MU-NLPC/Calc-aqua_rat huggingface dataset:
R is the set of positive even integers less than 51, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?	Choose the correct choice from the following
A) None B) Three C) Four D) Five E) Seven

Solution: R is the set of positive even integers less than 51, and S is the set of the squares of the integers in R.   How many elements does the intersection of R and S contain?   R=2,4,6,8,10,12...   S=4,16,36,64...   Numbers: 4, 16, and 36 are even integers (less than 51) that are in both sets.   Solution: Three   Answer: Three
Answer: B
If 6x = 10y = 14z, then what is a possible sum of positive integers x, y, and z?  Answers:	A) 213	B) 58	C) 84	D) 122	E) 168

Solution: 213nswer = D = 122   6x = 10y = 14z   3x = 5y = 7z   3(5*7) = 5(3*7) = 7(3*5)   213ddition = 35+21+15= 
35+21+15 = 71
71   213nswer would be multiple of 71 which is 213   213nswer : 213
Answer: A
In an examination 30% failed in Math and 70% failed in French. If 20% failed in both. What % of students passed in both. Pick one:
A) 25% B) 15% C) 20% D) 30% E) 10%

Solution: Passed in Math = 100 - 30= 
100 - 30 = 70
70%   Passed in French= 100 - 70= 
100 - 70 = 30
30%   Students who passed Math or French= 100 -20= 
100 -20 = 80
80%   Students passed in Math and French= (Passed in Math) + (Passed in French) - (Students who passed Math or French) = 70+30-80= 
70+30-80 = 20
20%   ANSWER:20%
Answer: C
In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?  Pick:
A) 87
B) 44
C) 88
D) 76
E) 54

Solution: Let the capacity of the can be T litres.   Quantity of milk in the mixture before adding milk = 4/9 (T - 8)   After adding milk, quantity of milk in the mixture = 6/11 T.   6T/11 - 8 = 4/9(T - 8)   10T = 792 - 352   => T = 44.   Answer:44
Answer: B
Winchard's average (arithmetic mean) test score on 4 tests is 78. What must be the student's score on a 5th test for the Winchard's average score on the 5 tests to be 80?	Choose the correct choice from the following answers:
A) 80
B) 82
C) 84
D) 86
E) 88

Solution: E. 88   Winchard must score at least an 80 for sure. If he scores an 8, then he will need to score 2 pots for each of the 4 other tests tomake upthe difference. They each were at 78 (at least the average is, but this is a small point and doesn't matter to the answer). So 4 tests that were each 2 points short of the 80 average that is desired means the next test must be 8 points higher than the desired average, so  80+8= 
 80+8 = 88
88.
Answer: E
Should a total ban be put on traping wild animals?
Arguments:
1. Yes. Trappers are making a lot of money
2. No. Bans on hunting and trapping are not effective  Choose the correct option
A) Only 1 is true
B) Only 2 is true
C) Either 1 or 2 is true
D) Neither 1 or 2 is true
E) Either 1 or 6 is true

Solution: Explanation:   Ban is necessary to protect our natural envoirnment .So none of the argument is strong enough   Answer: Neither 1 or 2 is true) Neither 1 or 2 is true
Answer: D
In one hour, a boat goes 11 km along the stream and 5 km against the stream. the sped of the boat in still water (in km/hr) is : Choose the correct choice:	A) 3	B) 5	C) 8	D) 9	E) 10

Solution: Solution   Speed in still water= 1/2(11+5) km/hr= 8kmph. Answer 8
Answer: C
Find the odd man out. 13, 16, 12, 24, 12, 34, 46	Pick:
A) 16	B) 46	C) 24	D) 13	E) 18

Solution: Explanation :   13 is the only odd number in the given series   Answer : Option 13
Answer: D
the two sides of a triangle are 32 and 68. the area is 960 sq.cm. find the third side of triangle? Choose the correct choice:
A) 45	B) 50	C) 60	D) 70	E) 80

Solution: we see 68^2-32^2=(68+32)*(68-32)=100*36=60^2   now  (1/2)*60*32= 
 (1/2)*60*32 = 960
960(match with given options)   (i.e area of a right angled triangle whose sides are 32,60,68)   third side=60   ANSWER:60
Answer: C
The ratio between the perimeter and the width of a rectangle is 5:1. If the area of the rectangle is 54 square centimeters, what is the length of the rectangle in centimeters? Choose the correct choice from the following choices:  A) 6  B) 7  C) 8  D) 9  E) 10

