C) Rs. 4100 D) Rs. 5200 E) None of these

Solution: Explanation :   Ratio of the initial investment = 7/2 : 4/3 : 6/5   = 105 : 40 : 36   From this ratio, we can assume that actual initial investments of A, B and C   are 105x, 40x and 36x respectively   A increases his share 50% after 4 months. Hence the ratio of their investments =   (105x * 4) + (105x * 150/100 * 8) : 40x * 12 : 36x : 12   = 105 + (105 * 3/2 * 2) : 40*3 : 36 * 3   = 105 * 4 : 40 *3 : 36 * 3   = 35 * 4 : 40 : 36   = 35 : 10 : 9   B's share = total profit * (10/54) = 22,140 * 10/54 = 4100. Answer : Option Rs. 4100
Answer: C
Which number, when found in the denominator of any given fraction, gives a terminating decimal?
Choose the correct choice from the following: A) 75 B) 80 C) 85 D) 90 E) 95

Solution: 75 = 3 * 5 * 5; 80 = 2^4 * 5; 85 = 5 * 17; 90 = 2 * 3^2 * 5; 95 = 5 * 19.   Only Option B has 2 and 5 as factors, hence terminating.   Option 80.
Answer: B
Anup start a bike at 6am. and rides it at 60kmph. Raghu started at 7pm with his car at 120kmph. When will Raghu overtake Anup?
Choose one
A) 8:00am  B) 9:40am  C) 10:00am  D) 12:00pm  E) 11:10am

Solution: Suppose bike is overtaken by car xhrs after 6am   Distance covered by the bike in x hrs = distance covered by the car in x-1 hr   60x = 120(x-1)   60x = 120   x = 2 hrs   Required time = 6+2= 
6+2 = 8
8:00am   8:00amnswer is 8:00am
Answer: A
The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?  Choose the correct choice from the following
A) 81:121	B) 81:131	C) 81:145	D) 81:167	E) 81:113

Solution: Ratio of the sides   = ³√729 : ³√1331 = 9 : 11   Ratio of surface areas   = 92 : 112 = 81:121   81:121nswer:81:121
Answer: A
The sum of three consecutive multiples of 3 is 99. What is the largest number?
Choose the correct choice from the following answers.
A) 36
B) 33
C) 30
D) 27
E) 24

Solution: Let the numbers be 3x, 3x + 3 and 3x + 6.   Then,   3x + (3x + 3) + (3x + 6) = 99   9x = 90   x = 10   Largest number = 3x + 6 = 36   36nswer : 36
Answer: A
Find the average of the series : 4555,250,355,450,150  Pick one.
A) 129 B) 1152 C) 267 D) 207 E) 174

Solution: Average = (4555+250+355+450+150)/5   = 5760/5= 
5760/5 = 1_152
1152   Answer: 1152
Answer: B
If x is a positive integer, then the least value of x for which x! is divisible by 1,000,0000 is?
Can someone please explain intuitively what the question is asking?
Choose the most appropriate option:
A) 5 B) 9 C) 25 D) 15 E) 30

Solution: In order x! to be divisible by 1,000, it should have at least 3 trailing zeros. A trailing 0 in factorial of a number is produced by 2 and 5 in it:   2*5= 
  2*5 = 10
10. So, we need 10 to be in x! at least in power of 3.   5!= 120 has 1 trailing zeros.   10! will have 2 trailing zeros.   15! will have 3 trailing zeros.   20! will have 5 trailing zeros.   25! will have 7 trailing zeros. 25
Answer: C
population is 20000. Pop increases by 10% every year, then the pop after 3 years is? Select the correct option
A) 26630 B) 26640 C) 36620 D) 26620 E) 26820

Solution: population after 1st year = 20000*10/100= 
20000*10/100 = 2_000
2000===> 20000+2000= 
20000+2000 = 22_000
22000   population after 2nd year= 22000*10/100= 
22000*10/100 = 2_200
2200===> 22000+2200= 
22000+2200 = 24_200
24200   population after 3rd year= 24200*10/100= 
24200*10/100 = 2_420
2420===> 24200+2420= 
24200+2420 = 26_620
26620   ANSWER:26620
Answer: D
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is: Choose the correct choice
A) 288
B) 66
C) 245
D) 77
E) 29

Solution: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.Answer: 245
Answer: C
The value of (4 3) + 2 is Options:
A) 33 B) 10 C) 14 D) 24 E) 11

