MU-NLPC/Calc-aqua_rat huggingface dataset:
If x is a negative integer, which of the following must be a negative integer? Choose the correct choice from the following answers:  A) x + 1  B) x/2+3  C) x^4  D) x – y  E) x^11

Solution: We need to check each option here:   A. x + 1   This will depend on the value of x. Nothing can be said   B. x/2+3   This will depend on the value of x. Nothing can be said   C. x^4   This will always be positive. Even powers of negative numbers are positive and odd powers are negative   D. x – y   This will depend on the value of x and y. Nothing can be said   E. x^11   This will always be negative. x^11ven powers of negative numbers are positive and odd powers are negative   Correct Option: x^11
Answer: E
The food in a camp lasts for 40 men for 30 days. If ten more men join, how many days will the food last? Choose the most appropriate option.
A) 32days  B) 30days  C) 28days  D) 26days  E) 24days

Solution: one man can consume the same food in 40*30= 
40*30 = 1_200
1200 days.   10 more men join, the total number of men= 50   The number of days the food will last = 1200/50= 
1200/50 = 24
24 days.   Answer: 24days
Answer: E
2 corner most boxes of a chess board(diagonally opposite) haven been cut out
there's a rectangular block = 2 sqaures of chess board , how many such blocks can be placed on the chess board ?”	Pick one
A) 27 B) 28 C) 29 D) 30 E) 31

Solution: chess board has 64 squares.so we can place 32 rectangular blocks,but 2 are cut off from the corner.   hence 32-2= 
32-2 = 30
30 blocks   ANSWER:30
Answer: D
A can finish a piece of work in 5 days. B can do it in 15 days. They work together for two days and then A goes away. In how many days will B finish the work?  Choose the correct choice from the following:
A) 3 days  B) 5 days  C) 4 days  D) 6 days  E) 7 days

Solution: 2/5 + (2 + x)/15 = 1 => x = 7 days   ANSW7 daysR:7 days
Answer: E
In Plutarch Enterprises, 70% of the employees are marketers, 20% are engineers, and the rest are managers. Marketers make an average salary of $60,000 a year, and engineers make an average of $80,000. What is the average salary for managers if the average for all employees is also $80,000? Choose the correct choice from the following options: A) $80,000 B) $130,000 C) $240,000 D) $290,000 E) $220,000

Solution: For sake of ease, let's say there are 10 employees: 7 marketers, 2 engineers, and 1 manager.   Average company salary * Number of employees = Total company salary   >>> $80,000 * 10 = $800,000   Subtract the combined salaries for the marketers (7 * $60,000) and the engineers (2 * $80,000)   >>> $800,000 - $420,000 - $160,000 = $220,000.   The correct answer is $220,000.
Answer: E
If |x - 20| = 40 what is the sum of all the values of x.
Choose the correct choice from the following choices
A) 0	B) 60	C) -80	D) 40	E) 80

Solution: There will be two cases   x-20 = 40 and x-20 = -40   Solve for x => x=40+20=> x=60 or x= -40 + 20 => x= -20   The sum of both values will be  60 + -20= 
 60 + -20 = 40
40   Answer is 40
Answer: D
If your mother asked you to bring her 7 water bottles, and one bottle costs 1.5 $, how much money should she give you?	Choose the correct choice from the following answers
A) 9 $ B) 9.5 $ C) 10 $ D) 10.5 $ E) 11 $

Solution: Simply multiply the cost of one bottle by its number you would buy.   The cost=7*1.5= 
7*1.5 = 10.5
10.5 $   So the correct choice is 10.5 $
Answer: D
At what rate of interest (compounded yearly)will Rs.10,000 amount to Rs.12100 in 2 years? Choose one.
A) 11%  B) 8%  C) 10%  D) 9%  E) 7%

Solution: 10%.I=P(1+R/100)^N   12100=10000(1+R/100)^2   121/100=(1+R/100)^2   (11/10)^2=(1+R/100)   R=10%   ANSWER:10%
Answer: C
15 and 5 are the first two terms in a geometric sequence. What is the arithmetic difference between the 7th term and the 9th term?  Pick.
A) (40/3) * (1/3)^7	B) (40/6) * (1/3)^7	C) (40/9) * (1/3)^7	D) (1/3)^7	E) (100/3) * (1/3)^7

Solution: Common ratio = 5/15 =1/3   7th term = 15*(1/3)^7   9th term = 15*(1/3)^9   Difference = 15 * ((1/3)^7 - (1/3)^9)   = 15 * (1/3)^7 *(1 - (1/3)^2)   = 15 * (1/3)^7 * (8/9)   = (120/9) * (1/3)^7....   = (40/3) * (1/3)^7   (40/3) * (1/3)^7
Answer: A
Convert the 18/42 m/s into kilometers per hour? Pick
A) 3.5 kmph.
B) 2.5 kmph.
C) 1.2 kmph.
D) 1.54 kmph.
E) 1.9 kmph.

