MU-NLPC/Calc-aqua_rat huggingface dataset:
Akhil borrowed a certain sum of money at the rate of 6%, 9% and 14% for a period of first two years, next three years and beyond the period of five years respectively. If at the end of nine years, he paid Rs. 8550 as interest, then find the sum of money he had borrowed.
Pick
A) Rs. 9,000 B) Rs.14,000 C) Rs.15,000 D) Rs.18,000 E) None of these

Solution: Explanation:   Let Rs.P be the money borrowed by Akhil.   I) R = 6%, T = 2 years   Simple Interest of 2 years = PRT/100   = P * 6 * 2/100 = 12P/100   II) R = 9%, T = 3 years   Simple Interest of 3 years = P * 9 * 3/100 = 27P/100   III) R = 14%, T = 4 years   Simple Interest of 3 years= P * 14 * 4/100 = 56P/100   Therefore, total Simple Interest of 9 years   = 12P/100 + 27P/100 + 56P/100   = 95P/100   The total interest paid after nine years = Rs.8550   95P/100 = 8550   Therefore, 95P = 855,000   P = 855,000/95 = Rs. 9,000   Amount of money borrowed by Akhil = Rs. 9,000   Rs. 9,000NSWER Rs. 9,000
Answer: A
A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?  Pick one
A) 70 B) 71 C) 72 D) 73 E) 74

Solution: Length = Speed * time   Speed = L/T   S = 400/20= 
400/20 = 20
20 M/Sec   Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 72 Kmph   Answer: Option 72
Answer: C
An alchemist discovered that the formula expressing the correct proportions needed to turn ordinary metal into gold is G = 3/2M + 15, where G is the number of gold bars and M is the number of metal bars. If a metal bar weighs twice as much as a gold bar, how many metal bars will yield an equal weight of gold Choose the correct choice from the following options.
A) a.	A - 40  B) b.	B - 15  C) c.	C – 22.5  D) d.	D – 30  E) e.	E – 67.5

Solution: A --- 120/2 + 15 = 75 --- CORRECT   B --- 45/2 + 15 = not an integer --- wrong   C --- 22.5(3/2) + 15 = not an integer --- wrong   D --- 90/2+15 = 60 --- wrong   This is one of those problems that will probably be easiest to solve by plugging in numbers. The algebra is do-able, but it's not worth the effort (in my opinion). I was able to solve it in under 30 seconds total with this method.   a.	A - 40
Answer: A
Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number
Options
A) 17
B) 15
C) 8
D) 3
E) 2

Solution: Explanation:   If the number is x,   Then, x + 17 =	60/x   x2 + 17x - 60 = 0   (x + 20)(x - 3) = 0   x = 3, -20, so x = 3 (as 3 is positive)   Answer: Option 3
Answer: D
In a class, the average age of 45 boys is 18 years and the average of 35 girls is 15 years. what is the average age of the whole class? Pick:	A) 11 Years	B) 12.6 Years	C) 13 Years	D) 16.6 Years	E) 14 Years

Solution: Total age of 80 students   (45X 18+35 X 15) = 1335   Average = 1335/80 = 16.6 Years   16.6 Years)
Answer: D
40, 45, 50, 50, 60, 75, 75, 100, 100, 100.
The list above shows the scores of 10 schoolchildren on a certain test. If the standard deviation of the 10 scores is 22.7, rounded to the nearest tenth, how many of the scores are more than 1 standard deviation below the mean of the 10 scores?	Options
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: The average of {40, 45, 50, 50, 60, 75, 75, 100, 100, 100} is 69.5.   1 standard deviation below the mean is 69.5 - 22.7 = 46.8. Hence there are two scores (40 and 45) more than 1 standard deviation below the mean.   Answer 2.
Answer: B
I chose a number and divide it by 6. Then I subtracted 15 from the result and got 5. What was the number I chose?
Choose the correct choice:
A) 600 B) 700 C) 120 D) 900 E) None

Solution: Solution:   Let xx be the number I chose, then   x/6âˆ’15=5   x/6=20   x=120   Answer 120
Answer: C
A rich merchant had collected many gold coins. He did not want anybody to know about them. One day, his wife asked, “How many gold coins do we have?” After pausing a moment, he replied, “Well! If I divide the coins into two unequal numbers, then 37 times the difference between the two numbers equals the difference between the squares of the two numbers.” The wife looked puzzled. Can you help the merchant’s wife by finding out how many gold are Choose the correct option.
A) 36 B) 37 C) 38 D) 39 E) 40

