MU-NLPC/Calc-aqua_rat huggingface dataset:
Balls of equal size are arranged in rows to form an equilateral triangle. the top most row consists of one ball, the 2nd row of two balls and so on. If 424 balls are added, then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did. How many balls made up the triangle?
Pick
A) 1176	B) 2209	C) 2878	D) 1210	E) 1560

Solution: As expected, this question boils down to 2 equation,   Consider total number of Balls in Triangle = T and number of balls in last row = x.   1+2+3+...+x = T   x(x+1)/2 = T ----(a)   As mentioned in the question, side of a square will be (x-8) and total number of Balls in square will be (T+424)   (x-8)^2 = T+424 -----(b)   Now the hardest part of the question will be to solve these 2 equations and this looks like time consuming BUT the easy way will be plug and play. Also, we've to find a value of T (from 5 optiosn given below) which can make a square of a a number. One we know this, it will be a cake walk.   We can see that option A fits this criteria in eq (b). Add - 1176+424 = 1600 = 40^2 = (x-8)^2 Hence, x = 48.   Cross check by putting in eq (a) = x(x+1)/2 = T = > 48*49/2= 
48*49/2 = 1_176
1176   Hence, answer is 1176.
Answer: A
If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 6-letter code words?
Pick one:	A) 1 to 5	B) 3 to 2	C) 2 to 1	D) 5 to 1	E) 6 to 1

Solution: Number of ways to form 5-letter code: 10!/5! = 10*9*8*7*6   Number of ways to form 6-letter code: 10!/4! = 10*9*8*7*6*5   Ratio: 1 to 5   1 to 5nswer : 1 to 5
Answer: A
The expression xy+x is odd when the x and y are integers. Which of the following expressions must be even?  Choose one:
A) x
B) y
C) x + y
D) xy - x
E) x + y^2

Solution: xy+x is odd   x and y are integers   If x were even xy+x would be even despite any value of y.   y can't be odd, so y must be even.   Ans : y
Answer: B
The ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger one. What are their present ages of the elder person Pick:	A) 11	B) 66	C) 28	D) 30	E) 99

Solution: Let's take the present age of the elder person = x   and the present age of the younger person = x – 16   (x – 6) = 3 (x-16-6)   => x – 6 = 3x – 66   => 2x = 60   => x = 60/2= 
60/2 = 30
30   Answer: 30
Answer: D
At an election 2 candidates are participated and a candidate got 45% of votes and defeated by 9000. and 83 votes are invalid. Find the total polled votes? Choose the correct choice from the following choices:
A) 84512	B) 78452	C) 65893	D) 90083	E) 74502

Solution: Winner votes = 100-45= 
100-45 = 55
55   polled votes= [(100*9000)/2*55-100]+83 = 90083   Answer is 90083
Answer: D
If a rectangular billboard has an area of 91 square feet and a perimeter of 40 feet, what is the length of each of the shorter sides?	Select the correct option.
A) 4	B) 7	C) 8	D) 13	E) 26

Solution: This question can be solved algebraically or by TESTing THE ANSWERS.   We're told that a rectangle has an area of 91 and a perimeter of 40. We're asked for the length of one of the SHORTER sides of the rectangle.   Since the answers are all INTEGERS, and the area is 91, the shorter side will almost certainly be less than 10 (since 10x10 = 100, but we're NOT dealing with a square).   Let's TEST Answer b: 7   IF...   The shorter side = 7...   The area = 91....91/7 = 13 = the longer side   Perimeter = 7+7+13+13= 
7+7+13+13 = 40
40   7
Answer: B
A train is 485 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length  Pick one:  A) 20 seconds  B) 30 seconds  C) 40 seconds  D) 50 seconds  E) None of these

Solution: Explanation:   Speed = 45 Km/hr = 45*(5/18) m/sec   = 25/2 m/sec   Total distance = 485+140= 
485+140 = 625
625 meter   Time= 50 secondsistance/speed   =625∗2/25=50seconds   Option 50 seconds
Answer: D
Pants, Shorts and Shirts in a dresser are in the ratio of 7: 7: 10. If there are 14 Pants, the number of Shirts in the dresser is:
Choices.
A) 14 B) 7 C) 20 D) 70 E) 35

