mathewhe/aqua_rat huggingface dataset:
Question: In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 17 years replaced by a new boy. The age of the new boy is?
(A) 14 years 8 months
(B) 15 years
(C) 13 years 8 months
(D) 17 years 10 months
(E) 17 years
Rationale: Total decrease = (20 x 2) months
= 3 years 4 months
Age of the new boy
= 17 years - 3 years 4 months.
= 13 years 8 months.
ANSWER:C
Answer: (C) 13 years 8 months
Question: There are 600 boys in a hostel. Each plays either hockey or football or both. If 75% play hockey and 55% play football, how many play both?
(A) 120
(B) 150
(C) 200
(D) 180
(E) 160
Rationale: n(A) = 75*600/100 = 450
n(B) = 55*600/100 = 330
n(AUB) = 600
n(AnB) = 450+330-600 = 180
Answer is D
Answer: (D) 180
Question: A certain team consists of 3 professors and 6 teaching assistants. How many different teams of 3 can be formed in which at least one member of the group is a professor? (Two groups are considered different if at least one group member is different.)
(A) 48
(B) 52
(C) 56
(D) 60
(E) 64
Rationale: The total number of ways to form a group of 3 from 9 people is 9C3 = 84
The number of ways to form a group without a professor is 6C3 = 20
The total number of ways to form a valid group is 84 - 20 = 64.
The answer is E.
Answer: (E) 64
Question: The probability that a man will be alive for 10more yrs is 1/4 & the probability that his wife will alive for 10 more yrs is 1/3. The probability that none of them will be alive for 10 more yrs, is
(A) 1/2
(B) 2/3
(C) 3/5
(D) 3/7
(E) 3/8
Rationale: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/2
Ans.(A)
Answer: (A) 1/2
Question: A five digit number is to be formed using each of the digits 1, 2, 3, 4 and 5 ONLY ONCE. How many numbers can be formed when 1 and 2 are not together ?
(A) 48
(B) 36
(C) 72
(D) 60
(E) 120
Rationale: No. of ways the 5 digit number can be formed = 5! = 120
Let us fuse 1 & 2.
No. of ways in which 1 and 2 are together = 4! x 2! (Multiplying by 2! because 1 and 2 can be arranged in 2! ways) = 24*2 = 48
No. of ways 1 & 2 wont be together = 120 - 48
=72
ANSWER:C
Answer: (C) 72
Question: A certain number X when divided by 253 leaves a remainder of 98. Which of the following can be subtracted from X to make X divisible by 81?
(A) 17
(B) 27
(C) 27
(D) 47
(E) 57
Rationale: Least possible value of the number is 253 + 98 = 351
Further it is given the number must be divisible by 81 .
351/81 = Gives remainder as 27
So, 27 must be subtracted from the number , answer is (C)
Answer: (C) 27
Question: During a Pizza buffet where A eats more times 2.4 than B, and B eats 6 times less than C.find the leat number of times all the three has to eat
(A) 50
(B) 60
(C) 70
(D) 80
(E) 85
Rationale: A eats more than B if B eats 1 times than the ratio of A and B is A:B is 2.4:1 or 12:5 and as B eat 6 times less the C the the ratio of B : C is 5:30 the the least number of times all three has eat is the LCM of A,B,C that is 60 ..
ANSWER:B
Answer: (B) 60
Question: X and Y together can completes a work in 12 days and Y complete the same work in 24 days. Then the number of days X required to complete the work will be?
(A) 15 days.
(B) 12 days.
(C) 24 days.
(D) 13 days.
(E) 16 days.
Rationale: X and y complete in one day =1/12 part, y completes in one day=1/24 parts. Therefore X alone can do in one day =1/24part. Therefore the work can be finished by X = 24 days. Ans: C
Answer: (C) 24 days.
Question: If the average (arithmetic mean) of a and b is 215, and the average of b and c is 160, what is the value of a − c?
(A) −220
(B) −100
(C) 100
(D) 110
(E) It cannot be determined from the information given
Rationale: Question: a - c = ?
(a + b)/ 2 =215 ===> a + b = 430
(b + c)/2 = 160 ===> b + c = 320
(a + b) - (b + c) =430- 320 ===> a + b - b - c = 110 ===> a - c = 110
Answer: D
Answer: (D) 110
Question: A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 27 m * 2 m * 0.75 m?
