mathewhe/aqua_rat huggingface dataset:
Question: A decade is defined as a complete set of consecutive nonnegative integers that have identical digits in identical places, except for their units digits, with the first decade consisting of the smallest integers that meet the criteria, the second decade consisting of the next smallest integers, etc. A decade in which the prime numbers contain the same set of units digits as do the prime numbers in the second decade is the
(A) fifth
(B) seventh
(C) eighth
(D) ninth
(E) eleventh
Rationale: From question stem, we know that the first decade consists the smallest integers that meet the above definition
1st decade - 00,01,02,03,04,05,06,07,08,09
The second decade has the next smallest integers that meet the criteria
2nd decade - 10,11,12,13,14,15,16,17,18,19
We need to find the decade in which the prime numbers contain the same set of units digits as do the prime numbers in the second decade
2nd decade - 10,11,12,13,14,15,16,17,18,19
3rd decade - 20,21 --> 21 is not prime . So stop and let's move to the next decade
4th decade - 30,31,32,33 --> 33 is not prime. Stop !
5th decade - 40,41,42,43,44,45,46,47,48,49 -- > 49 is not prime
6th decade - 50,51 --> 51 is not prime . Stop !
7th decade - 60,61,62,63 --> 63 is not prime. Stop!
8th decade - 70,71,72,73,74,75,76,77 --> 77 is not prime. Stop!
9th decade - 80,81 --> 81 is not prime. Stop!
All options have been eliminated except one. So Answer should be (E)
10th decade - 90,91,92,93 -->93 is not prime. Stop!
11th decade - 100,101,102,103,104,105,106,107,108,109 - Match !
Therefore, Correct Answer is (E) i.e eleventh decade
Answer: (E) eleventh
Question: The down stream speed of a boat is 100km/hr and its up stream speed is 50km/hr, then find the speed of stream?
(A) 20km/hr
(B) 50km/hr
(C) 100km/hr
(D) 25km/hr
(E) 15km/hr
Rationale: speed of stream = (100-50)/2 = 25 km/hr
Answer is D
Answer: (D) 25km/hr
Question: A garden center sells a certain grass seed in 5-pound bags at $13.80 per bag, 10-pound bags at $20.43 per bag, and 25-pound bags $32.25	per bag. If a customer is to buy at least	65 pounds of the grass seed,	but no more than 80 pounds,	what is the least possible cost of the grass seed that the customer will buy?
(A) $98.73
(B) $96.75
(C) $98.78
(D) $102.07
(E) $105.3
Rationale: there can be 2 cases
1)25+25+10+5=$98.73 or
2)25+25+25=$96.75
A
Answer: (A) $98.73
Question: Machine G and machine B are each used to manufacture 660 sprockets. It takes machine G 10 hours longer to produce 660 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine G. How many sprockets per hour does machine G produces?
(A) 6
(B) 6.6
(C) 60
(D) 100
(E) 110
Rationale: I think the correct answer is A.
Machine G produces at a speed of G sp/hour and B at a speed of B sp/hour.
so, 660/G=(660/B)+10 and B=1,1 G--->1,1*660=660+11G--->A=6, so answer A is correct
Answer: (A) 6
Question: Without the use of calculation, can you find how many seconds are there in a year ?
(A) 42536000
(B) 31536000
(C) 24536000
(D) 33536000
(E) 71536000
Rationale: B
== Mathematical Answer ==
Mathematical Answer = number of seconds in a minute * number of minute in an hour * number hour in a day * number of day in year
60 * 60 * 24 * 365 = 31536000
60 * 60 * 24 * 365.25 = 31557600 (if you want account for leap year)
== We are looking for trick answer (which is 24) ==
Every month contains only 2 second like
A) 2nd January ("second" January)
B) 22nd January (twenty"second" January)
Therefore 2 * 12 months = 24.
Answer: (B) 31536000
Question: if india=90 and france=146 then england equals to?
(A) 215
(B) 216
(C) 217
(D) 218
(E) 219
Rationale: I=9 N=14 D=4 I=9 A=1
(9*1)+(14*2)+(4*3)+(9*4)+(1*5) = 90
Multiply code of each lettr wid 1 2 3 in dat order...
Similarly france wil b
(6*1)+(18*2)+(1*3)+(14*4)+(3*5)+(5*6)= 146
In dat manner england will be 219
ANSWER:E
Answer: (E) 219
Question: There are 15 points in a given plane, no three of which are on the same line. If one of the points is represented as 'A', then how many triangles can be determined with the 15 points that contain the point A?
(A) 91
(B) 105
(C) 182
(D) 210
(E) 455
Rationale: Any 2 points out 14 points will create triangle with third point A, so the answer is C214=91.
Answer: A.
Answer: (A) 91
Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
Rationale: Explanation:
Let the son's present age be x years. Then, man's present age = (x + 24) years
=> (x + 24) + 2 = 2(x + 2)
=> x + 26 = 2x + 4
So, x = 22. Answer: C
Answer: (C) 22
Question: A, B and C enter into a partnership. They invest Rs. 60,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years ?