Solution: 18/42 m/s = 18/42 * 18/5 = 1 (27/50) = 1.54 kmph.   ANSWER:1.54 kmph.
Answer: D
The ratio of salary of a worker in July to that in June was 21⁄2 : 21⁄4, by what % the salary of July more than salary of June. Also find by what %, salary of June was less than that of July.  Choose the correct choice from the following options:
A) 11 1⁄9% and 10% B) 10% and 11 1⁄9% C) Both 10% D) Both 11 1⁄9% E) None of these

Solution: Let the salary of July be 5⁄2 x   and the salary of June be 9⁄4 x   Required percentages   = 5/2x−9/4x /9/4x×100 and 5/2x−9/4x /5/2x×100   = 100⁄9% and 100⁄10% = 11 1⁄9% and 10%   11 1⁄9% and 10%nswer 11 1⁄9% and 10%
Answer: A
In expressing a length of 77.470 km as nearly as possible with the three significant digits, find the percentage error Choose the correct choice from the following:
A) 0.39%  B) 0.34%  C) 0.039%  D) 0.035%  E) None of these

Solution: Explanation:   Error = (77.5 - 77.470)= 
(77.5 - 77.470) = 0.03
0.03   Required percentage=   0.03/ 77.470Ã—100=0.039   Option 0.039%
Answer: C
The average of 40 numbers is 32. If two numbers namely 34 and 39 are discarded, The average of
remaining numbers is? Options.
A) 31.7 B) 37.5 C) 39.5 D) 34.5 E) 38.5

Solution: Total of 50 numbers = 40 * 32= 
40 * 32 = 1_280
1280   31.7verage of 38 numbers= 1280-(34+39) / 38   = 1207 / 38 = 31.7   31.7nswer is 31.7.
Answer: A
The cube root of .000343 is	Answers
A) 0.7	B) 0.07	C) 0.007	D) 7	E) None of these

Solution: Explanation:   (.000343)1/3   = (343/106)1/3   = (7*7*7/ 102*102*102)1/3   = 7/102   = 7/100= 
7/100 = 7/100 = around 0.07
0.07   ANSWER 0.07
Answer: B
The probability that a arrow fired from a point will hit the target is 1/4. Three such arrows are fired simultaneously towards the target from that very point. What is the probability that the target will be hit? Choose the correct answer:	A) 19/64	B) 23/64	C) 23/67	D) 37/64	E) 37/50

Solution: Explanation :   Probability of a arrow not hitting the target =3/4.   Probability that none of the 3 arrow will hit the target:   =>(3/4)3.   =>27/64.   Probability that the target will hit at least once   =>1−(27/64).   =>37/64.   Answer : 37/64
Answer: D
A and B together can do a piece of work in 3 days. If A alone can do the same work in 20 days, then B alone can do the same work in?  Answers
A) 0.28 days	B) 0.45 days	C) 0.55 days	D) 0.25 days	E) 0.15 days

Solution: B = 1/2 – 1/20 =0.28 days   0.28 daysNSWER:0.28 days
Answer: A
By travelling at 60 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?  Choose the correct choice from the following answers.
A) 30 kmph
B) 28 kmph
C) 26 kmph
D) 24 kmph
E) 22 kmph

Solution: Let the time taken to reach the destination be 3x hours. Total distance = 60 * 3= 
60 * 3 = 180
180x km   He covered 2/3 * 180= 
2/3 * 180 = 120
120x km in 1/3 * 3x= x hours So, the remaining 60x km, he has to cover in 2x hours. Required speed = 60x/2x   =30 kmph.   30 kmphnswer: 30 kmph60 /2= 
60 /2 = 30
30 kmph.   30 kmphnswer: 30 kmph
Answer: A
Find the invalid no.from the following series 10, 17, 22, 29, 34, 36  Choose the correct choice from the following choices
A) 36
B) 18
C) 40
D) 37
E) 25