Solution: 37(x-y)=x^2-y^2. u no tht x^2-y^2=(x-y)(x+y).so (x-y) cancels on both sides to give x+y=37.so sum of unequal halves=37 which is the required answer.   Answer 37
Answer: B
How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9}  Pick one.
A) 27
B) 28
C) 29
D) 34
E) 60

Solution: The given digits are 1, 2, 3, 5, 7, 9   A number is even when its units digit is even. Of the given digits, two is the only even digit.   Units place is filled with only '2' and the remaining three places can be filled in ⁵P₃ ways.   Number of even numbers = 5P3 = 60.   Answer:60
Answer: E
If 145% of j is equal to 25% of k, 160% of k is equal to 50% of l, and 175% of l is equal to 75% of m, then 40% of m is equal to what percent of 200% of j ? Choose the correct choice from the following choices: A) 0.35 B) 3.5 C) 35 D) 700 E) 3500

Solution: IMO answer should be 350...   consider j=10, then k=50, l=150 and m=350....   40% of 350, comes out to be 140....   200% of 10 is 20....   (140*100)/20=700....   Ans : 700
Answer: D
A sum fetched total simple interest of 4016.25 at the rate of 14 p.c.p.a. in 5 years. What is the sum?  Choose the most appropriate option:
A) 5737.5
B) 8032.5
C) 4462.5
D) 8900
E) None of these

Solution: Let the sums be P.   Now, 70% of P = 4016.25   or, P = 5737.5   5737.5nswer 5737.5
Answer: A
Average Age of residents of a colony is 38 years with Standard deviation of 5 years
If Mr.X's age lies within 2 SD from mean and Mr.Y's age lies within 1 SD from mean then find
maximum values of (X/Y) = ?  Choose the correct choice from the following.
A) 48/38  B) 48/43  C) 48/33  D) 38/33  E) 48/35

Solution: Mean = 38   X = Mean + 2SD => 28 < x < 48   Y = Mean + 1SD => 33 < x < 43   So, Maximum Value of x/y = Maximum Value of x / Minimum Value of y = 48/33   Hence answer will be (48/33) 48/33
Answer: C
A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9hours. If both the taps are opened simultaneously then after how much time will the cistern get filled?	Choose the correct choice from the following answers:
A) 6hr
B) 5.6hr
C) 9.5hr
D) 7.2hr
E) 4hr

Solution: Net part filled in 1 hour 1/4 - 1/9 = 5/36   The cistern will be filled in 36/5= 
36/5 = 36/5 = around 7.2
7.2hr   Answer is 7.2hr
Answer: D
Find the simple interest on Rs 7000 at 50/3 % for 9 months
Answers.
A) Rs. 1075
B) Rs. 975
C) Rs. 875
D) Rs. 775
E) None of these

Solution: Explanation:   S.I. = P×R×T100   So, by puƫing the values in the above formula, our result will be.   Required result = 7000×50×93×12×100=875   [Please note that we have divided by 12 as we converted 9 months in a year format]   Answer: Rs. 875
Answer: C
Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?  Choose the correct choice:
A) 29
B) 29
C) 60
D) 19
E) 12

Solution: Let the speed of the slower train be x m/sec.   Then, speed of the train = 2x m/sec.   Relative speed = ( x + 2x) = 3x m/sec.   (100 + 100)/8 = 3x => x = 25/3.   So, speed of the faster train = 50/3 = 50/3 * 18/5= 
50/3 * 18/5 = 60
60 km/hr.   Answer:60
Answer: C
If the selling price is septuple,the profit is octupled,what is the percentage of profit?? Choose the correct choice from the following options.
A) 50%  B) 100%  C) 150%  D) 200%  E) 250%

Solution: we can make two equations from the given info..   let selling price be S and cost price be C..   so profit=P=S-C...   if S is doubled profit is tripled..   so 8P=7S-C..   or S=7P...   therefore C=P..   % of profit=P/P=100%   100%
Answer: B
N is a positive integer. When N + 1 is divided by 3, the remainder is 2. What is the remainder when N is divided by 3?
Choose the correct choice from the following answers
A) 1	B) 5	C) 4	D) 3	E) 2

Solution: N+1 = 3a+2   i.e. N+1 = 5, 8, 11, 14, ... etc.   i.e. N = 4, 7, 10, 13, ... etc.   When N is divided by 3 Remainder is always 1   1nswer: 1
Answer: A
Find the odd man out. 1,8,27,60,125  Choose the correct choice:
A) 216 B) 125 C) 185 D) 64 E) 14