Solution: Explanation :   Let Pants = 7x, Shorts = 7x & Shirts = 10x. Now, 7x = 14 hence x = 2.   Number of Apples = 10x = 20.   Answer : 20
Answer: C
At a certain bowling alley, it costs $0.50 to rent bowling shoes for the day and $1.75 to bowl 1 game. If a person has $12.80 and must rent shoes, what is the greatest number of complete games that person can bowl in one day? Choose the correct choice from the following answers:
A) 7	B) 8	C) 9	D) 10	E) 11

Solution: After renting bowling shoes the person is left with $12.80-$0.5=$12.30, which is enough for 12.3/1.7512.80- 0.5= 
12.80- 0.5 = 12.3
$12.30, which is enough for 12.3/1.75=7.02 -> ~7.   7nswer: 7.
Answer: A
Solution P is 20 percent lemonade and 80 percent carbonated water by volume; solution Q is 45 percent lemonade and 55 percent carbonated water by volume. If a mixture of PQ contains 72% percent carbonated water, what percent of the volume of the mixture is P?
Choose one
A) 48%  B) 54%  C) 60%  D) 64%  E) 68%

Solution: 72% is 8%-points below 80% and 17%-points above 55%.   So the ratio of solution P to solution Q is 17:8.   Mixture P is 17/25 = 68% of the volume of mixture PQ.   The answer is 68%.
Answer: E
If x and q are integers and 2x–q= 11, then 4x+ q CANNOT be Choose the correct choice from the following answers
A) –5	B) 1	C) 13	D) 17	E) 551

Solution: 2x-q=11....q=2x-11   4x+q=4x+2x-11=6x-11   6x-11=-5...x=1   6x-11=1... x=2   6x-11=13...x=4   6x-11=17..X is not integer   6x-11=551..X is not integer   I think the choice E is 55 not 551. Otherwise both E CANNOT be solution=17
Answer: D
A corporation that had $10 billion in profits for the year paid out $500 million in employee benefits. Approximately what percent of the profits were the employee benefits? (Note: 1 billion = 10^9)  Pick:	A) 50%	B) 20%	C) 5%	D) 2%	E) 0.2%

Solution: required answer = [employee benefit/profit] *100   =[(500 million)/(10 billion)]*100   =[(500*10^6)/(10*10^9)]*100   =(50/1000)*100= 
(50/1000)*100 = 5
5%   So answer is (5%)
Answer: C
The captain of a cricket team of 11 members is 30 years old and the wicket keeper is 5 years younger. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average of the team? Pick one:
A) 20  B) 23  C) 32  D) 19  E) 29

Solution: Let the average of the whole team be x years.   11x - (30 + 25) = 9(x - 1)   = 11x - 9x = 46   = 2x = 46 => x = 23   So, average age of the team is 23 years.   Answer:23
Answer: B
If $5,000 is invested in an account at a simple annual rate of r percent, the interest is $250. When $18,000 is invested at the same interest rate, what is the interest from the investment? Choose the correct choice from the following
A) $700 B) $750 C) $800 D) $850 E) $900

Solution: -> 250/5,000=5% and 18,000*5%=900.   Thus, $900 is the answer.
Answer: E
If the range of the set of numbers {140, 80, 135, 110, 175, 145, x, 123, 136} is 115, which of the following could be x?
Choices
A) 40  B) 45  C) 50  D) 55  E) 60

Solution: The range of the other 8 numbers is 175-80= 
175-80 = 95
95, so x must be either the smallest number or the largest number in the set.   Then x= 175-115= 
175-115 = 60
60 or x= 80+115= 
80+115 = 195
195   The answer is 60.
Answer: E
Sam ranked 9th from the top and 38th from the bottom in a class. How many students are there in the class ?
Choose the correct choice from the following options:
A) 22
B) 88
C) 46
D) 299
E) 77

Solution: Explanation:   Number of students in class = (8 + 1 + 37)= 
(8 + 1 + 37) = 46
46   Answer: 46) 46
Answer: C
A sum is invested for 3 years compounded at 5%, 10% and 20 % respectively. In three years, if the sum amounts to Rs. 1386, then find the sum.  Pick one:  A) Rs. 1500  B) Rs. 1000  C) Rs. 1200  D) Rs. 1400  E) Rs. 1600