Solution: The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 36 is wrong.   36nswer : 36
Answer: A
Present ages of X and Y are in the ratio 4:5 respectively. 6 years hence this ratio will become 5:6 respectively. What is X's present age in years?
Choose the correct choice from the following answers:
A) 35	B) 24	C) 37	D) 39	E) 40

Solution: Let the present ages of X and Y be 4x and 5x years respectively.   Then, (4x + 6)/(5x + 6) = 5/6   6(4x + 6) = 5(5x + 6) => 24x+36 = 25x+30 => x=6   X's present age = 4x = 4*6= 
4*6 = 24
24   ANSWER: 24
Answer: B
In a 2000 m race, A beats B by 100 meters or 50 seconds. Find the speed of B?
Choose the correct choice from the following choices
A) 10m/s  B) 2m/s  C) 5m/s  D) 7m/s  E) 3m/s

Solution: Since A beats B by 100 m or 50 seconds,   it implies that B covers 100 m in 50 seconds.   Hence speed of B = 100/50= 
100/50 = 2
2 m/s.   Answer: 2m/s
Answer: B
Two isosceles Triangles have equal vertical angles and their areas are in the ratio 16:36. Find the ratio of their corresponding heights .
Select
A) 4/6
B) 5/4
C) 3/2
D) 5/7
E) 2/3

Solution: We are basically given that the triangles are similar.   In two similar triangles, the ratio of their areas is the square of the ratio of their sides and also, the square of the ratio of their corresponding heights.   Therefore, area/AREA=height^2/HEIGHT^2=16/36 --> height/HEIGHT=4/6.   4/6nswer: 4/6.
Answer: A
The area of a square garden is Q square feet and the perimeter is P feet. If Q=2P+48, what is the perimeter of the garden in feet?  Select the correct option:
A) 36 B) 40 C) 44 D) 48 E) 52

Solution: Let x be the length of one side of the square garden.   x^2 = 8x + 48   x^2 - 8x - 48 = 0   (x-12)(x+4) = 0   x = 12, -4   P = 4(12) = 48   The answer is 48.
Answer: D
The perimeter of a triangle is 24 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?  Choose the most appropriate option: A) 30 cm2 B) 85 cm2 C) 65 cm2 D) 45 cm2 E) 35 cm2

Solution: Area of a triangle = r * s   Where r is the inradius and s is the semi perimeter of the triangle.   30 cm2rea of triangle = 2.5 * 24/2= 
2.5 * 24/2 = 30
30 cm2   30 cm2nswer:30 cm2
Answer: A
What is the rate percent when the simple interest on Rs.9100 amount to Rs.455 in 3 Years?	Choose one
A) 3.7%  B) 5.7%  C) 6.7%  D) 8.7%  E) 9.7%

Solution: 455 = (4100*3*R)/100   R = 3.7%   3.7%nswer: 3.7%
Answer: A
How many digits are in the number 50^8 × 8^3 × 11^2? Pick one:	A) 22	B) 20	C) 19	D) 18	E) 17

Solution: calculate the Number of 0's through the powers of 10   50^8 × 8^3 × 11^2 = (5^2*2)^8*2^9*11^2 = 5^16*2^17*11^2 = 2*11^2*10^16 = 242*10^16   Hence we would have 16 trailing 0's and the three digits from 242   Total digits = 3 + 16= 
3 + 16 = 19
19   19orrect Option: 19
Answer: C
. If the sides of two cubes are in the ratio 3: 1 the ratio of their total surface area is?	Choose the correct choice:
A) 3:2	B) 9:5	C) 9:1	D) 9:9	E) 9:7

Solution: Explanation:   a1 : a2 = 3 : 1   6 a12 : 6 a22 = 9: 1   Answer: Option 9:1
Answer: C
If mn > 0, which of the following must be negative? Select
A) mn	B) mn^2	C) m/-n	D) m/n	E) m+n

Solution: Given mn> 0 So both will be the positive integers. If both are positive, then A,B,D,E also positive.   Answer :m/-n
Answer: C
A thief goes away with a SANTRO car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start?  Choose the correct choice from the following answers:
A) 2 hours
B) 9 hours
C) 6 hours
D) 3 hours
E) 12 hours

