MU-NLPC/Calc-aqua_rat huggingface dataset:
The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
Choose the correct choice from the following answers:	A) 140	B) 287	C) 1267	D) 127	E) 212

Solution: Given that the area of the square = 1225 sq.units   => Side of square = √1225 = 35 units   The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35= 
2/5 * 35 = 14
14 units   Given that breadth= 10 units   140rea of the rectangle = lb = 14 * 10= 
14 * 10 = 140
140 sq.units   140nswer: 140
Answer: A
In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes?  Pick.
A) 24  B) 35  C) 64  D) 68  E) 90

Solution: Ans.(C)   Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways
Answer: C
If 10% of x = 20% of y, then x:y is equal to?
Choose the correct choice
A) 2:6  B) 2:1  C) 7:1  D) 2:8  E) 2:2

Solution: 10% of x = 20% of y   10x/100 = 20y/100 => x/10 = y/5   x/y = 10/5= 
10/5 = 2
2/1= 
2/1 = 2
2:1.   Answer:2:1
Answer: B
What is the total number of integers between 2 and 38 that are divisible by 4? Pick one:
A) 8
B) 9
C) 7
D) 6
E) 11

Solution: 4, 6, 8, ..., 32,36   This is an equally spaced list; you can use the formula:   n = (largest - smallest) / ('space') + 1 = (36 - 4) / (4)+ 1 = 32/4 + 1 = 8 + 1= 
8 + 1 = 9
9   Answer is 9
Answer: B
There are 18 stations between Ernakulam and Chennai. How many second class tickets have to be printed, so that a passenger can travel from one station to any other station?
Choose the correct choice from the following choices
A) 800 B) 380 C) 360 D) 478 E) 566

Solution: The total number of stations= 20   From 20 Stations we have to choose any two stations and the direction of travel (Ernakulam to Chennai is different from Chennai to Ernakulam) in 20P2 ways.   20P2= 20*19= 
20*19 = 380
380   ANSWER:380
Answer: B
Running at the same rate, 8 identical machines can produce 560 paperclips a minute. At this rate, how many paperclips could 30 machines produce in 6 minutes? Choose the correct choice from the following answers:
A) 1344 B) 3360 C) 8400 D) 12600 E) 67200

Solution: 8 machines produce 560 in 1 min   8 machines produce 560* 6 in 6 min   30 machine produce 560*6*(30/8) in 6 minutes     560*6*30/8= 
  560*6*30/8 = 12_600
12600 answer is 12600.
Answer: D
The side of a square is increased by 5% then how much % does its area increases? Choose the correct choice from the following choices: A) 15.00 % B) 10.25 % C) 10.00 % D) 12.25 % E) 12.50 %

Solution: a = 100 a2 = 10000   a = 105 a2 = 11025   ----------------   10000 --------- 1025   100 -------? => 10.25 %   Answer:10.25 %
Answer: B
The value of 1/(1-x) + 1/(1+x) + 2/(1+x^2) + 4/(1+x^4) Pick one.
A) 8/(1-x^8)
B) 4x/(1+x^2)
C) 4/(1-x^6)
D) 4/(1+x^4)
E) 4x/(1-x^4)

Solution: Highlighted part has mistake as the exponent of x must be 4 in last term   CORRECT QUESTION ISThe value of 1/(1-x) + 1/(1+x) + 2/(1+x^2) + 4/(1+x^4) = ?   Solution is as mentioned below...   one more way that could get the answer in the type of eqn and choices given is to substitute some value for x...   0 would be better as the eq has constant term free of term 'x'..   the Eq gives us 8 as the ans , as also only choice 8/(1-x^8)..
Answer: A
In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?	Choices:
A) 7 sec
B) 5 sec
C) 9 sec
D) 6 sec
E) 1 sec

Solution: T = 60/36 * 18/5= 
60/36 * 18/5 = 6
6 sec   Answer:6 sec
Answer: D
987.650 - ? + 56.98 = 126.654 Pick.
A) A)899.015 B) B)752.804 C) C)714.642 D) D)629.906 E) 917.976

Solution: 917.976xplanation:   917.976   Answer: Option 917.976
Answer: E
Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in?	Choices.
A) 1 13/17 hours
B) 2 8/11 hours
C) 3 9/17 hours
D) 4 1/2 hours
E) NONE