Solution: Explanation:   1386 = P(1+5/100)(1+10/100)(1+20/100)   1386 = P(21/20)(11/10)(6/5)   P = (1386 × 20 × 10 × 5)/(21 × 11 × 6) = (66 × 20 × 10 × 5)/(11 × 6 = 20 × 10 × 5) = Rs. 1000   i.e., the sum is Rs.1000   Answer: Option Rs. 1000
Answer: B
If $935 are divided between worker A and worker B in the ratio 5:12,what is the share that worker B will get?	Choose the correct choice from the following answers.
A) 62.15%
B) 64.26%
C) 66.37%
D) 68.48%
E) 70.59%

Solution: Worker B will get 12/17 = 70.59%   The answer is 70.59%.
Answer: E
The distance between West-Town to East-Town is 16 kilometers. Two birds start flying simultaneously towards one another, the first leaving from West-Town at a speed of 5 kilometers per minute and the second bird, leaving from East-Town, at a speed of 1 kilometers per minute. What will be the distance, in kilometers, between the meeting point and West-Town?	Choose the correct choice from the following:	A) 3.	B) 7.	C) 10.	D) 12.	E) 16.

Solution: Time taken by the birds to meet = 16/(5 + 1) = 4 mins   Distance traveled by the bird traveling from West-Town = 4 * 4= 
4 * 4 = 16
16   Answer: 16.
Answer: E
At what rate percent of simple interest will a sum of money double itself in 22 years? Choose the correct choice from the following answers:
A) 6.54 %	B) 4.54 %	C) 8 .2 %	D) 4.94 %	E) 5.54 %

Solution: Let sum = x. Then, S.I. = x.   Rate = (100 * S.I.) / (P * T) = (100 * x) / (x * 22)   = 100/22 = 4.54 %   ANSWER:4.54 %
Answer: B
A cylindrical barrel is filled with Kerosene at a rate of 33 cubic meters per hour, the level of kerosene in the barrel rises at a rate of 0.11 meters per hour. Which of the following best approximates the radius of the barrel in meters?
Choose the correct answer: A) √105/11 B) √102/11 C) 12 D) 52 E) 10

Solution: Here's my re-worked solution:   volume = 33 = pi (r^2)(0.11)   33 = 22/7 (11/10)(r^2)   r = sqrt(105/11)   √105/11ns: √105/11
Answer: A
Ten men and ten women have to sit around a circular table so that no 2 women are together. In how many ways can that be done?	Choose the most appropriate option
A) 5!*6!  B) 6!*6!  C) 5!*7!  D) 9!*10!  E) 10!*12!

Solution: The number of arrangements of n distinct objects in a row is given by n!.   The number of arrangements of n distinct objects in a circle is given by (n-1)!.   The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have: n!/n=(n-1)!   Now, 10 men in a circle can be arranged in (10-1)! ways and if we place 10 women in empty slots between them then no two women will be together. The # of arrangement of these 10 women will be 10! and not 9! because if we shift them by one position we'll get different arrangement because of the neighboring men.   So the answer is indeed 9!*10!.   9!*10!
Answer: D
45 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4m3 , then the rise in the water level in the tank will be:	Answers
A) 20 cm  B) 25 cm  C) 35 cm  D) 50 cm  E) None of these

Solution: None of thesexplanation:   Total volume of water displaced =(4 x 45) m3 = 180 m3   Rise in water level = 180/40Ã—20= 0.225m = 22.5cm   Answer: None of these
Answer: E
Pat, Kate, and Mark charged a total of 153 hours to a certain project. If Pat charged twice as much time to the project as Kate and 1/3 as much time as Mark, how many more hours did Mark charge to the project than Kate?
Choices: A) 85 B) 36 C) 72 D) 90 E) 108

Solution: 85   all u do is do   2:1:6=>2x+x+6x=153=>x= 17   34:17:102   102-17= 
102-17 = 85
85   85nswer 85
Answer: A
If 12 and 15 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?
I. 10
II. 15
III. 25	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: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.   Let x be the length of the third side.   15-12 < x < 15+12   3 < x < 27   The answer is I, II, and III.
Answer: E
Find the odd man out. 9,18,23,36,99
Pick one:
A) 9 B) 18 C) 23 D) 36 E) 99

Solution: All except 23 are multiples of 9   Answer is 23
Answer: C
A circle in the coordinate plane passes through points (-3, -2) and (1, 3). What is the smallest possible area of that circle?
Choose the correct choice from the following.
A) 10.5π
B) 26π
C) 262√π
D) 52π
E) 64π