Solution: Evaluating, (4 3) + 2 = 12 + 2= 
12 + 2 = 14
14.   correct answer 14
Answer: C
A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?  Choose the most appropriate option
A) 150 B) 878 C) 277 D) 992 E) 187

Solution: Length of the train be ‘X’   X + 150/15 = X + 250/20   4X + 600 = 3X + 750   X = 150m   150nswer: 150
Answer: A
A train ,125 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is Choose the correct answer:	A) 250 m	B) 245 m	C) 235 m	D) 220 m	E) 240 m

Solution: Explanation:   250 mssume the length of the bridge = x meter   Total distance covered = 125+x meter   total time taken = 30s   speed = Total distance covered /total time taken = (125+x)/30 m/s   => 45 Ã— (10/36) = (125+x)/30   => 45 Ã— 10 Ã— 30 /36 = 125+x   => 45 Ã— 10 Ã— 10 / 12 = 125+x   => 15 Ã— 10 Ã— 10 / 4 = 125+x   => 15 Ã— 25 = 125+x = 375   => x = 375-125= 
375-125 = 250
250   250 mnswer: Option 250 m
Answer: A
Three partners A,B and C invest Rs.18000, Rs.22500 and Rs.27000 respectively in a business. If total profit is Rs.18750 then B's share is (in Rs.) Choices:  A) 10000  B) 6250  C) 5000  D) 7500  E) 8500

Solution: 18000:22500:27000   4:5:6   6250's share=18750*5/15= 
18750*5/15 = 6_250
6250   ANSWER:6250
Answer: B
If the probability that the Chicago Bears win the Super Bowl is 1/20 and the probability that the Chicago Cubs win the World Series is 1/7, what is the probability that either the Bears win the Super Bowl or the Cub win the World Series (but not both)?
Choose the correct answer
A) 2/7  B) 3/16  C) 4/25  D) 5/28  E) 6/37

Solution: 19/20*1/7 + 1/20*6/7 = 25/140 = 5/28   The answer is 5/28.
Answer: D
The credit card and a global payment processing companies have been suffering losses for some time now. A well known company recently announced its quarterly results. According to the results, the revenue fell to $52.0 billion from $69.0 billion, a year ago. By what percent did the revenue fall?
Select
A) 20.8	B) 24.6	C) 31.8	D) 32.5	E) 33.8

Solution: $69-$52=17$   (17/69)*10069- 52= 
69- 52 = 17
17$   (17/69)*100=24.6%   ANSWER:24.6
Answer: B
What day of the week was 1 January 1701 Choose the correct choice from the following answers:
A) Tuesday
B) Monday
C) Friday
D) Saturday
E) Sunday

Solution: Explanation:   1 Jan 1701 = (1700 years + 1st Jan 1701)   We know that number of odd days in 400 years = 0   Hence the number of odd days in 1600 years = 0 (Since 1600 is a perfect multiple of 400)   Number of odd days in the period 1601-1700   = Number of odd days in 100 years   = 5   (As we can reduce perfect multiples of 7 from odd days without affecting anything)   1st Jan 1701 = 1 odd day   Total number of odd days = (0 + 5 + 1)= 
(0 + 5 + 1) = 6
6   6 odd days= Saturday   Hence 1 January 1701 is Saturday.   Answer: Option Saturday
Answer: D
An American cafeteria offers 3 flavors of pizza - chicken, Hawaiian and vegetarian. If a customer has an option (but not the obligation) to add extra cheese, mushrooms or both to any kind of pizza, how many different pizza varieties are available ?
Choose the correct option.
A) 4	B) 8	C) 12	D) 9	E) 32

Solution: 3 flavours * 3 choices = 3C1*3C1 = 3*3= 
3*3 = 9
9=9
Answer: D
Michael is twice as old as he was 8 years ago. What is his present age? Pick:
A) 10 years B) 4 years C) 8 years D) 6 years E) 16 years

Solution: Let Michael' spresent age be x.   2 ( x - 8 ) = 8   x = 16 years   Michael's present age is 16 years.   Answer : 16 years
Answer: E
Helen went to the stationers and bought things worth Euro 21, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? Choose the correct choice from the following choices
A) uro 16.70	B) uro 19.70	C) uro 13.70	D) uro 18.70	E) uro 15.70