Solution: Net part filled in 1 hour = 1/5 + 1/6 - 1/12 = 17/60   The tank will be full in 60/17 hrs, i.e., 3 9/17 hrs.   ANSWER:3 9/17 hours
Answer: C
What percent of 5 letter combinations that can be made from the letters of the word SERMONT and in which each letter can be used only once are the combinations in which the first letter is a vowel and the last letter is a consonant?  Choose the correct choice from the following answers
A) 20%	B) 23.8%	C) 25%	D) 30.2%	E) 35%

Solution: a) noof combinations when all 5 letters are different = 7*6*5*4*3   b) noof combinations when first letter is vowel and last is consonant = 2c1*5c1*5*4*3   b/a = 5/21= 0.238   23.8%
Answer: B
If x is a positive, single-digit integer such that 4/3*x, 2x, x, and x + 2, and 4x – 2 form a non-ordered list of consecutive integers, which of the following could be the median of that list?  Answers
A) 3 B) 4 C) 5 D) 6 E) 8

Solution: The big hints are thatx is a 1-digit integerAND (4/3)x, 2x, x, and x + 2, and 4x – 2 are ALLintegers   For (4/3)x to be an integer, x MUST BE A MULTIPLE OF 3. So, x can equal 3, 6, or 9.   Now let's plug each possible value of x into the terms and see which one yields a list ofconsecutive integers   When x =3, we get the following terms: (4/3)(3), 2(3),3,3+ 2, and 3(3) – 2.   When we evaluate these terms we get: 4, 6, 3, 5 and 10   Rearrange to get: 3, 4, 5, 6, 10. So, when x = 3, we getconsecutive integers.   In this case, the MEDIAN = 5   Since 5 is among the answer choices, we need not test the other 2 values of x (i.e., x = 6 and x = 9)   Answer:   5
Answer: C
1/2+[(2/6*6/32)+1]-9/16= Choose the most appropriate option
A) 29/16 B) 19/16 C) 15/16 D) 9/13 E) 0

Solution: 1/2 - [(2/6*6/32) + 1] + 9/16 =   1/2 - [(1/16) + 1] + 9/16 =   1/2 - [17/16] + 9/16 =   8/16 - 17/16 + 9/16= 
8/16 - 17/16 + 9/16 = 0
0   The answer is 0.
Answer: E
A baseball card decreased in value 20% in its first year and 30% in its second year. What was the total percent decrease of the card's value over the two years?
Choose the correct choice from the following choices:  A) 28%  B) 30%  C) 32%  D) 36%  E) 44%

Solution: consider the initial value of the baseball card as $100   After first year price = 100*0.8= 
100*0.8 = 80
80   After second year price= 80 *0.7= 
80 *0.7 = 56
56   final decrease= [(100 - 56)/100] * 100 = 44%   correct answer - 44%(100 - 56)/100  * 100= 
(100 - 56)/100  * 100 = 44
44%   correct answer - 44%
Answer: E
If A got 70 marks and B got 80 marks, then what percent of A's mark is B's mark? Select:  A) A)60%  B) B)80%  C) C)65%  D) D)87.5%  E) of these

Solution: A's marks =80 ; B's marks = 70.   Let x% of A = B => x/100 * 80 = 70   => x = (70 * 100)/80= 
(70 * 100)/80 = 175/2 = around 87.5
87.5   B's marks is 87.5% of A's marks.   ANSWER:87.5%
Answer: D
x, y and z are consecutive positive integers such that x < y < z; which of the following must be true?
1. xz is even
2. (z-x)(y-x+1) = 4
3. xy is odd
Choose the correct choice:
A) I only B) II only C) II only D) I and II only E) I, II, and III

Solution: Since x, y and z are consecutive integers such that x < y < z, we can say x = y-1 and Z = y+1   Statement 1can not be ascertain as is not related to y directly ---not true   Statement 2 can be simplified if we write everything in terms of y as ((y+1)-(y-1))*(y-(y-1)+1) = 2*2= 
2*2 = 4
4 So, always true   Statement 3 talks about xy Since x and y are consecutive integers one of them is odd and other is even so product would always be even and hence not true.   So, II are always true and hence answer is   II only
Answer: C
Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?  Pick one
A) Can't be determined  B) 40  C) 27  D) 24  E) None of these