Solution: The distance between the two points is sqrt(41).   radius = sqrt(41)/2   Area= pi*(sqrt(41)/2)^2   A. 10.5π
Answer: A
A shop sells chocolates at re.1 each. U can exchange 3 wrappers for 1 chocolate. If u have Rs.100, how many chocolates can you totally get? Choose the correct choice from the following choices
A) 147
B) 148
C) 149
D) 150
E) 141

Solution: 100 chocolates---- 99+1 wrappers   exchanging 99 wrappers;we are left with   33 chocolates+1 wrapper----- 33+1 wrapper   exchanging 33 wrappers,we are left with   11 chocolates +1 wrapper------12 wrappers   exchanging 12 wrappers,we are left with   4 chocolates------3+1 wrappers   exchanging 3 wrappers,we get   1 chocolate   at last we are left wid two wrappers that cannot be exchanged   therfore: no.of chocolates= 100+33+11+4+1= 
100+33+11+4+1 = 149
149   ANSWER:149
Answer: C
A and B complete a work in 9 days. A alone can do it in 18 days. If both together can do the work in how many days?	Choose the correct choice from the following choices.
A) 6 days	B) 8 days	C) 5 days	D) 7 days	E) 15 days

Solution: 1/9 + 1/18 = 1/6   6/1= 
6/1 = 6
6 days   6 daysnswer:6 days
Answer: A
If selling price of an article is Rs. 250, profit percentage is 25%. Find the ratio of the cost price and the selling price
Options.
A) 5:3  B) 3:5  C) 4:5  D) 5:4  E) 6:4

Solution: Selling price = 250   profit = 25%   cost price = 250*100/125= 
250*100/125 = 200
200   req ratio= 200:250 = 4:5   ANSWER 4:5
Answer: C
Calculate the % profit or loss, if the cost price of 9 apples is equal to the selling price of 11 apples.
Choose one:  A) 29.1%  B) 7.2%  C) 14.2%  D) 12.2%  E) 22.2%

Solution: Let the cost price of 1 apple be Rs 1   Cost of 9 apples = Rs 9   Selling price of 9 apples = 11   Gain/loss = 11 - 9= 
11 - 9 = 2
2   %=2/9âˆ—100= 22.2   Answer: 22.2%
Answer: E
A take twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in?	Choices:	A) 11 hours	B) 76 hours	C) 18 hours	D) 12 hours	E) 16 hours

Solution: Suppose A, B and C take x, x/2 and x/3 respectively to finish the work.   Then, (1/x + 2/x + 3/x) = 1/2   6/x = 1/2 => x = 12   So, B takes 6 hours to finish the work.   Answer: 76 hours
Answer: B
In a question on division with zero remainder, a candidate took 22 as divisor instead of 11. The quotient obtained by him was 35. The correct quotient is?	Choose the correct choice from the following
A) A)70
B) B)24
C) C)28
D) D)29
E) E)30

Solution: Number = (35 * 22)= 
(35 * 22) = 770
770   Correct quotient= 770/11= 
770/11 = 70
70   70)
Answer: A
A larger cube has 125 cubic inch as a volume and in the cube there are 125 smaller cubes such that their volume is 1 cubic inch. What is the difference between the surface areas’ sum of the 125 smaller cubes and the surface area of the larger cube, in square inch? Choose the correct answer.
A) 54	B) 600	C) 81	D) 108	E) 120

Solution: Volume of larger cube = 125 = 5^3   Side of larger cube = 5   Volume of smaller cube = 1 --> Side of smaller cube = 1   Surface area of larger cube = 6 * 5^2 = 150   Surface area of 27 smaller cubes = 125 * 6 * 1= 
125 * 6 * 1 = 750
750   Difference= 750 - 150= 
750 - 150 = 600
600   Answer: 600
Answer: B
Of the 130 employees at company X, 80 are full-time, and 100 have worked at company X for at least a year. There are 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year?	Choose one
A) 20	B) 30	C) 50	D) 80	E) 100

Solution: Full time employee who have NOT worked for at least one year = a   Full time employee who have worked for at least one year = b   NON Full time employee who have worked for at least one year = c   NON Full time employee who have NOT worked for at least one year = d   a+b+c+d = 150   a+b = 80   i.e. c+d = 70   b+c = 100   i.e. a+d = 50   d = 20   i.e. c = 70-20= 
70-20 = 50
50   i.e. b= 100-50= 
100-50 = 50
50   i.e. a= 80-50= 
80-50 = 30
30   b= 30   Answer: Option 30
Answer: B
Rs. 120 are divided among A, B, C such that A's share is Rs. 20 more than B's and Rs. 20 less than C's.
What is B's share	Choices: A) Rs 10 B) Rs 20 C) Rs 24 D) Rs 28 E) None of these

