MU-NLPC/Calc-aqua_rat huggingface dataset:
In a forest 160 deer were caught, tagged with electronic markers, then released. A week later, 50 deer were captured in the same forest. Of these 50 deer, it was found that 5 had been tagged with the electronic markers. If the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest, and if no deer had either left or entered the forest over the preceding week, what is the approximate number of deer in the forest?
Choose the correct choice from the following options
A) 150  B) 750  C) 1,250  D) 1,600  E) 2,500

Solution: The percentage of tagged deer in the second sample = 5/50*100= 
5/50*100 = 10
10%.   So, 160 tagged deers comprise 10% of total # of deers --> total # of deers= 160*10 = 1,600.   Answer: 1,600.
Answer: D
If each term in the sum T=a1+a2+a3+...+an either 2 or 22 and the sum equals 100, which of the following could be equal to n?	Select:
A) 38
B) 39
C) 40
D) 41
E) 42

Solution: Min value of 'n' can be 10 i.e 4*22+6*12=T => 22+22+22+22+2+2+2+2+2+2= 
22+22+22+22+2+2+2+2+2+2 = 100
100   Since we don't have 10 in the options proceed further, (10-1)+22/2=> 20 digits, which is again not in the options    (20-1) + 22/2= 
 (20-1) + 22/2 = 30
30 digits ( not in options)   (30-1) + 22/2= 
(30-1) + 22/2 = 40
40 digits   Hence 40.
Answer: C
When x + p is divided by p - 2, the quotient is n and there is no remainder. Which of the following must be the value of x?	Choose the most appropriate option:
A) n(p +1)
B) n(p − 1)
C) p(n + 1) + 2n
D) p(n - 1) + 2n
E) n(p + 1) (p − 1)

Solution: Given in question (x+p)/p-2= n   => x+p= n(p-2)   =>x= np+2n-p   or x= np-p+2n   Now we are good to check the options   x= p(n-1) + 2n   Answer p(n - 1) + 2n
Answer: D
Indu gave Bindu Rs.2500 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
Choose the correct choice from the following.
A) 1	B) 2	C) 3	D) 4	E) 5

Solution: 2500 = 4(100/4)2   4 = 4   Answer: 4
Answer: D
What was the day of the week on, 16th July, 1776? Choose the correct choice from the following options:
A) Tuesday B) Wednesday C) Monday D) Saturday E) SUNDAY

Solution: 16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776)   Counting of odd days :   1600 years have 0 odd day.   100 years have 5 odd days.   75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2 days) = 2 odd days.   1775 years have (0 + 5 + 2)= 
(0 + 5 + 2) = 7
7 odd days= 0 odd day.   Jan Feb Mar Apr May Jun Jul   31 + 29 + 31 + 30 + 31 + 30 + 16= 
31 + 29 + 31 + 30 + 31 + 30 + 16 = 198
198 days= (28 weeks + 2 days)   Total number of odd days = (0 + 2)= 
(0 + 2) = 2
2.   Required day was 'Tuesday'.   Tuesdaynswer:Tuesday
Answer: A
A horse is tethered to one corner of a rectangular grassy field 45 m by 25 m with a rope 22 m long. Over how much area of the field can it graze? Choose the correct choice from the following
A) 354 cm2	B) 380 m2	C) 350 m2	D) 407 m2	E) None of these

Solution: Area of the shaded portion   = 1⁄4 × π × (22)2 = 380 m2   Answer 380 m2
Answer: B
A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
Select the correct option
A) 20 hrs  B) 25 hrs  C) 35 hrs  D) Cannot be determined  E) None of these

Solution: Suppose pipe A alone takes x hours to fill the tank.   Then, pipes B and C will take x/2 and x/4 hours respectively to fill the tank.   1/x + 2/x + 4/x = 1/5   7/x = 1/5 => x = 35 hrs.   ANSWER:35 hrs
Answer: C
If 0 < a < b < c < 1 , which of the following are positive?
I.	b-c
II.	a-b
III.	c-a Choose the correct choice from the following answers:
A) I only
B) II only
C) III only
D) I and II
E) I and III