Solution: Explanation:   Let the present ages of Sameer and Anand be 5x years and 4x years respectively.   Then, (5x+3)/(4x+3)=119   ⇒ 45x + 27 = 44x + 33⇒ 9(5x + 3) = 11(4x + 3)   ⇒ 45x - 44x = 33 - 27= 
33 - 27 = 6
6.   Anand's present age= 4x = 24 years.   Answer: 24
Answer: D
Of 60 children, 30 are happy, 10 are sad, and 20 are neither happy nor sad. There are 22 boys and 38 girls. If there are 6 happy boys and 4 sad girls, how many boys are neither happy nor sad?	Choose the correct choice from the following answers
A) 2  B) 4  C) 6  D) 8  E) 10

Solution: Venn diagrams are useful for multiple values of a single variable e.g. State of mind - happy/sad/neither. When you have two or more variables such as here where you have gender - boy/girl too, it becomes unwieldy. In this case, either use the table or logic.   Table method is shown above; here is how you will use logic:   There are 6 happy boys.   There are 4 sad girls but total 10 sad children. So rest 6 sad children must be sad boys.   We have 6 happy boys and 6 sad boys. Total we have 22 boys. So  22 - 6 - 6= 
 22 - 6 - 6 = 10
10 boys must be neither happy nor sad.   Answer (10)
Answer: E
How many ltrs of water must beadded to 16 ltrs of milk and water containing 10% water to make it 20% water in it? Pick one:
A) 1 liter B) 2 liter C) 3 liter D) 4 liter E) 5 liter

Solution: 2 litery rule of alligation,   % Concentration   of water in pure water (100)	% Concentration   of water in the given mixture (10)   Mean % concentration   (20)   20 - 10= 
20 - 10 = 10
10	100 - 20= 80   => Quantity of water : Quantity of the mixture = 10 : 80 = 1 : 8   Here quantity of the mixture = 16 litres   => Quantity of water : 16 = 1 : 8   => Quantity of water =16×18=2 liter   2 liter
Answer: B
How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?	Answers
A) 6400
B) 2400
C) 5500
D) 7400
E) 3400

Solution: Number of bricks = Volume Of the wall / Volume of 1 brick = (800 x 600 x 22.5) / (25 x 11.25 x 6) = 6400   6400NSWER:6400
Answer: A
A company plans to award prizes to its top 3 salespeople, with the largest prize going to the top salesperson, the next-largest prize to the next salesperson, and a smaller prize to the third-ranking salesperson. If the company has 10 salespeople on staff, how many different arrangements of winners are possible?  Pick one.
A) 1,728	B) 1,440	C) 1,320	D) 220	E) 720

Solution: [quote=Bunuel]A company plans to award prizes to its top 3 salespeople, with the largest prize going to the top salesperson, the next-largest prize to the next salesperson, and a smaller prize to the third-ranking salesperson. If the company has 10 salespeople on staff, how many different arrangements of winners are possible?   10*9*8= 
10*9*8 = 720
720   Answer : 720
Answer: E
There are 399 doctors and nurses in a hospital. If the ratio of the doctors to the nurses is 8 : 11, then how many nurses are there in the hospital? Choose the correct choice from the following answers:  A) 152  B) 209  C) 57  D) 231  E) 181

Solution: Given,   The ratio of the doctors to the nurses is 8 : 11   Number of nurses = 11/19 x 399 = 231   ANSWER:231
Answer: D
After decreasing 24% in the price of an article costs Rs.988. Find the actual cost of an article?  Choose the most appropriate option:
A) 1667	B) 6789	C) 1300	D) 6151	E) 1421

Solution: 1300P* (76/100)   = 988   1300P1300 * (76/100)= 
1300 * (76/100) = 988
988   1300P= 13 * 100= 
13 * 100 = 1_300
> 1300P= 1300   Answer: 1300
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 : Answers:
A) 11/31	B) 13/37	C) 15/39	D) 16/37	E) 19/51