Solution: Perimeter = 2(W+L) = 5W   3W = 2L   W = 2L/3   WL = 54   2L^2/3 = 54   L^2 = 81   L = 9 cm   The answer is 9.
Answer: D
Two pipes A and B can separately fill a cistern in 60 min and 75 min respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 min. In how much time, the third pipe alone can empty the cistern?  Choose the correct answer.
A) 761 min	B) 100 min	C) 167 min	D) 367 min	E) 178 min

Solution: Work done by the third pipe in 1 min   = 1/50 - (1/60 + 1/75)   = - 1/100.   [-ve sign means emptying]   The third pipe alone can empty the cistern in 100 min.   Answer: 100 min
Answer: B
The grade point average of the entire class is 85. If the average of one third of the class is 97, what is the average of the rest of the class?	Options.
A) 76	B) 77	C) 78	D) 79	E) 80

Solution: Let x be the number of students in the class.   Let P be the average of the rest of the class.   85x = (1/3)97x + (2/3)(P)x   255 = 97 + 2P   2P = 158   P = 79.   The answer is 79.
Answer: D
The radius of a cylindrical vessel is 7cm and height is 3cm. Find the whole surface of the cylinder?  Select:  A) 872  B) 876  C) 440  D) 157  E) 452

Solution: r = 7 h = 3   2πr(h + r) = 2 * 22/7 * 7(10)   = 440   Answer: 440
Answer: C
A and B starts a business with Rs.8000 each, and after 8 months, B withdraws half of his capital . How should they share the profits at the end of the 10 months?  Options: A) 18:13 B) 18:16 C) 18:10 D) 18:14 E) 14:11

Solution: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 8 months and then withdraws Rs.4000. So, the investment of B for remaining 10 months is Rs.4000 only.   18:13 : B   8000*18 : (8000*8) + (4000*10)   14400 : 104000   18:13:B = 18:13   18:13nswer: 18:13
Answer: A
A spirit and water solution is sold in a market. The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has. A solution of 1 liter of spirit and 1 liter of water costs 40 cents. How many cents does a solution of 1 liter of spirit and 2 liters of water cost?
Choose the correct choice from the following answers
A) 40	B) 33	C) 50	D) 51	E) 52

Solution: Yes, ensure that you understand the relation thoroughly!   Cost per liter = K * Fraction of Spirit   40 cents is the cost of 2 liters of solution (1 part water, 1 part spirit). So cost per liter is 20 cents. Fraction of spirit is 1/2.   20 = K * (1/2)   K = 40   Cost per liter = 40 * (1/3) (1 part spirit, 2 parts water)   Cost for 3 liters = 40 * (1/3) * 3= 
40 * (1/3) * 3 = 40
40 cents   A. 40 cents
Answer: A
A real number x satisfying 1- (1/n) ≤ 3 + (1/n), for every positive integer n, is best described by ≤	Select: A) 1 < x < 4 B) 1 < x ≤ 3 C) 0 < x ≤4 D) 1 ≤ x ≤ 3 E) None of these

Solution: Explanation :   1- (1/n) ≤ 3 + (1/n)   Put n =1 , we get 0 < x ≤4.   Answer : 0 < x ≤4
Answer: C
Two locomotives are moving in the same direction at 62 mps and 26 mps. The faster train crosses the slower train in 8 seconds. What is the length of the faster train in meters?	Select:
A) 247 m
B) 316 m
C) 194 m
D) 270 m
E) 288 m

Solution: Relative speed = (62 - 26)= 
(62 - 26) = 36
36 mps.   Distance covered in 8 sec= 36 * 8= 
36 * 8 = 288
288 m.   The length of the faster train= 288 m.   Answer:288 m
Answer: E
In a six-sided polygon CQRSTV ∠C measures 48° less than the average (arithmetic mean) of the remaining five angles. What does ∠C equal to, in degrees?
Choose the correct choice from the following options:  A) 72  B) 80  C) 88  D) 96  E) 104