Solution: We could solve this easily using examples.   I is false since b<c and="" are="" b<c="" both="" c="" false="" ii="" iii="" is="" positive="" since="" true="">a and both are positive   So, the answer is III only.</c>
Answer: C
Evaluate combination
100C97=100!/(97)!(3)!
Pick one.
A) 161700
B) 151700
C) 141700
D) 131700
E) None of these

Solution: Explanation:   nCr=n!/(r)!(n−r)!   100C97=100!/(97)!(3)!   =100∗99∗98∗97!/(97)!(3)!   =100∗99∗98/3∗2∗1   =100∗99∗98/3∗2∗1=161700   Option 161700
Answer: A
Find the area of trapezium whose parallel sides are 26 cm and 18 cm long, and the distance between them is 15 cm.	Pick one: A) 227 B) 299 C) 330 D) 161 E) 212

Solution: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)   = 1/2 (26 + 18) * (15)   = 330 cm2   Answer: 330
Answer: C
X and Y started a business by investing Rs.36000 and Rs.42000 respectively after 4 months Z joined in the business with an investment of Rs.48000, then find share of Z in the profit of Rs.14080 ?	Choose the correct choice from the following answers:
A) 3200 B) 4000 C) 3250 D) 3825 E) 4096

Solution: Ratio of investment, as investments is for different time.   Investment x Number of units of time.   Ratio of investments X : Y : Z = 36000 : 42000 : 48000 => 6 : 7 : 8.   X = 6 x 12 Months = 72, Y = 7 x 12 = 84, Z = 8 X 8 = 64 => 18 : 21 : 16.   Ratio of investments => X : Y : Z = 18 : 21 : 16.   Investment Ratio = Profit sharing Ratio.   Z = 14080 Ã— 16/55 = Rs.4096.   Share of Z in the profit is Rs.4096.   Option 4096
Answer: E
Two persons start running simultaneously around a circular track of length 300 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
Choose the correct answer.
A) 16 seconds	B) 18 seconds	C) 19 seconds	D) 27 seconds	E) 10 seconds

Solution: Time taken to meet for the first time anywhere on the track   = length of the track / relative speed   = 300 / (15 + 25)5/18 = 300* 18 / 40 * 5   = 27 seconds.   Answer:27 seconds
Answer: D
If the manufacturer gains 10 %, the wholesale dealer 15 % and the retailer 25 %, then find the cost of production of a table if the retail price was Rs 1265 Choose the correct answer
A) Rs. 750
B) Rs. 800
C) Rs. 850
D) Rs. 900
E) None of these

Solution: Explanation:   Let the cost of Production = Rs. P   Then, as per question,   =>(125/100∗115/100∗110/100∗P)=1265   =>253/160P=1265   =>P=800   Option Rs. 800
Answer: B
The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?	Pick one.
A) 12
B) 16
C) 17
D) 19
E) 10

Solution: Speed of the boat downstream = 15 + 3= 
15 + 3 = 18
18 kmph= 18 * 5/18= 
18 * 5/18 = 5
5 m/s   Hence time taken to cover 60 m= 60/5= 
60/5 = 12
12 seconds.   12nswer: 12
Answer: A
A meeting has to be conducted with 5 managers.Find the number of ways in which the managers may be selected from among 8 managers,if 2 managers will not attend the meeting together. Select:
A) 1.35	B) 2.91	C) 3.12	D) 4.36	E) 5.15