(A) 22377
(B) 27000
(C) 27891
(D) 25000
(E) 18771
Rationale: 27 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x
27 = 1/1000 * x => x = 27000
Answer: B
Answer: (B) 27000
Question: Incomes of two companies A and B are in the ratio of 5 : 8. Had the income of company A been more by 20 lakh, the ratio of their incomes would have been 5 : 4. What is the income of company B?
(A) 32 lakh
(B) 50 lakh
(C) 40 lakh
(D) 60 lakh
(E) None of these
Rationale: Let the incomes of two companies A and B be 5x and 8x respectively.
From the question,
5x+20/8x=5/4 ⇒ 20x + 80 = 40x
∴ x = 4
∴ Income of company B = 8x = 32 lakh
Answer A
Answer: (A) 32 lakh
Question: Resident of town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and std deviation of 8 hrs. The number of hours that pat, a resident of town X, watched television last week was between 1 and 2 standard deviation below the mean. Which of the following could be the number of hours that Pat watched television last week?
(A) 30
(B) 20
(C) 18
(D) 12
(E) 6
Rationale: 21-12 < no of hrs < 21-8
9< no of hrs < 13.
D
Answer: (D) 12
Question: Meera is making telescopes, each consisting of 2 lenses, 1 tube, and 1 eyepiece. Lenses can be purchased only in packs of 50, tubes only in packs of 10, and eyepieces only in packs of 30. However, half of the lenses in each pack are not usable for telescopes. If all parts are used only for the telescopes, what is the minimum number of lenses Meera must purchase to make a set of telescopes with no leftover components other than the unusable lenses?
(A) 75
(B) 150
(C) 300
(D) 3600
(E) 7,500
Rationale: I'd use backsolving for this question.
Check D:
3600 lenses = 1800 usable lenses = 900 tubes = 900 eyepieces. We CAN buy 900 tubes and 900 eyepieces, so that not to have leftovers.
Answer: D.
Answer: (D) 3600
Question: Which of the following expressions CANNOT have a negative value
(A) |a + b| – |a – b|
(B) |a + b| + |a|
(C) |2a + b| – |a + b|
(D) a^2 - b^2 – 2|ab|
(E) |a^3 + b^3| – a – b
Rationale: Whenever you are required to find if the equation is a perfect square or not, try to bring everything in the form of a perfect square as they are always positive.
Of the given options, only option D can be written in from of a perfect square.
|a + b| + |a|
This will always be positive.
Correct Option: B
Answer: (B) |a + b| + |a|
Question: Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 210 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?
(A) 1120
(B) 672
(C) 560
(D) 192
(E) 1680
Rationale: Four members worked in ration 2:3:5:6, hence as everyone mentioned, individual work could be taken as 2x, 3x,5x, and 6x. Also this gives us total work as 16x.
But we are told that one of these individual works is 30hrs. hence, possible scenarios, if
(1)2x =210 => 16x = 1680 (2) 3x =210 => 16x = 1120 (3) 5x =210 => 16x = 672 (4) 6x =210 => 16x = 560
Hence Answer is D 192 which can not be any of these.
Answer: (D) 192
Question: On Wednesday, Kramer purchases exactly 3 new shirts, 2 new sweaters, and 4 new hats, On the following day and each subsequent day thereafter, Kramer wears one of his new shirts together with one of his new sweaters and one of his new hats. Kramer avoids wearing the exact same combination of shirt, sweater, and hat for as long as possible. On which day is this no longer possible?
(A) Tuesday
(B) Wednesday
(C) Thursday
(D) Friday
(E) Sunday
Rationale: Shirt combinations = 3!/1*(3-1)! = 3*2*1/1*2*1 = 3
Sweater combinations = 2!/1*(2-1)! = 2*1/1*1 = 2
Hat combinations = 4!/1!*(4-1)! = 4*3*2*1/1*3*2*1 = 4
Total Combinations = Shirt Combos*Sweater Combos*Hat Combos
3*2*4=24 combinations
24 / 7 (days of the week) = remainder of 3
Purchased on Wednesday, 3rd day is Saturday. Next day, which he won't have a new combination for, is Sunday. (E)
Answer: (E) Sunday
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 4 hours and 16 hours respectively. The ratio of their speeds is?