Solution: E   Euro 15.70   Let the amount taxable purchases be Euro x.   Then, 6% of x = 30/100   x = (30/100 x 100/6) = 5.   Cost of tax free items = uro 15.70uro [  21 - (5 + 0.30)= 
  21 - (5 + 0.30) = 15.7
uro 15.70uro 15.70
Answer: E
Set S has a mean of 10 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most?	Choose the correct answer.
A) {2, 10}
B) {16, 16}
C) {10, 18}
D) {9, 11}
E) {7, 13}

Solution: answer B,C, and E mean is not 10 therefore not accepted . D mean is 10 but S.D is one unit. therefore accepted   answer is D mean is 10 and S.D decreases minimum.   {9, 11}
Answer: D
A semicircle has a radius of 14. What is the approximate perimeter of the semicircle?
Choose the correct choice from the following answers
A) 72  B) 76  C) 80  D) 84  E) 88

Solution: The perimeter of a circle is 2*pi*r.   The perimeter of a semicircle is 2*pi*r/2 + 2r = pi*r + 2r   The perimeter is pi*14 + 2*14 which is about 72.   The answer is 72.
Answer: A
15 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men?  Choose the correct choice from the following options
A) 13	B) 65	C) 30	D) 88	E) 12

Solution: 3W = 2M   15M ------ 21 * 8 hours   21 W ------ x * 6 hours   14 M ------ x * 6   15 * 21 * 8 = 14 * x * 6   x = 30. Answer: 30
Answer: C
If the two-digit integers M and N are positive and have the same digits, but in reverse order, which of the following CANNOT be the sum of M and N?  Choose the correct choice from the following options:
A) 181 B) 165 C) 121 D) 99 E) 44

Solution: M=10x+y   N=10y+x   M+N=11x+11y=11(x+y)   In other words the answer is a multiple of 11.   Now the question becomes " which of the following is NOT a multiple of 11?"   181nswer -181   181NSWER:181
Answer: A
How many terms are there in 2,4,8,16……1024?
Select: A) 10 B) 12 C) 14 D) 16 E) 15

Solution: Clearly 2,4,8,16……..1024 form a GP. With a=2 and r = 4/2= 
4/2 = 2
2.   Let the number of terms be n . Then   2 x 2^n-1=1024 or 2^n-1=512 = 2^9.   n-1=9 or n=10   10nswer is 10.
Answer: A
Rs 50000 is divided into two parts One part is given to a person with 10% interest and another part is given to a person with 20 % interest. At the end of first year he gets profit 8000 Find money given by 10%?
Pick.
A) 20000	B) 40000	C) 50000	D) 60000	E) 70000

Solution: let first parrt is x and second part is y then x+y=50000----------eq1   total profit=profit on x +profit on y   8000=(x*10*1)/100 + (y*20*1)/100   80000=x+2y-----------------------------------eq2   80000=50000+y   so y=30000 then x =50000-30000= 
50000-30000 = 20_000
20000   first part=20000   20000NSWER:20000
Answer: A
Seven cards numbered from 1 to 7 are placed in an empty bowl. First one card is drawn and then put back into the bowl, and then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 9, what is the probability that one of the two cards drawn is numbered 6?  Pick:
A) 1/3 B) 2/3 C) 1/5 D) 2/5 E) 2/7

Solution: There are 6 ways to get a total sum of 9.   2 of these ways include the number 6.   The probability that one of the cards is a 6 is 2/6 = 1/3   The answer is 1/3.
Answer: A
If a number W between 0 and 1 is selected at random, which of the following will the number most likely be between? Choose the correct choice
A) 0 and 3/20
B) 3/20 and 1/5
C) 1/5 and 1/4
D) 1/4 and 3/10
E) 3/10 and 1/2

Solution: The number W will most likely be between the largest range.   A. 0 and 3/20 --> range 3/20;   B. 3/20 and 4/20 --> range 1/20;   C. 4/20 and 5/20 --> range 1/20;   D. 5/20 and 6/20 --> range 1/20;   E. 6/20 and 10/20 --> range 4/20.   Answer: 3/10 and 1/2.
Answer: E
A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 5 miles per hour and returns along the same road at an average speed of 6 miles per hour. What is the bicyclist’s average speed for the round trip, in miles per hour? Choose the correct choice from the following.
A) (a) 60/11 B) (b) 5 C) (c) 26/5 D) (d) 27/5 E) (e) 28/5

Solution: from the uphill we can find out the distance = 5*2= 
5*2 = 10
10   average speed= total distance/total time   = 20/ (2+ (10/6)) = 60/11   (a) 60/11nswer is (a) 60/11.
Answer: A
the perimeter of an equilateral triangle is 45.if one of the side is the side of an isoceles triangle of perimeter 40 then what is the lenght of base of isoceles triangle.
Options
A) 10 units
B) 20 units
C) 30 units
D) 40 units
E) 15 units