Solution: Explanation:   Let C = x. Then A = (x�20) and B = (x�40).   x + x - 20 + x - 40 = 120 Or x=60.   A:B:C = 40:20:60 = 2:1 :3.   B's share = Rs. 120*(1/6) = Rs. 20   Answer: Rs 20
Answer: B
What is the sum of odd integers from 35 to 75, inclusive?  Choose the correct choice from the following options
A) 1,560
B) 1,500
C) 1,240
D) 1,155
E) 1,100

Solution: Number of odd integers = (75-35)/2 + 1   = 40/2 + 1= 
40/2 + 1 = 21
21   Sum of odd integers= (35+75)/2 * 21= 
(35+75)/2 * 21 = 1_155
1155   Answer 1,155
Answer: D
P and Q started a business with respective investments of Rs. 4 lakhs and Rs. 10 lakhs. As P runs the business, his salary is Rs. 5000 per month. If they earned a profit of Rs. 2 lakhs at the end of the year, then find the ratio of their earnings?  Choose the correct choice from the following answers
A) 1:5
B) 1:8
C) 1:2
D) 1:1
E) 1:6

Solution: Ratio of investments of P and Q is 2 : 5   Total salary claimed by P = 12 * 5000 = Rs. 60000   Total profit = Rs. 2 lakhs.   Profit is to be shared = Rs. 140000   Share of P = (2/7) * 140000 = Rs. 400000   Share of Q = Rs. 100000   Total earnings of P = (60000 + 40000) = Rs. 100000   Ratio of their earnings = 1:1   Answer: 1:1
Answer: D
In Albert house,One tap, working alone at its maximum constant rate, can fill a certain tank in 250 seconds. A second tap, working alone at its maximum constant rate, can fill the same tank in 254 seconds. If both taps work together at their respective maximum constant rates, the time it will take to fill the tank is closest to
Options
A) 126 seconds
B) 150 seconds
C) 177 seconds
D) 200 seconds
E) 250 seconds

Solution: Tap 1 : 250 secs   Tap 2 : 254 secs   Considering the average of these 2 taps : 252 secs.   So 1 tap can fill the tank in 252 secs, so 2 taps can fill the tank in 252/2= 
252/2 = 126
126 secs.   Closest answer is 126 seconds.
Answer: A
X, Y and Z, each working alone can complete a job in 2, 4 and 6 days respectively. If all three of them work together to complete a job and earn $2000, what will be Z's share of the earnings? Choose the correct choice from the following choices
A) $1080.90
B) $1000.90
C) $1070.90
D) $1050.90
E) $1090.90

Solution: The dollars earned will be in the same ratio as amount of work done   1 day work of Z is 1/6 (or 2/12)   1 day work of the combined workforce is (1/2 + 1/4 + 1/6) = 11/12   Z's contribution is 2/9 of the combined effort   Translating effort to $ = 6/11 * 2000 = $1090.90   hence:$1090.90
Answer: E
A is a working partner and B is a sleeping partner in the business. A puts in Rs.20000 and B Rs.25000, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is? Answers.
A) 1978 B) 2707 C) 7728 D) 4800 E) 7291

Solution: 20:25 => 4:5   9600*10/100= 
9600*10/100 = 960
960   9600 - 960= 
9600 - 960 = 8_640
8640   8640*4/9= 
8640*4/9 = 3_840
3840 + 960= 
3840 + 960 = 4_800
4800   Answer: 4800
Answer: D
The ratio of A and B is 5:3.After 2 years their ratio is 3:2.What is the age of B?  Choose the correct option:	A) 5	B) 3	C) 6	D) 7	E) 8

Solution: The ratio of A and b is 5x and 3x years.   After 2 years, their ratio will be 3 and 2.   (i.e) (5x+2)/(3x+2)=3/2   10x+4=9x+6   x=2   B's age=3x=3(2)=6 years   Answer is option 6
Answer: C
A machine fills 150 bottles of water every 8 minutes. How many minutes it takes this machine to fill 675 bottles? Choices:
A) 32 minutes	B) 28 minutes	C) 29 minutes	D) 30 minutes	E) 31 minutes