(A) 4:6
(B) 4:3
(C) 4:9
(D) 4:4
(E) 4:2
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= âˆšb : âˆša = âˆš16 : âˆš4 = 4:2.Answer: E
Answer: (E) 4:2
Question: 26 : 62 :: 32:?
(A) 49
(B) 25
(C) 36
(D) 64
(E) 23
Rationale: Ans 23
Reverse of 32
ANSWER:E
Answer: (E) 23
Question: What least number must be subtracted from 9671 so that the remaining number is divisible by 5?
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
Rationale: On dividing 9671 by 5, we get remainder = 1.
Required number be subtracted = 1
ANSWER:E
Answer: (E) 1
Question: Harkamal purchased 8kg of grapes at the rate of 80 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
(A) A)1135
(B) B)1075
(C) C)1065
(D) D)1070
(E) E)1080
Rationale: Cost of 8 kg grapes = 80 × 8 = 640.
Cost of 9 kg of mangoes = 55 × 9 = 495.
Total cost he has to pay = 640 + 495 = 1135.
A)
Answer: (A) A)1135
Question: A property was originally on a 99 years lease and two thirds of the time passed is equal to the four fifth of the time to come.how many years are there to go.
(A) 33
(B) 80
(C) 79
(D) 27
(E) 111
Rationale: Answer:B
Answer: (B) 80
Question: Crazy Eddie has a key chain factory. Eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price, and thus increased the profit from the sale of each key chain from 40% of the selling price to 50% of the selling price. If the manufacturing cost is now $50, what was it before the decrease?
(A) $20
(B) $40
(C) $50
(D) $80
(E) $60
Rationale: Deargoodyear2013,
I'm happy to help.This is a relatively straightforward problem, not very challenging. BTW,Crazy Eddiewas the actually name of an electronics chain on the East Coast of the USA back in the 1970s.
Manufacturing now is $50. They now are making a 50% profit, so the selling price must be $100.
They had this same selling price, $100, before they made the change, and had a profit of 40%, so the manufacturing must have been $60. Answer = (E).
Answer: (E) $60
Question: Find out the square of a number which when doubled exceeds its one sixth by 11 ?
(A) 36
(B) 25
(C) 19
(D) 26
(E) 17
Rationale: A
Let the number be p, then the square will be p^2
According to question:
2p = (p/6) + 11
=> 12p = p + 66
=> p = 6
p^2 = 6^2 = 36.
Answer : A
Answer: (A) 36
Question: A dinner has 2 coffee pitchers; Each can hold 8 cups of coffee. During Monday's morning rush, a customer orders 10 cups of coffee. At the time this customer orders the coffee, one coffee pitcher is 1/4 full while the other is 3/8 full. How much of the customer's order can be filled without making more coffee.
(A) 1/3
(B) 5/8
(C) 3/4
(D) 2/3
(E) 1/2
Rationale: One pitcher has 2 cups of coffee and the other has 3 cups of coffee. This means there is a total of 5 cups of coffee. That means 5 of the 10 cups of coffee can be given to the customer before the dinner makes more coffee. 5/10 simplifies to 1/2. (Answer: E)
Answer: (E) 1/2
Question: A family has two children. find the probability that both the children are boys given that at least
one of them is a boy?
(A) 1/3
(B) 1/5
(C) 1/7
(D) 2/7
(E) 2/9
Rationale: Let g stand for girl and b for boy. The sample space of the experiment is
S = {(g, g), (g, b), (b, g), (b, b)}
Let E and F denote the following events :
E : ‘both the children are boys’
F : ‘at least one of the child is a boy’
Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}
Now E n F = {(g,g)}
Thus P(F) = 3/4
and P (E n F )= 1/4
Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3
A)
Answer: (A) 1/3
Question: Surekha started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs. 10,000 and Rajesh joined him with an amount of Rs. 35,000. In 2001, Surekha invested another additional amount of Rs.10,000 and Jay joined them with an amount of Rs.35,000. What will be Rajesh's share in the profit of Rs.1,80,000 earned at the end of 3 years from the start of the business in 1999?
(A) Rs 45000
(B) Rs 60000
(C) Rs 70000
(D) Rs 75000
(E) None
Rationale: Surekha:Rajesh:Jay= (25000×12+35000×12+45000×12):(35000×24) : (35000×12) = 1260000 : 840000 : 420000 = 3 : 2 : 1. Rajesh's share =Rs.(180000×2/6) = Rs.60000.