Solution: Explanation :   1^3=3   2^3=8   3^3=27   4^3=64   5^3=125   Hence, it is clear that 64 should have come instead of 60   Answer : Option 64
Answer: D
On dividing 161 by a number, the quotient is 10 and the remainder is 1. Find the divisor.  Pick one.
A) A)12 B) B)14 C) C)16 D) D)18 E) E)22

Solution: d = (D-R)/Q   = (161 - 1)/10   = 160/10= 
160/10 = 16
16   16)
Answer: C
A metallic sphere of radius 24 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire? Choose the correct choice from the following options.
A) 26 cm  B) 45 cm  C) 58 cm  D) 63 cm  E) 72 cm

Solution: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.   π(16)^2 * h = (4/3)π (24)^3 => h   = 72 cm   Answer:72 cm
Answer: E
A car travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. What is the average speed for the first 320 km of the tour?	Choose the correct option:
A) 70.24km/hr	B) 74.24km/hr	C) 71.11km/hr	D) 72.21km/hr	E) 75.32km/hr

Solution: Explanation:   Average Speed =2x64x80 / 64+80   =71.11km/hr   Answer is 71.11km/hr
Answer: C
The edges of cuboid are 4 cm; 5 cm and 6 cm. Find its surface area?  Choose the correct option.
A) 376  B) 148  C) 216  D) 168  E) 178

Solution: 2(4*5 + 5*6 + 4*6)   = 148   Answer: 148
Answer: B
The EastBank Choir out sold the WestBank Choir by 40% of the 100 boxes of donuts they ordered. The EastBank Choir hustled and made all of the last sales closing the sale with an average of only 25%. How many more sales did the choir make to reach this average? Choose the correct answer:
A) 20	B) 5	C) 10	D) 15	E) 25

Solution: Explanation: Identify the parts, set up equation, and solve.   Number of boxes of donuts initially sold by EastBank Choir:   40% * 100 = 40   Total boxes sold by the end of the sale leaving an average at 25%. (Let x represent the unknown number of additional boxes sold by the EastBank Choir.) Therefore, the total number of boxes sold is 100+x, and the total number of boxes sold by the EastBank Choir is 40+x. This gives the equation as:   25%*(100+x)=40+x   Solve: Let's get rid of the percent sign   25/100*(100+x)=40+x   1/4 *(100+x)=40+x   Get rid of the fraction:   4[1/4 * (100+x)]=4(40+x)   1 * (100+x) =160+4x   100+x =160+4x   (100-160)+x = (160-160)+4x   -60+x= 4x   -60=3x   20=x   20nswer: 20
Answer: A
A mixture contains alcohol and water in the ratio 4 : 3. If 5 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture
Answers.
A) 20  B) 30  C) 15  D) 10  E) 25

Solution: Let the quantity of alcohol and water be 4x litres and 3x litres respectively   4x/(3x+5)=4/5 20x=4(3x+5)8x=20 x=2.5   Quantity of alcohol = (4 x 2.5) litres = 10 litres.   ANSWER 10
Answer: D
Which of the following integers is NOT a divisor of x if x = (21)(3^7) – (127)? Select
A) 2  B) 4  C) 5  D) 12  E) 25

Solution: (21)(3^7) is divisible by 3 but 127 is not divisible by 3.   Therefore (21)(3^7) - 127 is not divisible by 3 and thus not divisible by 12.   The answer is 12.
Answer: D
The average of the two-digit numbers, which remain the same when the digits interchange their positions, is?
Pick one
A) 56
B) 86
C) 55
D) 87
E) 88

Solution: Average = (11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99)/9   = [(11 + 99) + (22 + 88) + (33 + 77) + (44 + 66) + 55]/9   = [(4 * 110) + 55]/9 = 495/9= 
495/9 = 55
55.   Answer:55
Answer: C
A certain sum of money at simple interest amounted Rs.870 in 10 years at 3% per annum, find the sum?  Options: A) 665.23 B) 666.23 C) 667.23 D) 668.23 E) 669.23

Solution: 870 = P [1 + (10*3)/100]   P = 669.23   Answer: 669.23
Answer: E
Find the compound ratio of (2:3), (6:11) and (11:6) is
Select the correct option:  A) 3:2  B) 2:1  C) 1:2  D) 4:5  E) 2:3