Solution: The sum of interior angle in a polygon is (n-2)*180   so for a six sided figure, (6-2)*180 = 720   let the A.M of the other 5 angles be 'm'   --> m*5 + ∠C = 720, we know ∠C=m-48   --> m*5 + m - 48 = 720, solving we get m=128   hence ∠C= 128-48= 
128-48 = 80
80   Ans 80.
Answer: B
There are 3 sections with 5 questions each. If three questions are selected from each section, the chance of getting different questions is________ Choose the correct choice from the following options:
A) 10 B) 100 C) 1000 D) 10000 E) 6000

Solution: we have to select three questions from each section so the chances are 510003.510003.510003=1000   ANSWER:1000
Answer: C
An investor can sell her MicroTron stock for 36$ per share and her Dynaco stock for 48$ per share, If she sells 300 shares altogether, some of each stock, at an average price per share of 40$, how many shares of Dynaco stock has she sold?  Choose the correct choice from the following options:
A) 52 B) 75 C) 92 D) 100 E) 184

Solution: w1/w2 = (A2 - Aavg)/(Aavg - A1) = (48 - 40)/(40 - 36) = 8/4= 
8/4 = 2
2/1= Number of MicroTron stocks/Number of Dynaco stocks   So for every 2 MicroTron stock, she sold 1 Dynaco stock.   So out of 300 total stocks, (1/3)th i.e. 300/3 = 100 must be Dynaco stock.   Answer (100)
Answer: D
Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in? Pick:
A) 13 min
B) 7 min
C) 9 min
D) 12 min
E) 15 min

Solution: 1/10 + 1/15 - 1/x = 1/18   x = 9   ANSWER 9 min
Answer: C
The number of sequences in which 5 players can throw a ball, so that the youngest player may not be the last is ?  Choose the most appropriate option: A) 100 B) 96 C) 8 D) 62 E) 10

Solution: x Not younger   The last ball can be thrown by any of the remaining 5 players. The first 4 players can throw the ball in 4P4 ways.   The required number of ways = 4(4!)   = 96   Answer:96
Answer: B
If x is an integer, which of the following must also be an integer?
I. xy
II. y/x
III. y Choose the correct choice from the following answers
A) I alone	B) II alone	C) III alone	D) I and III	E) None of the above

Solution: Lets take X = 11 and Y = 2   Then XY = 22 which is an integer.   But X/Y = 11/2 --> Not an integer.   Y/X = 2/11 --> Not an integer.   y alone is 2. which is an integer.   Hence I and III.
Answer: D
If x^2 – 2y^2 = 2xy, then (x - y)^2 = Pick.
A) x^2	B) 3x^2	C) 4xy	D) 3y^2	E) – y^2

Solution: (x-y)^2 = x^2 + y^2 - 2xy = x^2 + y^2- x^2+2y^2 = 3y^2   Correct option : 3y^2
Answer: D
If I walk at 3 kmph, I miss the train by 2 min, if however, I walk at 4 kmph. I reach the station 2 min before the arrival of the train. How far do I walk to reach the station?
Choose the correct option.
A) 4/5  B) 4/9  C) 4/8  D) 4/1  E) 4/2

Solution: x/3 – x/4 = 4/60   x = 4/5 km   4/5nswer: 4/5
Answer: A
A van takes 6 hours to cover a distance of 180 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?  Pick one
A) 50 Kmph	B) 60 Kmph	C) 70 Kmph	D) 80 Kmph	E) 20 Kmph

Solution: Time = 6   Distence = 180   3/2 of 6 hours = 6 * 3/2= 
6 * 3/2 = 9
9 Hours   Required speed= 180/9= 
180/9 = 20
20 Kmph   20 Kmph
Answer: E
Three independent strategies A, B and C have been initiated for cost cutting in a company producing respectively 20%, 40% and 10% savings. Assuming that they operate independently, what is the net saving achieved?  Choose the correct answer:
A) 56.8%  B) 64%  C) 62.2%  D) 68%  E) 61%

Solution: If initial cost is Rs 100, then   Final cost will be 100*0.8*0.6*0.9 = Rs. 43.2   savings = 100-43.2= 
100-43.2 = 56.8
56.8   so 56.8%   56.8%NSWER:56.8%
Answer: A
You collect baseball cards. Suppose you start out with 16. Since you're nice, you give John 5 baseball cards. How many baseball cards do you have at the end?  Pick:
A) 11  B) 12  C) 13  D) 14  E) 15