Answer B
Answer: (B) Rs 60000
Question: A picnic attracts 240 persons. There are 30 more men than women, and 30 more adults than children. How many men are at this picnic?
(A) 240
(B) 75
(C) 85
(D) 130
(E) 200
Rationale: Adult + Children = 240
Let, Children = y
then, Adult = y+30
i.e. y+(y+30) = 210
i.e. y = 115
i.e. Adult = 115+30 = 145
Adults include only Men and Women
i.e. Men + Women = 145
Let women, W = x
then Men, M = x+30
i.e. x+(x+30) = 2x+30 = 145
i.e. x = 55
i.e. Men, M = 55+30 = 85
Answer: Option C
Answer: (C) 85
Question: If a boat goes 8km upstream in 80 minutes and the speed of the stream is 5 kmph, then the speed of the boat in still water is ?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Rate upsteram =(8/80*60)kmph=6kmph.
speed of the stream =5kmph let speed in still water be xkm/hr. then speed upstream=(x-5)km/hr. x-5=6==>x=11km/hr Answer(D)
Answer: (D) 11
Question: A car runs 375 km in 3 hours. What's the car's speed?
(A) 124
(B) 125
(C) 126
(D) 127
(E) None
Rationale: Solution:
375 ÷ 3 = 125
Answer B
Answer: (B) 125
Question: The ratio of spinsters to cats is 2 to 7. If there are 35 more cats than spinsters, how many spinsters are there?
(A) 14
(B) 21
(C) 28
(D) 35
(E) 42
Rationale: Let 2x be the number of spinsters. Then 7x is the number of cats.
7x-2x=35
x=7 and the number of spinsters is 2(7)=14.
The answer is A.
Answer: (A) 14
Question: A train running at the speed of 60 km/hr crosses a pole in 6 seconds. Find the length of the train.
(A) 110 meter
(B) 120 meter
(C) 100 meter
(D) 90 meter
(E) 105 meter
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 6 = 100 meter
Answer:C
Answer: (C) 100 meter
Question: Find the missing figures: 0.1% of ? = 0.24
(A) 12
(B) 120
(C) 24
(D) 240
(E) 36
Rationale: Let 0.1% of x = 0.24. Then , 0.1*x/100 = 0.24
X= [(0.24*100)/0.1] = 240.
Answer is D.
Answer: (D) 240
Question: Two cubes of their volumes in the ratio 64 : 343. The ratio of their surface area is:
(A) 1.5:5
(B) 2:5
(C) 3:5
(D) 1:5
(E) 4:7
Rationale: The ratio of their surface area is
64 : 343
4 : 7
Answer is E.
Answer: (E) 4:7
Question: A person took some amount with some interest for 4 years, but increase the interest for 1%, he paid Rs.160/- extra, then how much amount he took?
(A) Rs.5500/-
(B) Rs.6000/-
(C) Rs.4000/-
(D) Rs.7000/-
(E) None of these
Rationale: Explanation:4 years = Rs.160/-year = 160/4Rate of Interest = 1%100/1% × 160/4 = Rs.4000/-P = Rs.4000/- Answer: Option C
Answer: (C) Rs.4000/-
Question: A shopkeeper sold an article at $100 with 10% profit. Then find its cost price?
(A) $120
(B) $100
(C) $91
(D) $72
(E) $69
Rationale: cost price = selling price *100/(100+profit)
C.P. = 100*100/110 = $91(approximately)
Answer is C
Answer: (C) $91
Question: Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled?
(A) 2
(B) 3
(C) 3.5
(D) 4
(E) 4.5
Rationale: Part filled by A + B + C in 1 hour = 1/5 + 1/10 + 1/30 = 1/3
All the three pipes together will fill the tank in 3 hours.
ANSWER B
Answer: (B) 3
Question: The difference between the place values of 8 and 3 in the number 587435 is
(A) 75200
(B) 79970
(C) 75460
(D) 24580
(E) None
Rationale: Sol.= (Place value of 8) – (place Value of 3)= (80000 - 30)= 79970 Answer B
Answer: (B) 79970
Question: Car Dealership X, the total profit from sales increased by 10 percent over the previous years, while the number of cars sold decreased by 10 percent over the previous years. Approximately what was the average percent increase in profit per car over the previous year.