Solution: base of isoceles triangle is 40-15-15= 
40-15-15 = 10
10 units.   10 unitsNSWER:10 units
Answer: A
What annual payment will discharge a debt of Rs. 1090 due in 2 years at the rate of 5% compound interest?
Choices:
A) 993.2 B) 586.21 C) 534.33 D) 543.33 E) 646.33

Solution: Explanation:   Let each installment be Rs. x. Then,   x/(1 + 5/100) + x/(1 + 5/100)2 = 1090   820x + 1090 * 441   x = 586.21   So, value of each installment = Rs. 586.21   Answer: Option 586.21
Answer: B
The average (arithmetic mean) of four distinct positive integers is 10. If the average of the smaller two of these four integers is 10, which of the following represents the maximum possible value of the largest integer? Choose the correct choice:
A) 4	B) 6	C) 20	D) 10	E) 1

Solution: Let the distinct number be A,B,C, and D   Its given A > B > C > D   also A + B + C + D =40 and A + B = 10 means C + D = 30   Since the question ask for the largest possible number we should choose the least value for A and B,C. So D should be 20. If D=20 then 20 = 10 > A,B <10   Answer : 20
Answer: C
A man can row with a speed of 23 kmph in still water. If the stream flows at 9 kmph, then the speed in downstream is? Choices:
A) 32 B) 26 C) 20 D) 87 E) 24

Solution: M = 23   S = 9   DS = 23 + 9= 
23 + 9 = 32
32   32nswer: 32
Answer: A
A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup? Select the correct option
A) 7/11
B) 6/7
C) 1/5
D) 2/7
E) None of these

Solution: Explanation :   Let, the vessel initially contains 8 litres of liquid.   Let x litres of this liquid be replaced with water then quantity of water in new mixture   =>3−(3x/8)+x litres.   Quantity of syrup in new mixture =5−5x/8 litres.   Therefore,   =>3−(3x/8)+x=5−5x/8.   =>5x+24=40−5x.   =>x=8/5.   So part of the mixture replaced,   =>(8/5)×(1/8)=1/5.   Answer : 1/5
Answer: C
Three photographers, Lisa, Mike and Norm, take photos of a wedding. The total of Lisa and Mikes photos is 80 less than the sum of Mike's and Norms. If Norms photos number 10 more than twice the number of Lisa's photos, then how many photos did Norm Take?
Pick:
A) 40 B) 50 C) 150 D) 80 E) 90

Solution: L+M=M+N-80 / N=2L+10   80=M+N-L-M   80=N-L   80=2L+10-L   70=L   2(70)+10=150   150
Answer: C
What approximate value should come in place of the question mark (?) in the following equation?
152√? + 795 = 8226 – 3486  Choose the correct choice from the following answers:
A) 425 B) 985 C) 1225 D) 1025 E) 675

Solution: 152√? ≈   8200 - 3500 - 800= 
  8200 - 3500 - 800 = 3_900
3900   ∴ √?= 3900⁄152   = slightly less than (4000⁄150) = 26.67 i.e., 26   ∴ √? = (26)2 = 676 ≈ 675   Answer 675
Answer: E
The average of seven numbers is 27. If one number is excluded, the average becomes 25. The excluded number is	Choose the correct choice from the following options
A) 25
B) 27
C) 30
D) 39
E) 40

Solution: Sol.   Therefore excluded number   = (27 × 7) - ( 25 × 6)   = 189 – 150   = 39.   Answer 39
Answer: D
If a young child was 14 months old one year ago, how old was the child, in months, x months ago?	Choose one.
A) x − 26 B) x − 12 C) 14 − x D) 24 − x E) 26 − x

Solution: The child's age today is 14 months + 12 months = 26 months   x months ago, the child's age was (26 - x) months old.   The answer is 26 − x.
Answer: E
A solution of X pounds of water and sugar is boiled until 20% of the water content evaporates. Originally w% of sugar was present in the solution. After evaporation, what percentage of the solution is sugar?  Pick one
A) 100w/(1-w)  B) 80w/(1-w)  C) 75w/(1-w)  D) 100w/(80-0.2w)  E) 100w/(80+0.2w)

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 w = 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 100w/(80+0.2w): 100w/(80+0.2w) >>> 100x10 / 82
Answer: E