Solution: 8 managers, but two of them cannot attend the meeting together.   We can split it into two cases.   1. Meeting without these two managers in it. That would mean selecting 5, from the remaining 6 which is 6C5 = 6   2. Meeting with one of the two managers. select 1 manager from two, and then select 4 from the remaining 6, which is 2C1 X 6C4 = 15.   So, answer is   30 + 6= 
  30 + 6 = 36
36.   Answer : 4.36
Answer: D
If 0.25 of a number is equal to 0.05 of another number, the ratio of the numbers is :  Choose one.
A) 2 : 5  B) 3 : 4  C) 1 : 5  D) 20 : 5  E) 30:7

Solution: 0.25A = 0.05B   -> A/B = 0.05/0.25 = 5/25 = 1/5   :. A : B = 1 : 5   ANSWER:1 : 5
Answer: C
The average weight of A,B,C is 45 Kg. The avgwgt of A & B be 40Kg & that of B,C be 43Kg. Find the wgt of B.	Select the correct option.
A) 23
B) 43
C) 21
D) 31
E) 43

Solution: Sol. Let A,B,c represent their individual wgts.   Then,   A+B+C=(45*3)= 
(45*3) = 135
135Kg   A+B=(40*2)= 
(40*2) = 80
80Kg & B+C=(43*2)= 
(43*2) = 86
86Kg   B=(A+B)+(B+C)-(A+B+C)   =(80+86-135)= 
(80+86-135) = 31
31Kg.   ANSWER 31
Answer: D
A family made a down payment of $20
and borrowed the balance on a set of
encyclopedias that cost $120. The
balance with interest was paid in 7
monthly payments of $15.2 each and a
final payment of $7. The amount of
interest paid was what percent of the
amount borrowed?
Choose the correct choice from the following options.
A) 6%
B) 12%
C) 13.4%
D) 16%
E) 20%

Solution: interest paid = 15.2*7+7 - 100= 
15.2*7+7 - 100 = 13.4
13.4   % off the balance= (13.4/100) * 100= 
(13.4/100) * 100 = 13.4
13.4 %   Answer is 13.4%.
Answer: C
If x^2 = 161, which of the following is closest to a potential value of x?  Choose the correct choice from the following options: A) -127 B) -11 C) 12 D) 13 E) 131

Solution: Here the thing we must not forget is that X^even has two potential solutions   => x =+- √161 => +- 13 (approx)   this value is closer to 13   Hence 13 is correct.
Answer: D
What least number should be subtracted from 1398 so that the remainder when divided by 7, 9, and 11 will leave in each case the same remainder 5 ?
Pick one.
A) 6
B) 7
C) 8
D) 10
E) 11

Solution: The LCM of 7, 9, and 11 is 693. The next multiple is  2*693= 
 2*693 = 1_386
1386.   1386 + {remainder}= 1386 + 5= 
1386 + 5 = 1_391
1391, which is 7 less than 1398.   Answer: 7.
Answer: B
If 1 + 9 + 11 = 1, Then what is the value of
12 + 11 + 9 = ?  Choose the correct choice
A) 12 B) 7 C) 11 D) 9 E) 10

Solution: 10   10xplanation:   10quation 1 + 9 + 11 = 1 can be derived from   One (o) + nine (n) + eleven (e) = one => 1   Similarly for equation,   12 + 11 + 9   Twelve (t) + eleven (e) + nine (n) => ten (10)
Answer: E
If 90% of A =30% of B and B=x% of A, then the value of x is? Choose the correct choice:	A) 800	B) 300	C) 700	D) 400	E) None of these

Solution: 0.9 A= 0.3 300   so b=3A means 300% of A   ANSWER:300
Answer: B
During the first two weeks of May, the total rainfall in Springdale was 35 inches. If the rainfall during the second week was 1.5 times the rainfall during the first week, what was the rainfall in inches during the second week of May? Select the correct option: A) 12 B) 15 C) 18 D) 21 E) 24

Solution: Let x be the rainfall in the first week. Then 1.5x was the rainfall in the second week.   2.5x = 35   x = 14   The rainfall during the second week was  1.5 * 14= 
 1.5 * 14 = 21
21 inches   The answer is 21.
Answer: D
An athlete runs 200 metres race in 25 seconds. What is his speed?  Pick one
A) 23 B) 38 C) 37 D) 30 E) 28.8