Solution: 8 minutes are needed to fill 150 bottles. How many groups of 150 bottles are there in 675 bottles?   675 /150= 
675 /150 = 9/2 = around 4.5
4.5= 4 and 1/2   For each of these groups 8 minutes are needed. For 4 groups and 1/2   8 * 4 + 4 = 32 + 4= 
32 + 4 = 36
36 minutes. (4 is for 1/2 a group that needs half time)   We can also find the final answer as follows   4.5 x 8= 32 minutes   correct answer 32 minutes
Answer: A
A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good.  Pick
A) 20/31  B) 20/63  C) 5/31  D) 6/31  E) 26/31

Solution: Required probability = (⁵C₃ . ⁴C₁)/⁹C₄ = (10 * 4)/126 = 20/63   ANSWER:20/63
Answer: B
A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?
Choose the correct choice from the following.
A) 2 8 ½ kmph	B) 8 2 ½ kmph	C) 2 9 ½ kmph	D) 2 2 ½ kmph	E) 3 2 ½ kmph

Solution: 100 --- 10 2 2 ½ kmphS = 10   ? ---- 1   75 ---- 15 US = 5   ? ----- 1 S = (10 - 5)/2   = 2 2 ½ kmph   Answer: 2 2 ½ kmph
Answer: D
How many integers between 324,700 and 418,600 have tens digit 1 and units digit 3?
Select:
A) 652
B) 827
C) 939
D) 1045
E) 1136

Solution: The integers are:   324,713   324,813   etc...   418,513   The number of integers is   4186 - 3247= 
  4186 - 3247 = 939
939   The answer is 939.
Answer: C
Suppose you flip a fair coin 7 times. What is the probability that, in 7 flips, you get at least one head? Select the correct option
A) 57/58
B) 23/28
C) 127/129
D) 127/128
E) 64/65

Solution: Best way of solving an at least 1 type of question is to compute 1 - probability of flipping 0 heads   probability of flipping either a head or a tail = 1/2   probability of flipping 3 tails in a row (1/2)^5   probability of flipping at least 1 head = 1 - (1/2)^7 = 127/128   Answer : 127/128
Answer: D
Find the odd man out. 12, 21, 32, 45, 60, 77, 95 Choose the correct choice.
A) 95  B) 45  C) 32  D) 21  E) 77

Solution: Explanation :   12 + 9= 
12 + 9 = 21
21   21 + 11= 
21 + 11 = 32
32   32 + 13= 
32 + 13 = 45
45   45 + 15= 
45 + 15 = 60
60   60 + 17= 
60 + 17 = 77
77   77 + 19= 
77 + 19 = 96
96   Hence, 95 is wrong. 96 should have come in place of 95   95nswer : Option 95
Answer: A
What is the 56743 rd term in the series 1234567891011121314…….?	Select the correct option.
A) 1 B) 6 C) 5 D) 4 E) 7

Solution: Explanation:   1 to 9 = 9 no.s 1 digit each no.   9 to 99 = 90 no.s 2 digit each,Total digit = 90 × 2 = 180 terms   99 to 999 = 900 no.s 3 digit each,total digit = 900 × 3 = 2700   999 to 9999 = 9000 no.s 4 digit each,total digit = 9000 × 4 = 36,000   Till Now 999,we have = 9 + 180 + 2700= 
9 + 180 + 2700 = 2_889
2889 digits   Upto 9999 we have= 2889 + 36000= 
2889 + 36000 = 38_889
38889 digits   56743 – 38889= 17854   After 9999 each no. has 5 digit   So 17584/5= 3570 with remainder 4.   3570th no after 9999 =9999+3570= 
9999+3570 = 13_569
13569   Next term=13570.   4th digit =7 so answer=7   Answer: 7
Answer: E
Two cards are drawn together from a pack of 52 cards the probability that one is the spade and one is a heart is ?  Choose the most appropriate option
A) 85/852	B) 45/69	C) 18/456	D) 13/102	E) 23/125

Solution: let S be the sample space then   n(S)=52C2=(52*51)/(2*1)= 
(52*51)/(2*1) = 1_326
1326   let E be the event of getting 1 spade kings and 1 heart   let n(E)=number of ways of chossing 1 spade out of 13 and 1 heart out of 13=(13C1*13C1)=13*13= 
13*13 = 169
169   P(E)=n(E)/n(S)   =169/1326   =13/102 Answer(13/102)
Answer: D