Solution: Explanation:   |-----------20--------------------|   50 40   D = 20   RS = 50 – 40 = 10   T = 20/10= 
20/10 = 2
2 hours   2 hoursnswer: Option 2 hours
Answer: A
If the radius of a circle is increased by 20% then the area is increased by: Select the correct option:	A) 44	B) 219	C) 16	D) 18	E) 11

Solution: Explanation:   Let say radius = πr2πr2 = π102π102 = 100π100π   New radius = 10 × 120% = 12   New area = π122π122 = 144π144π   Increment = 144π−100π100π×100144π−100π100π×100 = 44%   44nswer: 44
Answer: A
A certain fruit stand sold apples for $0.70 each and guava for $0.50 each. If a customer purchased both apples and bananas from the stand for a total of $6.30, what total number of apples and bananas did the customer purchase ?
Choose the correct choice.
A) 12 B) 13 C) 11 D) 14 E) 5

Solution: Some multiple of 7 + Some multiple of 5 should yield 63. To get to a some multiple of 5, we should ensure that a 3 or 8 (5+3) should be a multiple of 7.   63 is a direct multiple of 7, however in this case there won't be any guava. Hence the next option is to look for a multiple of 7 that has 8 as the unit digit. 28 satisfies this hence no. of apples is 4 and no of bananas is 7 .   11
Answer: C
Cathy and Jim begin running at the same time and they start at the same place on a straight path. Cathy runs at 10 miles per hour, and Jim runs at 6 miles per hour. After 18 minutes, Cathy stops to stretch. If it takes Cathy 27 minutes to stretch and Jim continues to run during this time, how many minutes will it take Cathy to catch up to Jim? Choose one: A) 20.5 B) 21.5 C) 22.5 D) 23.5 E) 24.5

Solution: In 18 minutes, Cathy runs 3 miles.   In 45 minutes, Jim runs 4.5 miles.   Cathy can catch Jim at a rate of 4 miles per hour.   Since Jim is ahead by 1.5 miles, it will take Cathy 1.5 / 4 hours = 22.5 minutes to catch Jim.   The answer is 22.5.
Answer: C
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 600 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?  Pick one.
A) 2880.  B) 4320.  C) 5780.  D) 5760.  E) 6380.

Solution: Efficiency per machine = 600 watt/hr   Efficiency due to increase in wind speed = 600*120% => 720 watt/hr   Production by each machine in 2 hours is  720*2= 
 720*2 = 1_440
> 1440 watt   Production by 3 machines=> 1440 watt * 3 = 4320 watt   Answer will be (4320.)
Answer: B
A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:
Choose the most appropriate option
A) 130  B) 360  C) 500  D) 540  E) 580

Solution: L = 800 m   S = 78kmph = 65/3 mps   Time to pass tunnel = 1min = 60 sec   t.f (800+X)/(60) = (65/3)   =500   ANSWER:500
Answer: C
Find the sum of all 2 digit numbers divisible by 3. Pick:	A) 99	B) 199	C) 1665	D) 2452	E) 2547

Solution: All 2 digit numbers divisible by 3 are :   12, 51, 18, 21, ..., 99.   This is an A.P. with a = 12 and d = 3.   Let it contain n terms. Then,   12 + (n - 1) x 3 = 99 or n = 30.   Required sum = 30 x (12+99) = 1665.   ANSWER 1665 1665
Answer: C
The speed of a boat in still water is 60kmph and the speed of the current is 40kmph. Find the speed downstream and upstream?
Answers:	A) 87 kmph	B) 40 kmph	C) 16 kmph	D) 20 kmph	E) 18 kmph kmph

Solution: Speed downstream = 60 + 40= 
60 + 40 = 100
100 kmph   Speed upstream= 60 - 40= 
60 - 40 = 20
20 kmph   Answer:20 kmph
Answer: D
If pipe A can fill the tank in 45 minutes and pipe B in 30 minutes, find the time to fill the tank if both the pipes are opened together. Select:  A) 12 minutes  B) 20 minutes  C) 18 minutes  D) 15 minutes  E) None of these

Solution: Explanation:   In 1 minute pipe A can fill 1/45th part of the tank and pipe B can fill 1/30th part of the tank. If they are opened simultaneously then in 1 minute they can fill (1/45   + 1/30) part of the tank = 1/18th part of the tank.   Hence, in 18 minutes the tank gets filled if pipes A & B are opened together.   ANSWER 18 minutes
Answer: C
The average of 5 quantities is 11. The average of 3 of them is 4. What is the average of remaining 2 numbers?  Choose the correct choice from the following choices.
A) 21.5	B) 10.6	C) 8	D) 9.5	E) None of these