Solution: Speed=Distance/Time = 200/25= 
200/25 = 8
8 m/s= 8 * 18/5= 
8 * 18/5 = 144/5 = around 28.8
28.8 km/hr   Answer :28.8
Answer: E
If 5 machines can produce 20 units in 10 hours, how long would it take 25 to produce 100 units? Choose one.
A) 5  B) 9  C) 6  D) 10  E) 2

Solution: 5 machines would produce 100 units in 50 hours. Increasing the amount of machines by 5 would mean dividing 50 hours by 5.   50/5= 
50/5 = 10
10   Answer : 10
Answer: D
A can do a piece of work in 21 days and B in 28 days. Together they started the work and B left after 4 days. In how many days can A alone do the remaining work? Choose the correct choice from the following answers.
A) 22 B) 88 C) 27 D) 14 E) 99

Solution: Let A worked for x days.   x/21 + 4/28 = 1 => x/21 = 6/7 => x = 18   A worked for 18 days. So, A can complete the remaining work in   18 - 4= 
  18 - 4 = 14
14 days.   Answer: 14
Answer: D
Four milkmen rented a pasture. A grazed 24 cows for 3 months; B 10 for 5 months; C 35 cows for 4 months and D 21 cows for 3 months. If A's share of rent is Rs. 1440, find the total rent of the field. Choose one.
A) 6500	B) 3550	C) 4250	D) 2250	E) 3250

Solution: Ratio of shares of A, B, C, D = (24 x 3) : (10 x 5) : (35 x 4) : (21 x 3) = 72 : 50 : 140 : 63.   Let total rent be Rs. x. Then, A’s share = Rs. (72x)/325   (72x)/325=1440 = x=(1440 x 325)/72 = 6500   Hence, total rent of the field is Rs. 6500.   6500nswer is 6500.
Answer: A
Which of the following is equal to (x+2)!/x!? Choices
A) x-1	B) 1+(1/x)	C) 1	D) x+1	E) (x+1)(x+2)

Solution: (x + 1)! = (x + 1) (x+2)* x!   (x + 1)!/x! = (x + 1)(x+2)   Answer: (x+1)(x+2)
Answer: E
A can do a job in 8 days and B can do it in 20 days. A and B working together will finish twice the amount of work in ------- days?	Choose the correct option:  A) 21 ½ days  B) 11 3/7 days  C) 23 ½ days  D) 12 ½ days  E) None of these

Solution: Explanation:   1/8 + 1/20 = 7/40   40/7 = 40/7 *2 = 11 3/7 days   Answer: 11 3/7 days
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 choices:
A) 11 B) 99 C) 28 D) 20 E) 87

Solution: In 1hr, the bus covers 60 km without stoppages and 40 km with stoppages.   Stoppage time = time take to travel (60 - 40) km i.e 20 km at 60 km/hr.   stoppage time = 20/60 hrs = 20 min.   Answer:20
Answer: D
The price of 3 tables and 4 chairs is Rs. 3300. With the same money one can buy 2 tables and 10 chairs. If one wants to buy 1 table and 1 chair, how much does he need to pay?
Pick one:
A) Rs.940 B) Rs.1050 C) Rs.1040 D) Rs.950 E) Rs.960

Solution: Explanation :   Let price of a table = t   and price of a chair = c   3t + 4c = 3300 ---(Equation 1)   2t + 10c = 3300   => t + 5c = 1650 ---(Equation 2)   (Equation 2) × 3 => 3t + 15c = 4950 ---(Equation 3)   (Equation 3) - (Equation 1) => 11c = 1650   => c = 150   Substituting the value of c in equation 1, we get   3t + (4 × 150) = 3300   => 3t = 3300 – 600 = 2700   =>t = 2700/3= 
2700/3 = 900
900   Cost of 1 table and 1 chair= c + t = 150 + 900= 
150 + 900 = 1_050
1050   Answer : Rs.1050
Answer: B
All the stocks on the over-the-counter market are designated by either a 6 letter or 5 letter codes that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes? Pick one:
A) 2(26^5)
B) 26(26^4)
C) 27(26^6)
D) 26(26^5)
E) 27(26^5)