Solution: Solution   Start with 16 baseball cards.   John takes 5 baseball cards from you:   16 - 5= 
  16 - 5 = 11
11 baseball cards.   So you have 11 at the end.   Correct answer : 11
Answer: A
A train passes a station platform in 36 seconds and a man standing on the platform in 10 seconds. If the speed of the train is 36 km/hr, what is the length of the platform?
Options:
A) 338
B) 60
C) 287
D) 267
E) 191

Solution: Speed = (36* 5/18) m/sec = 10 m/sec. Length of the train = (10 x 10)m = 100 m. Let the length of the platform be x meters. Then, (x + 100)/36 = 10==> x + 300 = 360 ==> x = 60 m.   Answer: 60
Answer: B
In how many ways can the letters of the word INTELLIGENCE be arranged? Answers:
A) 2580
B) 2500
C) 200067
D) 9979200
E) 3420456

Solution: INTELLIGENCE has 12 words, but I, N and L are repeated two times and E is repeated three times. Thus ways = 12! / 2!*2!*2!*3! = 9979200ways   9979200
Answer: D
A certain list of 300 test scores has an arithmetic mean of 70 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 302 test scores with a standard deviation less than d?  Choices
A) 70 and 70  B) 80 and 85  C) 70 and 75  D) 75 and 75  E) 70 and 80

Solution: Deviation means spreading of the numbers from one median point value..   as the set is already established and we need to add only two numbers, this means we can only add numbers which are closer to the median to reduce the deviation.   so 70 and 70 are the most close numbers and they will increase the number of elements in the set without changing the median value.   70 and 70
Answer: A
A windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 400 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day?	Choose the correct choice from the following options:
A) 2880.
B) 4860.
C) 5780
D) 5760
E) 6380.

Solution: Normal Day = 400 kw/h   Stormy Day = 400*1.2= 
400*1.2 = 480
480 kw/h   3 windmills for 2 hours on stormy day     480*3*2= 
  480*3*2 = 2_880
2880   2880.nswer: 2880.
Answer: A
Mike had 200 watermelons. Sally came over and took some. After Sally left mike had 136 watermelons. How many watermelons did Sally take?	Choose the correct choice from the following answers:
A) 33	B) 87	C) 264	D) 5	E) 64

Solution: 200-X=136   X=200-136= 
200-136 = 64
64   Sally took 64 watermelons   64.64
Answer: E
You have a pair of unbiased dices. You throw them together till you get a sum of 4 or 7.
What is the probability that you get a sum of 4 before the sum of 7?  Choices
A) 1/6 B) 5/7 C) 2/8 D) 3/7 E) 2/5

Solution: E   2/5   Explanation:   This problem can be solved with different approaches. Let us not go into the complicated generic stuff to avoid confusion and try to solve it with simpler means.   Let us find the results separately. There can be 4 different results that give the sum of 5 and there can be 6 different results that give the sum of 7.   Thus, the probability that we get the sum of 4 before the sum of 7 will be:   4/(4+6) = 4/10 = 2/5.
Answer: E
How many 3 digit positive integers T exist that when divided by 7 leave a remainder of 5? Choices:
A) 128	B) 142	C) 143	D) 141	E) 129

Solution: Minimum three digit number is 100 and maximum three digit number is 999.   The first three digit number that leaves remainder 5 when divided by 7 is 103.   14 * 7= 
14 * 7 = 98
98 +5= 
98 +5 = 103
103   The second three digit number that leaves remainder 5 when divided by 7 is 110.   15 * 7= 
15 * 7 = 105
105 +5= 
105 +5 = 110
110   The third three digit number that leaves remainder 5 when divided by 7 is 117   and so on   The last three digit number that leaves remainder 5 when divided by 7 is 999   142 * 7= 
142 * 7 = 994
994 + 5= 
994 + 5 = 999
999   Therefore, we identify the sequence   103,110,117.....999   use the formula of last term   Last term= first term + (n - 1) * common difference   you will get the answer 129 that is definitely 129.
Answer: E
A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?
Choose the correct choice from the following.
A) 3:9
B) 3:4
C) 3:2
D) 3:1
E) 3:6