Solution: Required ratio = 2/3 * 6/11 * 11/6 = 2/1= 
2/1 = 2
2:3   Answer is 2:3
Answer: E
A three-person committee must be chosen from a group of 7 professors and 20 graduate students. If at least one of the people on the committee must be a professor, how many different groups of people could be chosen for the committee? Choose one:	A) A)70	B) B)1785	C) C)630	D) D)1,260	E) E)1,980

Solution: Total number of ways to select at least one professor = Number of ways to select 3 people from 20 students and 7 professors - Number of ways to select 3 people from 20 student (i.e. without including any professor)   = 27C3 - 20C3 = 2925 - 1140= 
2925 - 1140 = 1_785
1785   ANSWER:1785
Answer: B
When 5% is lost in grinding wheat, a country has to import 20 million bags; but when only 2% is lost, it has to import only 15 million bags. Find the quantity of wheat, which grows in the country?	Choose the most appropriate option.
A) 166 2/7 B) 166 2/1 C) 166 2/2 D) 166 2/3 E) 166 2/8

Solution: 5% - 2% = 3%   3% ---- 5   100% ---- ?   5  - 2= 
5  - 2 = 3
3%   3% ---- 5   100% ---- ?=> 166 2/3   Answer:166 2/3
Answer: D
The speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 40 kms. what was the total distance traveled in 12 hours?
Choose the most appropriate option
A) 252 kms B) 152 kms C) 612 kms D) 752 kms E) 152 kms

Solution: Explanation:   Total distance travelled in 12 hours =(40+42+44+.....upto 12 terms)   This is an A.P with first term, a=40, number of terms,   n= 12,d=2.   Required distance = 12/2[2 x 40+{12-1) x 2]   =6(102)   = 612 kms.   Answer: 612 kms
Answer: C
he average of 10 numbers is 23. If each number is increased by 4, what will the new average be?
Choose the correct choice from the following
A) 26	B) 27	C) 88	D) 99	E) 12

Solution: Sum of the 10 numbers = 230   If each number is increased by 4, the total increase =   4 * 10= 
4 * 10 = 40
40   The new sum= 230 + 40= 
230 + 40 = 270
270 The new average= 270/10= 
270/10 = 27
27.   Answer: 27
Answer: B
If x is a positive integer, and two sides of a certain triangle have lengths 5x+1 and x respectively, which of the following could be the length of the third side of the triangle?
I. x + 1
II. x + 0
III. 8x  Choose the correct choice from the following answers.
A) I only B) II only C) I and II only D) II and III only E) I, II and III

Solution: Let the third side of triangle be AB   Triangle rule states that:   Difference of other 2 sides < any side < sum of other two sides   So 5x+1 - (x) < AB < 5x+1 + (x)   i.e. 4x + 1 < AB < 6x + 1   Let's take x = 1 :   So 5 < AB < 7   Check if the options lies between 5 and 7.   I: x+1 = 2 ; could be a possible value.   II: x+0 = 1 ; could be a possible value.   III: 8x = 8; could not be a possible value.   I and II could be a possible value.   Answer: I and II only
Answer: C
A certain list consists of 21 different numbers. If n is in the list and n is 7 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?  Choose one
A) 7/27  B) 1/6  C) 1/5  D) 4/21  E) 5/21

Solution: series : a1, a2....a20,n   sum of a1+a2+...+a20 = 20*x (x = average)   so, n = 7*x   Hence, a1+a2+..+a20+n = 27x   So, the fraction asked = 7x/27x = 7/27   7/27nswer 7/27
Answer: A
The smallest of three consecutive even integers is 40 less than three times the largest. What is the largest of these integers? Select the correct option:
A) 14
B) 17
C) 18
D) 19
E) 20

Solution: let the three numbers be a,b and c..   now The smallest of three consecutive even integers is 40 less than three times the largest means 3c-40=a..   3c-a=40..   2c+c-a=40..   c-a=4, as a,b,and c are consecutive even integers..   2c+4=40..   2c=36 or c=18   ANSWER:18
Answer: C
A car after travelling 100 km from point A meets with an accident and then proceeds at 3/4 of its original speed and arrives at the point B 90 minutes late. If the car meets the accident 60 km further on, it would have reached 15 minutes sooner. Find the original speed of the train?
Select the correct option:
A) 60km/hr  B) 80km/hr  C) 100km/hr  D) 120km/hr  E) None of these