Solution: with 4 letters: 26^6   with 5 letters: 26^5   26^6 + 26^5 = 27*(26^5)   27(26^6)
Answer: C
If (10^86) – 23 is written as a base 10 integer, which of the following options is the sum of the digits in that integer?	Answers
A) 780 B) 775 C) 790 D) 730 E) 770

Solution: We know that (10^86) is ending 00, so (10^86) – 23=9....9977   total number of digits in (10^86) – 23 is 86, or 84 digits of 9 and two digits 7 and 7.   answer choice is   84*9+14= 
  84*9+14 = 770
770   Answer is 770 770
Answer: E
On dividing 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor.
Select the correct option:	A) 12	B) 14	C) 16	D) 18	E) 22

Solution: d = (D-R)/Q   = (109 - 1)/9   = 108/9= 
108/9 = 12
12   12)
Answer: A
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 + 21) both lie on the line defined by the equation x = (y/7) - (2/5), what is the value of p?
Options.
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: x = (y/7) - (2/5), and so y = 7x + 14/5. The slope is 7.   (n+21-n) / (m+p-m) = 7   p = 3   The answer is 3.
Answer: C
Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr? Options.
A) 45 m	B) 60 m	C) 56 m	D) 67 m	E) 70 m

Solution: Let breadth = x metres.   Then, length = (x + 20) metres.   Perimeter = 5300 m = 200 m.   26.50   2[(x + 20) + x] = 200   2x + 20 = 100   2x = 80   x = 40.   Hence, length = x + 20 = 60 m   60 m
Answer: B
A student was asked to find 4/5 of a number. But the student divided the number by 4/5, thus the student got 36 more than the correct answer. Find the number.  Choose the correct choice.
A) 60  B) 70  C) 80  D) 90  E) 100

Solution: Let the number be x.   (5/4) * x = (4/5)*x + 36   25x = 16x + 720   9x = 720   x = 80   The answer is 80.
Answer: C
Every year an amount increases by 1/6th of itself. How much will it be after two years if its present value is Rs.64000? Choose the correct choice.
A) 87111  B) 81007  C) 81008  D) 81066  E) 81022

Solution: 64000* 7/6 * 7/6 = 87111   87111nswer:87111
Answer: A
Find the missing number: ? - 1936248 = 1635773 Pick one:  A) 3572021  B) 3572012  C) 3770221  D) 3570221  E) None of them

Solution: Let x - 1936248=1635773.   Then, x = 1635773 + 1936248= 
1635773 + 1936248 = 3_572_021
3572021.   Answer is 3572012.
Answer: B
The perimeter of one square is 40 cm and that of another is 20 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?	Select the correct option
A) 11.2√2  B) 13√2  C) 23√2  D) 12√4  E) 13√9

Solution: 4a = 40 4a = 20   a = 10 a = 5   a2 = 100 a2 = 25   Combined area = a2 = 125 => a = 11.2   d = 11.2√2   11.2√2nswer: 11.2√2
Answer: A
If john makes a contribution to a charity fund at school, the average contribution size will increase by 50% reaching $75 per person. If there were 2 other contributions made before john's, what is the size of his donation?  Pick:
A) $125
B) $150
C) $200
D) $250
E) $450

Solution: Cavg = average contribution before John   Cavg*1.5 = 75, therefore the average cont is $50 before John.   If he needs to increase the average contribution by $25, he must put in $25 for each of the 2 people.   so $50.   But, he also has to put in the average for himself (the threeth person), so add $75.   So $125 is your answer.   $125nswer $125
Answer: A
If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area ?	Choose one: A) 108 sq.cm B) 112 sq.cm C) 116 sq.cm D) 120 sq.cm E) 130 sq.cm