Solution: Explanation:   They should share the profits in the ratio of their investments.   The ratio of the investments made by A and 3:4 =   6000 : 8000 => 3:4   Answer: 3:4
Answer: B
A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 30 percent of the drive from the center, what percent of the round-trip has the technician completed?
Answers
A) 60  B) 65  C) 55  D) 50  E) 55

Solution: round trip means 2 trips i.e.to and fro. He has completed one i.e 50% completed. then he traveled another 30% of 50% i.e 15%. so he completed   50 +15= 
  50 +15 = 65
65 % of total trip.   65
Answer: B
A shopkeeper sold 15 articles at the cost price of 20 articles. Then find the profit% or lost%  Answers.
A) 30%  B) 31%  C) 20%  D) 33.33%  E) 40%

Solution: here 15 articles selling price = 20 articles cost price   so the difference = 20-15= 
20-15 = 5
5   % of profit= 5*100/15 = 33.33%   correct option is 33.33%
Answer: D
the stock price of xyz inc. has suffered a decline of 18% in the last 6 months. Financial Analysts believe that the shares will bounce back and gain 5% in the next 3 months. this gain will bring the share value to $700. What was the approximate price of the stock 6 months ago?  Choose the correct choice from the following choices:
A) 706
B) 750
C) 760
D) 900
E) 813

Solution: -18+5-(18*5)/100=-13.9% net decrease   let initial price be Y   Y(1-13.9/100)=700   Y=700/0.861 = ~813   Ans is 813)
Answer: E
The number of permutations of the letters of the word 'MESMERISE' is?
Choose the correct choice from the following answers
A) 9!/(2!)2 3! B) 9!/(2!)7 3! C) 9!/(2!)9 3! D) 9!/(2!)2 8! E) 9!/(2!)1 3!

Solution: n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways.   The letter pattern 'MESMERISE' consists of 10 letters of which there are 2M's, 3E's, 2S's and 1I and 1R.   Number of arrangements = 9!/(2!)2 3!   9!/(2!)2 3!nswer:9!/(2!)2 3!
Answer: A
The mean age of john,william,sam and katy is 25.the age of jhon is 22,age of sam is 30 and age of katy is 24.then tell me the age of william.
Answers
A) 23	B) 24	C) 25	D) 26	E) 27

Solution: solution   let age of william be x.   now, the mean of four age=(22+x+30+24)/4=25   76+x=100   so x=24.   answer 24
Answer: B
Q-1) Of the 64 parents who attended a meeting at a
school, 35 volunteered to supervise children during
the school picnic and 11 volunteered both to supervise
children during the picnic and to bring refreshments to
the picnic. If the number of parents who volunteered
to bring refreshments was 1.5 times the number of
parents who neither volunteered to supervise children
during the picnic nor volunteered to bring
refreshments, how many of the parents volunteered to
bring refreshments? Choose the correct choice from the following.
A) 24
B) 36
C) 38
D) 42
E) 45

Solution: i used the following formula: total = group1 + group2 + neither - both   using the information from the question stem, we have:   64 total people   35 who supervise (group1)   x who neither supervise nor bring refreshments   1.5x people who bring refreshments (group2)   11 who supervise AND bring refreshments (both)   therefore...   64 = 35 + 1.5x + x - 11   solving, we get x = 16   since we want the value of those who bring refreshments 24ND supervise:   1.5(16) = 24   answer is 24
Answer: A
A customer pays 70 dollars for a coffee maker after a discount of 20 dollars
What is the original price of the coffe maker?  Choose the correct choice from the following answers.
A) 50
B) 40
C) 90
D) 60
E) 20

Solution: Let x be the original price.   x - 20 = 70   x - 20 + 20 = 70 + 20   x + 0 = 90   x = 90   Answer is 90
Answer: C
Fresh grapes contain 70% by weight while dried grapes contain 10% water by weight. What is the weight of dry grapes available from 100 kg of fresh grapes?	Options
A) 18.33 kg
B) 21.50 kg
C) 25.00 kg
D) 33.33 kg
E) 40.39 kg