Solution: P( selecting atleast one couple) = 1 - P(selecting none of the couples for the prize)   = 15/39   15/39
Answer: C
Mohan purchased 15 kgs of rice at the rate of Rs.26 per kg and 8 kgs of pulses at the rate of Rs.26 per kg. Whaat is the total amount that he paid to the shopkeeper? Choose the correct choice from the following:
A) Rs.598
B) Rs.594
C) Rs.596
D) Rs. 595
E) None of these

Solution: Explanation:   Price of 15 kgs of rice at Rs.26/kg = 15x26 = Rs.390   Price of 8 kgs of pulses at Rs.26/kg = 8x26 = Rs.208   Therefore, Total amount = Rs.390+Rs.208 = Rs.598.   Rs.598nswer: Option Rs.598
Answer: A
The average age of 15 students of a class is 15 years. Out of these, the average age of 7 students is 14 years and that of the other 7 students is 16 years. The age of the 15th student is	Choices:  A) 9 years  B) 11 years  C) 15 years  D) 21 years  E) 25 years

Solution: Solution   Age of the 15th student	=[15x15-(14x7+16x7)]   = (225 - 210)= 
(225 - 210) = 15
15 years.   Answer 15 years
Answer: C
A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it?
Choose the correct choice from the following answers:
A) 13 8/3 days B) 13 1/3 days C) 13 6/3 days D) 63 1/3 days E) 13 5/3 days

Solution: 5/30 + 20/x = 1   x = 24   1/30 + 1/24 = 3/40   40/3 = 13 1/3 days   Answer:13 1/3 days
Answer: B
David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?	Choose the most appropriate option
A) 15	B) 20	C) 25	D) 35	E) 30

Solution: Suppose their paths cross after x minutes.   Then, 11 + 57x = 51 - 63x = 120x = 40   x = 1/3   Number of floors covered by David in (1/3) min. = (1/3 x 57)= 19.   So, their paths cross at (11 +19) i.e., 30th floor.   Answer is 30.
Answer: E
A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?  Answers.
A) 42.3  B) 560.45m  C) 79m  D) 26m  E) 111.12m

Solution: Explanation:   A runs 1000 m while B runs 900 m and C runs 800 m.   The number of meters that C runs when B runs 1000 m,   = (1000 * 800)/900 = 8000/9 = 888.88 m.   B can give C = 1000 - 888.88= 
1000 - 888.88 = 111.12
111.12 m.   ANSW111.12mR 111.12m
Answer: E
A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained? Choose the correct option:
A) 2681	B) 1892	C) 1000	D) 1345	E) 1623

Solution: Along one edge, the number of small cubes that can be cut   = 100/10= 
100/10 = 10
10   Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut= 10 * 10 * 10= 
10 * 10 * 10 = 1_000
1000   Answer: 1000
Answer: C
Susan, John, Daisy, Tim, Matt and Kim need to be seated in 6 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ?
Choose the correct answer
A) 360 B) 120 C) 80 D) 240 E) 60

Solution: Total number of arrangements = 6! = 720   In exactly half, Susan will be to the left of Tim, which gives us 360 arrangements   Option (360)
Answer: A
A team of three entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score?	Pick
A) 288
B) 245
C) 168
D) 127
E) 664

Solution: Explanation:   3 * 84= 
3 * 84 = 252
252 - 7= 
252 - 7 = 245
245   Answer:245
Answer: B
For all positive integers n and m, the function A(n) equals the following product:
(1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/6 + 6^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number, while B(m) equals the sum of the reciprocals of all the positive integers from 1 through m, inclusive. The largest reciprocal of an integer in the sum that B(25) represents that is NOT present in the distributed expansion of A(5) is	Pick.
A) 1/4  B) 1/5  C) 1/6  D) 1/7  E) 1/8