Solution: Explanation:   The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.   Area of the triangle =1/2 x base x height => 1/2 x 24 x 10 = 120 sq.cm   ANSWER IS 120 sq.cm
Answer: D
P sells an article to Q at 10 % profit. Q sells it to R at 25 % profit. If R pays Rs. 250 for it, What did P pay for it ?
Choose the correct answer
A) Rs. 181.81	B) Rs. 181.88	C) Rs. 181.82	D) Rs. 181.89	E) Rs. 181.812

Solution: Explanation:   Selling price of P = Cost price of Q   Selling Price of Q = Cost price of R = Rs. 250 ….. Given   Q sold it to R with 25 % profit.   Cost price of Q = 100/125 * 250/1 = Rs. 200 = Selling price of P.   P sold it to Q with 10 % profit.   Cost price of P = 100 / 110 * 200 / 1 = Rs. 181.81   Rs. 181.81NSWER: Rs. 181.81
Answer: A
If 4 women can color 48 m long cloth in 2 days, then 6 women can color 36 m long cloth in  Choose the correct choice from the following options
A) 2 days
B) 3 days
C) 1 day
D) 4 days
E) 5 days

Solution: The length of cloth painted by one woman in one day = 48 / 4 × 2 = 6 m   No. of days required to paint 36 m cloth by 6 women = 36/ 6 × 6 = 1 day.   1 day
Answer: C
Ann and Bob drive separately to a meeting. Ann's average driving speed is greater than Bob's avergae driving speed by one-third of Bob's average driving speed, and Ann drives twice as many miles as Bob. What is the ratio W of the number of hours Ann spends driving to the meeting to the number of hours Bob spends driving to the meeting?
Pick one
A) 8:3  B) 3:2  C) 4:3  D) 2:3  E) 3:8

Solution: Say the rate of Bob is 3mph and he covers 6 miles then he needs 6/3= 
6/3 = 2
2 hours to do that.   Now, in this case the rate of Ann would be 3+3*1/3= 
3+3*1/3 = 4
4mph and the distance she covers would be   6*2= 
  6*2 = 12
12 miles, so she needs   12/4= 
  12/4 = 3
3 hours for that.   The ratio W of Ann's time to Bob's time is 3:2.   Answer: 3:2.
Answer: B
A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.840 find the share of A.	Pick.
A) 240 B) 388 C) 379 D) 277 E) 320

Solution: 320xplanation:   (3*8 + 2*4):(4*8 + 5*4)   8:13   8/21 * 840= 
8/21 * 840 = 320
320   Answer: 320
Answer: E
3x^2-6x+3 = 0
Find the above equation find the value of x  Pick:
A) 0
B) 1
C) 2
D) 4
E) 5

Solution: a = 3, b = -6, c = 3   x1,2 = (6 ± √( (-6)2 - 4×3×3)) / (2×3) = (6 ± √(36-36)) / 6 = (6 ± 0) / 6   x1 = x2 = 1   1
Answer: B
If x#y is defined to equal x^2/y for all x and y, then (-1#2)#2 =  Options:
A) 4/3 B) 1/3 C) 1/12 D) 1/8 E) -4/3

Solution: (-1)^2 / 2 = 1/2   (1/2)^2 / 2 = 1/8   so 1/8 is my answer
Answer: D
A coin is tossed until sequence HTH appears (H denotes the fall of heads, T denotes the fall of tails). What is the probability Z that the game will end after the fourth throw?  Choose the correct choice
A) 1/16	B) 3/32	C) 1/8	D) 3/16	E) 1/4