Solution: From the question we know: 100kg * 70% = 70kg of water in the fresh grapes   100kg - 70kg of water = 30kg of non-water mass   We are looking for the weight of the dry grapes (X).   Since the question tells us that 10% of the weight of the dry graps is water and we know that 30kg is non-water mass we can set up the following equation:   X = 1/10(X) + 30kg   9/10(X) = 30kg   X = 33.33 kg   Answer- 33.33 kg
Answer: D
The area of a triangle is with base 2m and height3m?	Choose the correct option:	A) 11	B) 10	C) 787	D) 3	E) 12

Solution: 1/2 * 2 * 3= 
1/2 * 2 * 3 = 3
3 m2   Answer: 3
Answer: D
It costs $6 for the first 1/4 hour to use the copier at Kinkos. After the first ¼ hour it costs $8 per hour. If a certain customer uses the copier for 4 hours and 25 minutes, how much will it cost him?	Choose the correct choice from the following answers.
A) $23.45 B) $65.33 C) $40 D) $38.27 E) $39.33

Solution: 4 hrs 25 min = 265 min   First 15 min ------> $6   Time left is 250 min...   Now, 60 min costs $ 8   1 min costs $ 8/60   250 min costs $ 8/60*250 => $ 33.33   So, Total cost will be $33.33 + $6 => $ 39.33   The answer will be ($39.33) $ 39.3333.33 +  6= 
33.33 +  6 = 39.33
> $ 39.33   The answer will be ($39.33) $ 39.33
Answer: E
A merchant purchased a jacket for $56 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 30 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale?	Choose the correct choice from the following.
A) $0  B) $8  C) $4  D) $12  E) $15

Solution: Actual Cost = $56   SP = Actual Cost + Mark up   = Actual Cost + 30% SP   = 56*100/70= 
56*100/70 = 80
80/100(56*100/70)= 64   Gross profit = $8   Answer is $8
Answer: B
An order was placed for a carpet whose length and width were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and width were in the ratio 2 : 1 but were was no change in its perimeter. What is the ratio of the areas of the carpets?	Choices
A) 7:5	B) 12:11	C) 17:15	D) 22:17	E) 27:25

Solution: Let the length and width of one carpet be 3x and 2x.   Let the length and width of the other carpet be 2y and y.   2(3x + 2x) = 2(2y + y)   5x = 3y   (5/3) * x = y   The ratio of the areas of the carpet in both cases:   = 3x * 2x : 2y * y   = 6x^2 : 2y^2   = 6x^2 : 2*(25/9) * x^2   = 54 : 50   = 27:25   The answer is 27:25.
Answer: E
A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
Answers:  A) 2477  B) 387  C) 698  D) 377  E) 212

Solution: Explanation:   S.I. for 1 year = Rs. (854 - 815) = Rs. 39.   S.I. for 3 years = Rs.(39 x 3) = Rs. 117.   Principal = Rs. (815 - 117) = Rs. 698   Answer: 698) 698
Answer: C
Sum of the squares of 3 no. is 149 and the sum of their products taken two at a time is 70. Find the sum? Choose the correct choice from the following.
A) 17 B) 19 C) 21 D) 13 E) 18

Solution: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 149 + 2* 70   a + b + c = âˆš289 = 17   17nswer 17
Answer: A
A wheel that has 8 cogs is meshed with a larger wheel of 16 cogs. When the smaller wheel has made 24 revolutions, then the number of revolutions mad by the larger wheel is: Choose the correct choice from the following answers:  A) 10  B) 11  C) 15  D) 14  E) 12

Solution: E   12   Let the required number of revolutions made by larger wheel be x.   Then, More cogs, Less revolutions (Indirect Proportion)   16 : 8 :: 24 : x <-> 16 x x = 8 x 24   x = (8x 24)/16   x = 12
Answer: E
Gopi gives Rs. 90 plus one turban as salary to his servant for one year. The servant leaves after 9 months and receives Rs. 40 and the turban. Find the price of the turban.
Choices:
A) 27 B) 36 C) 29 D) 10 E) 110

Solution: Let the price of turban be x.   Thus, for one year the salary = (90 + x)   For 9 months he should earn 3434 (90 + x).   Now he gets one turban and Rs. 40.   Thus, 3434 (90 + x) = 40 + x or 270 + 3x = 160 + 4x or x = 110   Answer:110
Answer: E