Solution: For all positive integers n and m,   A(n) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number,   note:i think there's a typo in the above function, A(n) could be (1 + 1/2 + 1/2^2)(1 + 1/3 +1/3^2)(1 + 1/5 +1/5^2)…(1 + 1/p_n + 1/p_n^2)   B(m) = sum of the reciprocals of all the positive integers from 1 through m, inclusive.   A(5), here 5 represents the 5th smallest prime number; the 5th smallest prime number is 11 {2, 3, 5, 7, 11, ...}   A(5) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)(1 + 1/7 + 1/7^2)(1 + 1/11 + 11^2)   The distributed expansion of A(5) = 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 +1/7 + 1/9+ 1/10 + 1/11 +1/12 + 1/14+ ...   missing numbers are 1/8, 1/13, 1/16, ....   B(25) = (1 + 1/2 + 1/3 + 1/4 + ... + 1/16 + 1/17 + ... + 1/25)   here the largest reciprocal is 1 and the reciprocals are arranged in descending order based on their values   The largest reciprocal that present in B(25) but not in 1/4(5) is 1/4   1/4nswer 1/4
Answer: A
The product of the digits of the four-digit number h is 36. No two digits of h are identical. How many different numbers are possible values of h? Choose the correct choice from the following choices.
A) 6	B) 12	C) 24	D) 36	E) 48

Solution: Since the product of the four non-repeating digits is 36, the only possibility is if 1, 2, 3 and 6 are used. These digits can be arranged in 4! ways. Therefore, answer is 24.   ANS :24
Answer: C
The average temperature of a city in the first four days of a month was 36°. The average for the 2nd, 3rd, 4th and 5th day was 38°. If the temperature of the 1st and 5th day were in the ratio 4 : 5, then what is the temperature on the fifth day ? Pick.
A) 32°
B) 35°
C) 38°
D) 40°
E) None of these

Solution: Explanation:   The temperature for first 4 days = 4 * 36= 
4 * 36 = 144
144   The temperature for last 4 days= 4 * 38= 
4 * 38 = 152
152   The difference between the temperatures is (152 – 144)= 8   The ratio of temperature between first and fifth day is 4 : 5   The temperature on fifth day is   5*8= 
  5*8 = 40
40   ANSWER 40°
Answer: D
Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.96 at the candy store. What is John’s weekly allowance? Select:
A) $3.00	B) $3.20	C) $3.40	D) $3.60	E) $3.80

Solution: x = 3x/5 + 1/3*2x/5 + 96   4x/15 = 96   x = $3.60 = $3.60   The answer is $3.60.
Answer: D
The C.I. on a certain sum for 2 years Rs.41 and the simple interest is Rs.40. What is the rate percent?	Select: A) 7% B) 5% C) 8% D) 6% E) 9%

Solution: SI = 20 + 20   CI = 20 + 21   20 ---- 1   100 ---- ? => 5%   Answer:5%
Answer: B
If a is an integer greater than 9 but less than 26 and b is an integer greater than 14 but less than 31, what is the range of a/b?  Select the correct option:
A) 1  B) 1/2  C) 5/6  D) 2/3  E) 4/3

Solution: Range of a/b = max(a/b) - min(a/b)   to get max(a/b) => max(a)/min(b) = 25/15   to get min(a/b) => min(a)/max(b) = 10/30   Range = 25/15 - 10/30   = 4/3
Answer: E
Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?	Select:
A) 2400 m^2	B) 2420 m^2	C) 2520 m^2	D) 2600 m^2	E) 2630 m^2

Solution: Solving the two equations, we get: l = 63 and b = 40.   Area = (l x b) = (63 x 40) m2 = 2520 m^2   2520 m^2
Answer: C
The ratio of the present ages of Giri and Hari is 5:8. 12 years hence, the ratio of their ages will be 11:14. Find the difference in their present ages?	Choose the correct choice from the following:
A) 7 years B) 6 years C) 9 years D) 5 years E) 4 years

Solution: Let the present ages of Giri and Hari be 5x and 8x years respectively.   (5x + 12)/(8x + 12) = 11/14   70x + 168 = 88x + 132 => x = 2   Difference in their ages will be the same at all times.   This difference = Difference of their present ages   => 8x - 5x = 3x 8  - 5= 
8  - 5 = 3
3x=> 6 years   Answer: 6 years
Answer: B
A trader bought a car at 30% discount on its original price. He sold it at a 80% increase on the price he bought it. What percent of profit did he make on the original price? Answers.
A) 18%
B) 26%
C) 12%
D) 32%
E) 15%