Solution: Explanation :   let distance between A and B be D km and real speed of the car be S km/hr   First time car takes 90 minutes more and second time car takes 75 minutes more than scheduled time.   So, T1 – T2 = 15/60 = 100   15/60 = [100/s + (D -100)/(3s/4)] – [160/s + (D – 160)/(3s/4)] Solve this D will be cancelled and S comes out to be 80km/hr   Answer –80km/hr
Answer: B
A 220 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
Select the correct option:
A) 230m
B) 240m
C) 250m
D) 260m
E) 280m

Solution: speed = (120 + 80)km/h (because direction is opposite hence relative velocity is added)= 500/9 m/s   time= 9sec   let the lenght of second train is x   total distance covered= 220 + x   therefore, D= speed*time   thus 220 + x = 500/9 * 9= 
500/9 * 9 = 500
500-220= 
500-220 = 280
280 m   ANSW280mR:280m
Answer: E
A restaurant has 89 yellow dishes and 11 white dishes. If I go there with my wife, and we ordered one service each one, what is the probability that both dishes will be white? Pick one
A) 1/100
B) 2/100
C) 1/90
D) 2/90
E) 1/89

Solution: There are 11 white dishes in a group of 89 + 11 that is 100 dishes. Thus the probability of taking 2 white dishes is: (11/100)(10/99) = 1/90. The correct answer is 1/90.
Answer: C
The average of 9 numbers is 13.8. If the average of the first five numbers is 13.6 and that of the last five numbers is 13.4,then the middle number is?
Choose the correct choice from the following options
A) 11.8
B) 10.8
C) 9.8
D) 8.8
E) 8.6

Solution: Middle number = 13.6*5 + 13.4*5- 13.8*9 = 68+67-124.2= 
68+67-124.2 = 10.8
10.8   Answer is 10.8
Answer: B
A bank offers 4.5% compound interest calculated on half-yearly basis. A customer deposits $ 1500 in 1st month. At the end of the year, the amount he would have gained by way of interest is?  Answers.
A) 100 B) 90 C) 60 D) 77 E) 85

Solution: Amount = (1500)* (1 + (4.5/2*100))^2   Amount = 1500 * (1+0.0225)^2 = 1577 ------(for investment in 1st month)   Interest = 1577-1500 = 77.............. Ans -77
Answer: D
According to a survey, at least 80% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three? Choose the correct choice from the following options.
A) 15%	B) 20%	C) 25%	D) 0%	E) 35%

Solution: It seems that something is wrong with your answer options.   1) minimum applesbananas:   [XXXXXXXXXXXXXX------] - apples   [-----XXXXXXXXXXXXXXX] - bananas   mimimum ab = 80 - (100-75)= 
80 - (100-75) = 55
55%   2) minimum (applesbananas)cherries:   [XXXXXXXXX-----------] - applesbananas   [----XXXXXXXXXXXXXXXX] - cherries   mimimum ab= 55 - (100-80)= 
55 - (100-80) = 35
35%   35%
Answer: E
What is the volume of an tetrahedron with edge length of 1?
Pick one: A) sqr(2)/12 = 0.11785113 B) sqr(2)/14=0.13571785 C) sqr(2)/12=0.15798562 D) sqr(2)/13=0.21254478 E) sqr(2)/12=0.12457896

Solution: The following can be derived using the Pythagorean theorem:   The height of a face is 3.5/2.   The area of any face is 3.5/4.   The distance from any corner to the center of a joining face is 1/3.5.   The height of the tetrahedron is (2/3).5   The area is 1/3*base*height =   (1/3) * 3.5/4 * (2/3).5 = 21/2/12.
Answer: A
Solve the given two equations and find the inequality of X and Y. (a) 225X^2-4 = 0 and (b) (225y)^(1/2) +2 = 0 Choose the correct choice from the following.
A) If x>y
B) If x>=y
C) If x<y
D) If x<=y
E) x=y or relationship cannot be established

Solution: Solution:-   X= +2/15 and -2/15   Y= 4/225   Comparing we get X>Y and X<Y   Hence, no relationship can be established   x=y or relationship cannot be established
Answer: E
A sum of Rs. 1800 amounts to Rs. 9000 in 4 years at the rate of simple interest. What is the rate of interest? Choose the correct choice from the following answers.
A) 50%	B) 75%	C) 100%	D) 60%	E) 25%