(A) 18%
(B) 20%
(C) 22%
(D) 23%
(E) 25%
Rationale: Let Profit be x and cars sold be y
Originally Profit/Car = x/y
Now it is 1.1x / 0.9 y = 11/9 (x/y)
Increase in profit per car = ((2/9) (x/y)) / (x/y) * 100 = 22.22%
Answer = C
Answer: (C) 22%
Question: At Parkins gym class can be divided into 8 teams with an equal number of players on each team or into 12 teams with an equal number of players on each team. What is the lowest possible number of students in the class?
(A)  20
(B)  24
(C)  36
(D)  48
(E)  96
Rationale: We are given that Parkins gym class can be divided into 8 teams or 12 teams, with an equal number of players on each team. Translating this into two mathematical expressions we can say, where G is the total number of students in the gym class, that:
G/8 = integer and G/12 = integer
This means that G is a multiple of both 8 and 12.
We are asked to determine the lowest number of students in the class, or the lowest value for variable “G”. Because we know that G is a multiple of 8 and of 12, we need to find the least common multiple of 8 and 12. Although there are technical ways for determining the least common multiple, the easiest method is to analyze the multiples of 8 and 12 until we find one in common.
Starting with 8, we have: 8, 16, 24, 32
For 12, we have: 12, 24
For the multiples of 12, we stopped at 24, because we see that 24 is also a multiple of 8. Thus, 24 is the least common multiple of 8 and 12, and therefore we know that the lowest possible number of students in the gym class is 24.
Answer B.
Answer: (B)  24
Question: In a 1300 m race Usha beats Shiny by 50 m. In the same race, by what time margin Shiny beat Mercy who runs at 4 m/s ?
(A) 65 sec.
(B) 50 sec
(C) 25 sec
(D) Data not sufficient
(E) None of these
Rationale: Speed of Shiny = 50/ 10 = 5m/s
Time taken by shiny to complete the race is B = 1300/5 = 260 sec.
Time taken by Baley to complete the race is D = 1300/4 = 325 sec.
Hence, D-B = 65 sec
ANSWER:A
Answer: (A) 65 sec.
Question: If the price has fallen by 10% what percent of its consumption be: increased so that the expenditure may be the same as before?
(A) 11 1/0%
(B) 11 1/5%
(C) 11 1/9%
(D) 11 2/9%
(E) 11 1/4%
Rationale: 100 – 10 = 90
90------10
100------? => 11 1/9%
Answer: C
Answer: (C) 11 1/9%
Question: If a man buys 40 purse for $110 and sold them for $3 dollars each determine his gain.
(A) $ 20
(B) $ 10
(C) $ 30
(D) $ 5
(E) $ 25
Rationale: Cost of 40 purse = $110
Sold each purse for $3
So he sold 40 purse for $(40 × 3) = $120
Loss = $(120 – 110) = $10
Therefore, gain = $ 10.
Answer:B
Answer: (B) $ 10
Question: How many such letter-pairs are there in the word BONAFIDE having same number of letters left between them as they have in the series?
(A) 2
(B) 3
(C) 4
(D) 1
(E) None of these
Rationale: BF,NO,AD,AE,DF,DE 6 POSSIBILITES ARE THERE
so none of these
ANSWER:E
Answer: (E) None of these
Question: A rectangular field is 72 yards long and 33 yards wide. A fence is needed for the perimeter of the
field. Fencing is also needed to divide the field into three square sections. How many feet of fencing
are needed? (It is a good idea to make a drawing for this one.)
(A) 630 ft
(B) 830 ft
(C) 430 ft
(D) 828 ft
(E) 830 ft
Rationale: 72 + 33 + 72 + 33 = 210 yds. for
outside of field.
33 + 33 = 66 yds. for dividing sections
210+ 66 = 276 yds. of fencing
276 x 3 = 828 ft. of fencing
correct answer D
Answer: (D) 828 ft
Question: Winson leaves home everyday at 4 p.m to pick his son from school and returns home at 6 p.m. One day, the school was over at 4 p.m and the son started walking home from school. Winson, unaware of this, starts from home as usual and meets his son on the way and returns home with him 15 minutes early. If the speed of Winson is 30 km\hr, find the speed of his son.
(A) 15km/hr
(B) 6 km/hr
(C) 4.28 km/hr
(D) 9 km/hr
(E) 4.12 km/hr
Rationale: Winson leaves home everyday at 4 p.m to pick his son from school and returns home at 6 p.m. One day, the school was over at 4 p.m and the son started walking home from school. Winson, unaware of this, starts from home as usual and meets his son on the way and returns home with him 15 minutes early. If the speed of Winson is 30 km\hr, find the speed of his son.