Solution: Another approach:   Two likely scenarios would be : HHTH or THTH   for each of the scenarios probability would be 1/16   So Probablilty Z is 1/16 + 1/16 = 1/8.1/8
Answer: C
A rectangular lawn of dimensions 70 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?  Choose the correct choice from the following:	A) s.3988	B) s.3900	C) s.3228	D) s.3922	E) s.3600

Solution: Area = (l + b – d) d   (70 + 60 – 10)10 => 1200 m2   1200 * 3   = Rs.3600   Answer:s.3600
Answer: E
A team of eleven footballers has an average height of 170 cm. Four footballers whose average height is 140 cm, left the team and four new others whose average height is 124 cm, joined. Calculate the new average height of the footballers (in cm) is?  Choose the correct choice from the following options:
A) 166.2 cm
B) 154.2 cm
C) 364.2 cm
D) 124.2 cm
E) 164.2 cm

Solution: Total height = 170 * 11= 
170 * 11 = 1_870
1870 cm.   Total height of those who left= 140 * 4= 
140 * 4 = 560
560   Total height of those who joined= 124 * 4= 
124 * 4 = 496
496   New average= [1870 - 560 + 496 ] / 11 = 1806/11 cm.   = 164.2 cm   Answer:164.2 cm
Answer: E
A square is drawn by joining the mid points of the sides of a given square in the same way and this process continues indefinitely. If a side of the first square is 4 cm, determine the sum of the areas all the square.	Choose the correct choice from the following options
A) 32 Cm2 B) 16 Cm2 C) 20 Cm2 D) 64 Cm2 E) None of these

Solution: Solution: Side of the first square is 4 cm.   side of second square = 2 √2 cm.   Side of third square = 2 cm.   and so on. i.e. 4, 2 √, 2, √2, 1 ......   Thus, area of these square will be,   = 16, 8, 4, 2, 1, 1/2 ....... Hence, Sum of the area of first, second, third square ......   = 16+8+4+2+1+ .....   = [16/{1-(1/2)}] = 32 Cm2.   32 Cm2nswer: Option 32 Cm2
Answer: A
If f(a)=4a-6, what is the value of (f(5a)-f(a))/2 ? Choose the correct choice from the following choices:
A) 12a-6
B) 10a+5
C) 5a/6
D) 4a-6
E) 20a+6

Solution: f(a)=4a-6   f(5a) = 20a-6   (f(5a)-f(a))/2 = (20a-6+4a-6)/2 = 12a-6   12a-6nswer is
Answer: A
A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?  Choose the most appropriate option:
A) 229  B) 238  C) 500  D) 288  E) 211

Solution: Speed = 78 * 5/18 = 65/3 m/sec.   Time = 1 min = 60 sec.   Let the length of the train be x meters.   Then, (800 + x)/60 = 65/3   x = 500 m.Answer: 500
Answer: C
If the time is currently 1:30pm, what time will it be in exactly 842 hours? Choose the correct choice from the following choices
A) 12:30am	B) 3:30am	C) 12:30pm	D) 2:30pm	E) 10:30pm

Solution: Every 24 hours will bring us to the same 1:30pm. 840 is divisible by 24 (35*24=840), so if it were 840 hours we would have 1:30pm, but since it's 842 hours then it will be 2 hour more, so 13:30pm.   Answer: 3:30am
Answer: B
n is a positive integer, and k is the product of all integers from 1 to n inclusive. If k is a multiple of 1440, then the smallest possible value of n is Answers:
A) 8  B) 12  C) 16  D) 18  E) 24

Solution: When we say k is the product of all integers from 1 to n, we mean k = n!   Now 1440 = 1.2.3.4.5.6.2   Now if k is a multiple of 1440, it has to be at least 8!. This is so because it cannot be 6! due to the extra 2 factor at the end; it cannot be 7! either, again because the extra 2 in the end will be unaccounted for.   If k = 8! = 1.2.3.4.5.6.7.8, then k = 1440*7*4 i.e. k will be a multiple of 1440.   8nswer 8
Answer: A