Solution: S.I. = (9000 - 1800) = Rs. 7200\   Rate = (100 * 7200) / (1800* 4)= 
(100 * 7200) / (1800* 4) = 100
100%   Answer: 100%
Answer: C
Look at this series: 14, 7, (7/2), (7/4), ... What number should come next?
Choices:
A) 1/8  B) 3/8  C) 7/8  D) 5/8  E) 6/8

Solution: Explanation:   28/2= 
28/2 = 14
14   14/2= 
14/2 = 7
7   7/2= 7/2   (7/2)/2 = 7/4   (7/4)/2 = 7/8 and so on.   Answer: Option 7/8
Answer: C
A pharmacist has 4 quarts of a 15% solution of iodine. How much alcohol must be added to
reduce it to a 10% solution of iodine? Answers:	A) 1 quart	B) 2 quarts	C) 3 quarts	D) 4 quarts	E) 5 quarts

Solution: What’s being added? Hopefully, you said alcohol. Therefore our equation will look like this:   ALCOHOL + ALCOHOL = ALCOHOL   4 qts + x qts = (4 + x) qts   We start off with 4 quarts, add x quarts, then end up with (4 + x) quarts.   + =   4 x (4 + x)   Notice that you started with 4 quarts and added x quarts on the left side of the equation and you   ended up with (4 + x) on the other side. The parentheses indicate that it’s one container, Neato!   Of the original 4 quarts, 15% is iodine. Since we are doing the problem in terms of what we are   adding – alcohol, we must change 15% iodine solution to an 85% solution of alcohol. Let’s write   the equation.   .85(4) + x = .90(4x)   Where’d the .90 come from? Well, since I wanted to end up with a 10% solution of iodine, that   meant it must be a 90% solution of alcohol.   Multiplying both sides of the equation by the common denominator – 100, we have   85(4) + 100x = 90(4 + x)   340 + 100x = 360 + 90x   10x = 20   x = 2   You would have to add 2 quarts of alcohol to reduce the mixture to 10% iodine.   correct answer 2 quarts
Answer: B
If x ¤ y = (x + y)^2 - (x - y)^2. Then √2 ¤ √2 =  Choose the most appropriate option:	A) 0	B) 8	C) 10	D) 15	E) 20

Solution: X = √2 and Y also =√2   Applying the function (√2+√2)^2 - (√2-√2)^2 = (2√2)^2 - 0 = 4 x 2 = 8.   Note: Alternative Approach is the entire function is represented as X^2 - Y^2 = (X+Y)(X-Y) which can be simplified as (x+y+x-y)(x+y-(x-y)) = (2x)(2y)=4xy. Substituting x=√2 and y = √2 you get the answer 8.   Answer 8
Answer: B
The first Republic Day of India was celebrated on 26th January, 1950. It was :  Choose the correct answer.
A) Tuesday	B) Wednesday	C) Thursday	D) Friday	E) None of these

Solution: 26th Jan., 1950 = (1949 years + Period from 1st Jan.,1950 to 26th Jan., 1950)   1600 years have 0 odd day. 300 years have 1 odd day.   49 years = (12 leap years + 37 ordinary years)   = [(12 × 2) + (37 × 1)] odd days = 61 odd days   = 5 odd days.   Number of days from 1st Jan. to 26th Jan. = 26   = 5 odd days   Total number of odd days = (0 + 1 + 5 + 5)= 
(0 + 1 + 5 + 5) = 11
11= 4 odd days   ∴ The required days was ‘Thursday’   Answer Thursday
Answer: C
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:	Pick one.
A) 247 m
B) 256 m
C) 245 m
D) 527 m
E) 725 m

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 m
Answer: C
What is the reciprocal of (AB)/(A+B)^2?	Pick.
A) (AB)/(A^2+2AB+B^2)
B) A/B+B/A+AB
C) B/A+A/B+2
D) (A+B)^2/AB
E) A/B+2AB

Solution: Answer:   Reciprocal = (A+B)^2/AB   = (A^2+B^2+2AB)/AB = B/A + A/B +2   ANSWER:B/A+A/B+2
Answer: C
8 couples attend a dance show in a TV channel. A lucky draw in which 4 persons picked up for a prize is held, then the probability that there is at least 1 couple will be selected is :	Choose the correct choice from the following choices:
A) 1/41  B) 11/23  C) 15/39  D) 15/18  E) 21/31

Solution: P( selecting atleast one couple) = 1 - P(selecting none of the couples for the prize)   = 15/39   15/39
Answer: C