The distance from home to school is 30 km. The round trip distance = 60 km. Because he returns home 15 minutes early, I thought it might be easier to break his trip up into 8 identical 15 minute blocks, each of which he traveled at 7.5 km/hour.
Because we are dealing with a round trip here, Winson would have stopped 7.5 minutes short of the school. This means he traveled Distance=rate* time .5Km/hour*52.5 minutes or 26.25 KM. His son therefore traveled 3.75km/hour by the time he met his dad at 4:52.5. It took the son 52.5 minutes to travel 3.75 km. Because we are trying to find the son's rate per hour (i.e. 60 minutes) and we have his speed for 52.5 minutes it's best to convert to km/minute then multiply by 60 to get km/hour
3.75km/52.5 = .07 km/minute
.07km/minute*60 minutes = 4.28 km/hour.
Answer: C. 4.28 km/hr
Answer: (C) 4.28 km/hr
Question: In a factory, there are 40% technicians and 60% non-technicians. If the 60% of the technicians and 40% of non-technicians are permanent employees, then the percentage of workers who are temporary is?
(A) 82%
(B) 58%
(C) 52%
(D) 22%
(E) 42%
Rationale: Total = 100
T= 40 NT= 60
40*(60/100)=24 60*(40/100)=24
24 + 24 = 48 => 100 - 48 = 52%
Answer: C
Answer: (C) 52%
Question: At a certain high school, a student’s popularity is determined by his or her locker number. Whoever has the locker number with the greatest number of distinct prime factors is the most popular student in the school. If Johanna, Jamal, Brianna, and John get lockers with the numbers 200, 400, 150, and 420, respectively, who is the most popular student?
(A) Johanna
(B) John
(C) Brianna
(D) Jamal
(E) They have equal popularity
Rationale: Distinct prime factors of 200 (Johanna) : 2, 5
Distinct prime factors of 400 (Jamal): 2 and 5.
Distinct prime factors of 150 (Brianna): 2,3, and 5
Distinct prime factors of 420 (John): 2,3,5 and 7.
So most popular student - John
Answer B
Answer: (B) John
Question: In a company of 148 employees, 92 are females. A total of 78 employees have advanced degrees and the rest have a college degree only. If 31 employees are males with college degree only, how many employees are females with advanced degrees?
(A) 50
(B) 51
(C) 52
(D) 53
(E) 54
Rationale: The number of males is 148-92=56.
The number of males with advanced degrees is 56-31=25.
The number of females with advanced degrees is 78-25=53.
The answer is D.
Answer: (D) 53
Question: There are 8 points marked on the circumference of a circle. How many hexagons can be formed by connecting 6 points of the 8 points?
(A) 26
(B) 28
(C) 30
(D) 32
(E) 34
Rationale: 8C6=28
The answer is B.
Answer: (B) 28
Question: If n = 4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?
(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight
Rationale: n=4p
since n = 4p then even divisors are:
4p/4p = 1
4p/2p = 2
4p/4 = p
4p/2 = 2p
so the answer is (C)
Answer: (C) Four
Question: What is the tens digit of 7^1415?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: 7^1 = 7
7^2 = 49
7^3 = 343
7^4 = 2401
7^5 = 16807
7^6 = 117649
We should see this as pattern recognition . We have a cycle of 4 . (We can multiply the last 2 digits only as we care about ten's digit )
0 , 4 , 4 , 0 .
1415= 4*353 + 3
The ten's digit will be 4 .
Answer E
Answer: (E) 4
Question: If each day a tree loses half its remaining leaves, what fraction of its leaves will it have lost after 8 days ?
(A) X-1/8
(B) X-1/32
(C) X-1/64
(D) X-1/128
(E) X-1/256
Rationale: LET NO OF LEAVES IX X ..IST DAY X/2 ..2ND DAY X/4 ..3RD DAY X/8 , FOURTH DAY X/16 , 5TH DAY X/32 , 6TH DAY X/64 SO ON SO FOURTH.
FINALLY ON LEAVE WILL BE LEFT ..SO ON 3RD DAY LEAVE LOST IS X-1/256 ANSWER E
Answer: (E) X-1/256