Solution: 21.5NSWER: 21.5   (5x11-3x4)/2=21.5
Answer: A
How many cubes of 5cm edge can be cut out of a cube of 15cm edge Choose the most appropriate option.
A) 36
B) 232
C) 27
D) 48
E) None of these

Solution: Explanation:   number of cubes=(15 x 15 x 15) / (5 x 5 x 5) = 27   Answer: 27
Answer: C
Sum of the squares of three numbers is 431 and the sum of their products taken two at a time is 265. Find the sum?
Choose one
A) 32  B) 35  C) 25  D) 31  E) 29

Solution: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 431 + 2* 265   a + b + c = √961 = 31   31
Answer: D
In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 63 as quotient. What is the correct quotient ?
Answers.
A) 0  B) 36  C) 13  D) 20  E) 25

Solution: 12*63= 
12*63 = 756
756   756%21=36   ANSWER:36
Answer: B
Suresh drives his car to a place 150 km away at an average speed of 50 km/hr and returns at 30 km/hr. What is his average speed for the whole journey ?  Options:
A) 32.5 km/hr  B) 35 km/hr  C) 37.5 km/hr  D) 40 km/hr  E) 42 km/hr

Solution: Explanation:   If a car covers a certain distance at x kmph and an equal distance at y kmph. Then,   average speed of the whole journey = 2xy/x+y kmph.   Therefore, average speed   =2×50×30/50+30=2×50×30/80   =2×50×3/8=50×3/4   =25×3/2=75/2= 
75/2 = 75/2 = around 37.5
37.5   Answer: Option 37.5 km/hr
Answer: C
The average height of 30 students in a class was calculated as 175 cm. It has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 136 cm. What was the actual average height of the students in the class? Choices:  A) 174.5  B) 173.5  C) 172.5  D) 171.5  E) 170.5

Solution: The total height was 15 cm too much.   The average height should be reduced by 15 cm/30 = 0.5 cm   The answer is 174.5.
Answer: A
What is the value of n if the sum of the consecutive odd intergers E from 1 to n equals 169?  Choices:
A) 47  B) 25  C) 37  D) 33  E) 29

Solution: Before you tackle this question you must first understand that the question is comprised of two key parts, 1st is finding out how manytermsis in that sequence and 2nd whatactual number valuethat term is. In an arithmetic progression, in this case consecutive odd integers 1, 3, 5, ...., there are two set of rules.   Rule #1 (Arithmetic Sequence): xn = a + d(n-1) Identifies what the actual # in the sequence would be. Each number in the sequence has a term such as 1(is the first term), 3(is the second term) and so on. So if I were to ask you to find out what the 10th term is of that sequence you would use that formula to find that value.   a=1 (first term)   d=2 (the common difference) remember in the sequence 1, 3, 5, 7 the common difference is always 2   *On a side note we use n-1 because we don't have d in the first term, therefore if we were solving for the first term we would get 0 as n-1 and 0 times d would give us 0, leaving only the first term. This works regardless what your first term is in any sequence.   But remember the question asksWhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169?which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is, in this case it would be the last number in that sequence. In order to find that we first need to knowhow many terms(how many of the n there is) in order to be able to plug n in this formula given we know what the sum is. For that to happen we need to use Rule #2.   Rule #2 (Summing an arithmetic series): 169 = n/2(2a+(n-1)d). Given the question gives us what the sum is (169 in this case) we would simply use this formula to solve for n. Once we solve for n (13 in this case) we can simply plug n into the first formula (rule 1) and find the value.   It feels very confusing and difficult at first, but once you identify the steps all you need to do is plug and play. We have the sum (169) of a sequence, the number of terms in that sequence is (unknown). Rule #2 tells us how many numbers there are in that sequence and Rule #1 gives us what that last term is.
Answer: B
A class is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. Find the least number of square tiles of equal size required to cover the entire floor of the class room ?
Select.
A) 115  B) 117  C) 116  D) 114  E) 113