Solution: Original price = 100   CP = 70   S = 70*(180/100)= 
70*(180/100) = 126
126   100 - 126= 26%   Answer: 26%
Answer: B
If 11.25 m of a uniform steel rod weighs 42.75 kg. what will be the weight of 7 m of the same rod?	Options
A) 22.8 kg  B) 26.6 kg  C) 28 kg  D) 26.5 kg  E) None of these

Solution: Explanation :   Let the required weight be x kg. Then, Less length, Less weight (Direct Proportion)   => 11.25 : 7 :: 42.75 : x   => 11.25 x x = 7 x 42.75   => x = (7 x 42.75) / 11.25   => x = 26.6   Answer : 26.6 kg
Answer: B
The radius of a semicircle is 7. What is the approximate perimeter of the semicircle?
Options:
A) 36	B) 25	C) 15	D) 28	E) 37

Solution: perimeter of a circle =2pi*r   perimeter of a semicircle = pi*r + 2r   aprox perimiter = 3.14*7 + 2*7= 
3.14*7 + 2*7 = 35.98
35.98 approximately 36   answer 36
Answer: A
A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long? Choose the correct choice from the following answers:
A) 2  B) 3  C) 76  D) 6  E) 1

Solution: D = 25 * 60 + 1500= 
25 * 60 + 1500 = 3_000
3000 m   T= 3000/60 * 18/5= 
3000/60 * 18/5 = 180
180 sec= 3 mins.Answer: 3
Answer: B
Determine the value of 27/31+54/62 Choose the correct choice from the following options
A) 86/31 B) 87/31 C) 88/31 D) 89/31 E) none

Solution: Solution:   Both fractions should be reduced before performing arithmetic operations. We get 27/31+2.27/2.31=27/31+27/31=2(27/31)=89/31   Answer 89/31
Answer: D
Praveen age after 10years will be 3 times his age 3years back. what is the present age of Chris? Choose the correct answer: A) 20 B) 25 C) 10 D) 30 E) 15

Solution: Chris present age= x   after 10years = x+10   3years back = x-3   x+10= 3(x-3)   x=20   20nswer is 20
Answer: A
Mr. Karan borrowed a certain amount at 6% per annum simple interest for 9 years. After 9 years, he returned Rs. 8310/-. Find out the amount that he borrowed.	Choose the correct option:
A) s. 5266
B) s. 5396
C) s. 5228
D) s. 5218
E) s. 52192

Solution: Explanation:   Let us assume Mr. Karan borrowed amount is Rs. A. (the principal)   By formula of simple interest, S.I. = PRT / 100   Where P = The principal, R = Rate of interest as a %, T = Time in years   S.I. = (P * 6 * 9)/100 = 54 P/100   Amount = Principal + S.I.   8310 = P + (54P/100)   8310 = (100P + 54P)/100   8310 = 154P/100   P = (8310 * 100)/154 = Rs. 5396.104   ANSWER: s. 5396
Answer: B
The total age of A and B is 11 years more than the total age of B and C. C is how many years younger than A.?	Choose the correct option:	A) 16	B) 12	C) 11	D) 20	E) 10

Solution: (A+B)-(B-11)=11   A-11=11   Answer is 11
Answer: C
When 17 is divided by positive integer x, the remainder is 1. For how many values of x is this true? Choose the most appropriate option:	A) 1	B) 2	C) 3	D) 4	E) 5

Solution: When 17 is divided by x, the remainder is 1 i.e. 1 orange left over after grouping, so x must be greater than 1.   It also means that 16 is completely divisible by x.   Factors of 16 are 1, 2, 4, 8, 16.   Out of these, x can be 2, 4, 8, and 16.   Answer (4).
Answer: D
In an election, candidate A got 80% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favor of candidate?	Choose the correct option
A) 355600  B) 380800  C) 356500  D) 356800  E) 357000

Solution: Total number of invalid votes = 15 % of 560000   = 15/100 × 560000   = 8400000/100= 
8400000/100 = 84_000
84000   Total number of valid votes 560000 – 84000= 476000   Percentage of votes polled in favour of candidate A = 80 %   Therefore, the number of valid votes polled in favour of candidate A = 80 % of 476000   = 80/100 × 476000   = 38080000/100= 
38080000/100 = 380_800
380800   380800)
Answer: B