Solution: Explanation:   Length = 6 m 24 cm = 624 cm   Width = 4 m 32 cm = 432 cm   HCF of 624 and 432 = 48   Number of square tiles required = (624 x 432)/(48 x 48) = 13 x 9 = 117.   ANSWER IS 117
Answer: B
If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is  Choose the correct option:
A) 1/4
B) 1/2
C) 3/4
D) 3/5
E) None of these

Solution: The number of exhaustive outcomes is 36.   Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2   P(E) = 1 - 1/2 = 1/2.   Answer : 1/2
Answer: B
How many terms are there in 2, 4, 8, 16,..., 16384?
Choose the correct choice from the following.
A) 14
B) 11
C) 12
D) 10
E) 8

Solution: 2, 4, 8, 16, ..., 16384 is a G.P with a =2   and r =4/2= 
4/2 = 2
2   Let the number of terms be n. Then   2 x 2 ^n-1= 16384   or 2^n-1 = 8192 = 2^13   Thus n - 1 =13   n= 14   14NSWER:14
Answer: A
The probability that A speaks truth is 3/5 and that of B speaking truth is 2/7. What is the probability that they agree in stating the same fact?	Choose the correct option:
A) 18/35
B) 18/38
C) 18/36
D) 16/35
E) 18/31

Solution: If both agree stating the same fact, either both of them speak truth of both speak false.   Probability   = 3/5 * 2/7 + 2/5 * 5/7   = 6/35 + 10/35   = 16/35   Answer: 16/35
Answer: D
If the TV is selling for $1200 its cost price is $800. Then what is the profit percentage	Choose the correct choice.
A) 60%  B) 70%  C) 80%  D) 90%  E) 50%

Solution: Explanation:   Let the S.P = 1200   then C.P. = 800   Profit = 400   Profit% = (400/800) * 100= 
(400/800) * 100 = 50
50%. Answer: 50%
Answer: E
A hotel has 4 available rooms. One room has a view to the garden and the others has a view to the pool. If you sleep in the hotel, what is the probability that you get a room in the side of the garden?	Pick:
A) 1/4
B) 1/2
C) 1/3
D) none
E) 2

Solution: the total number of rooms is 4   and the number of rooms in the side of the garden is 1   then, in one chance the probability to pick a room in the side of the garden is   1/4   1/4nswer 1/4
Answer: A
If 425/999=0.125, what is the 81st digit to the right of the decimal point in the decimal equivalent of the fraction?  Choose the correct answer.
A) 0
B) 2
C) 3
D) 4
E) 5

Solution: 0.[u]125[/u = 0.425425425.....   Every 3rd digit is 5 and every multiple of 3 will be the digit 5. Since 81 is multiple of 3, the 81st digit is 5.   Answer 5
Answer: E
In what time will a train 80 m long cross an electric pole, it its speed be 144 km/hr?
Choose the correct choice from the following answers:
A) 2.0 sec
B) 2.8 sec
C) 7.5 sec
D) 2.3 sec
E) 1.5 sec

Solution: Speed = 144 * 5/18= 
144 * 5/18 = 40
40 m/sec   Time taken= 80/40= 
80/40 = 2
2.0 sec.   2.0 secnswer:2.0 sec
Answer: A
A company selected 250 zip codes in Northeastern, Florida, Arizona and California in order to mail a product catalog. The number of Northeastern zip codes was twice Florida's, and four times Arizona's, and 4/3 California's. 300,000 catalogues were mailed to California and 25% resulted in product orders. What is the ratio of the number of orders to the number of California's zip codes?	Choose the correct choice from the following answers:
A) a) 500	B) b) 750	C) c) 1,000	D) d) 1,250	E) e) 1,500

Solution: Since N = 2F, no of Florida zip codes (F) will be N/2.   Since N = 4A, no of Arizona zip codes (A) will be N/4   Since N = (4/3)c) 1,000, no of c) 1,000alifornia zip codes (c) 1,000) will be 3N/4   N + N/2 + N/4 + 3N/4 = 5N/2 = 250   N = 100   c) 1,000 = 3N/4 = 75   No of orders is 25% of 300,000 = 75,000   So required ratio = 75,000/75 = 1000   Answer c) 1,000
Answer: C
The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 20 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam.  Pick:	A) 15	B) 25	C) 35	D) 45	E) 55

Solution: Let the number of students who wrote the exam be x.   Total marks of students = 80 x.   Total marks of (x - 5) students = 90(x - 5)   80x - (5 * 20) = 90(x - 5)   350 = 10x => x = 35   ANSWER:35
Answer: C