(A) 9 : 14 : 8
(B) 9 : 8 : 14
(C) 9 : 4 : 2
(D) 9 : 4 : 1
(E) 9 : 4 : 5
Rationale: A : B : C = (60000 x 36) : (80000 x 12 + 40000 x 24) : (120000 x 24 + 40000 x 12)
= 216 : 192 : 336
= 9 : 8 : 14.
Answer: B
Answer: (B) 9 : 8 : 14
Question: A woman purchased $100 of groceries which included $40 worth of vegetables and $60 worth of meat. What % of her total bill went toward purchasing meat?
(A) 25 %
(B) 30 %
(C) 60 %
(D) 50 %
(E) 80 %
Rationale: Number of dollars spent on vegetables = 100 - (40)
= 100 - (40)
= 60
Now, we need to calculate 60 is what percent of 100.
=> 60/100 * 100 = 60 %
C
Answer: (C) 60 %
Question: A toy RC car goes 3 feet per second. A boy wants to add an updated part to his RC that will allow the RC car to travel at 6 feet per second. How far will the upgraded car travel in 1 minute? Round to the nearest hundredth.
(A) 200 feet
(B) 250 feet
(C) 300 feet
(D) 360 feet
(E) 400 feet
Rationale: 6 feet per sec x 60= 360 feet
Answer D
Answer: (D) 360 feet
Question: There are n members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 78 possible combinations in which Michael is not selected, what is the value of n?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: The combinations of two people, in which Michael was not selected = 28
The number of ways two people can be selected from m people = m*(m-1)/2
Let m be the number of people excluding Michael.
Then m*(m-1) = 156 = 13*12
Thus, n = m + 1(Michael) = 14
The answer is C.
Answer: (C) 14
Question: Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.9000. How much third person will get?
(A) 2400
(B) 4000
(C) 2699
(D) 2662
(E) 1821
Rationale: First persons investment = x
Second persons investment = x + 1000
Third persons investments = x + 2000
x + x + 1000 + x + 2000 = 9000
3x = 9000
x = 2000
Ratio = 2000 : 3000 : 4000
2:3:4
4/9 * 9000 = 4000
Answer: B
Answer: (B) 4000
Question: A sum of Rs. 350 made up of 110 coins, which are of either Re.1 or Re.5 denomination. How many coins are of Re.1?
(A) 60
(B) 70
(C) 80
(D) 90
(E) 100
Rationale: 1x+5y= 350
x+y=110
solving the two quations we get x= 50, y= 60 coins.
ANSWER:A
Answer: (A) 60
Question: If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
(A) 10
(B) 20
(C) 25
(D) 30
(E) 35
Rationale: 2:3
2x + 10 : 3x + 10 = 3 : 4
4[2x + 10] = 3[3x + 10]
8x + 40 = 9x + 30
9x - 8x = 40 - 30
x = 10
Then smallest number is = 2
2x = 20
B)
Answer: (B) 20
Question: At what rate percent per annum will a sum of money double in 16 years
(A) 6 ¼ % p.a
(B) 6 % p.a
(C) 8¼ % p.a
(D) 3 ¼ % p.a
(E) 7 ¼ % p.a
Rationale: Let principal = P. Then, S.l. = P and T = 16 yrs.
Rate = (100 x P)/(P*16)% = 6 ¼ % p.a
Answer is B.
Answer: (B) 6 % p.a
Question: If 4 girls can color 48 m long cloth in 2 days, then 6 girls can color 36 m long cloth in
(A) 1 1/5 days
(B) 1/5 day
(C) 1 day
(D) 2 days
(E) 3 days
Rationale: The length of cloth painted by one girl in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 girls = 36/ 6 × 6 = 1 day.
C
Answer: (C) 1 day
Question: m and n are the x and y coordinates, respectively, of a point in the coordinate plane. If the points (m, n) and (m + p, n + 12) both lie on the line defined by the equation x = (y/4) - (2/5), what is the value of p?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: x = (y/4) - (2/5), and so y = 4x + 8/5. The slope is 4.
(n+12-n) / (m+p-m) = 3
p = 3
The answer is C.
Answer: (C) 3
Question: In a box of 10 pencils, a total of 2 are defective. If a customer buys 3 pencils selected at random from the box, what is the probability that neither pencils will be defective?
(A) 1/12
(B) 7/15
(C) 2/13
(D) 2/15
(E) 1/17
Rationale: First, there are 8C3 ways you can select 3 good pencils from 4 good ones.
Second, there are 10C3 ways you select 3 pencils from 6 ones in the box.
Then, the probability that neither pen will be defective is: 8C3/10C3=56/120 =7/15
Answer is B
Answer: (B) 7/15
Question: A class consists of 15 biology students and 10 chemistry students. If you pick two students at the same time, what's the probability that one is maths and one is chemistry ?
(A) 2/7
(B) 5/7
(C) 1/2
(D) 3/7
(E) 1/2
Rationale: P(1st b, 2nd c) = 15/25*10/24 = 150/600 = 1/4;
P(1st c, 2nd b ) = 10/25*15/24 = 150/600 = 1/4.
P = 1/4 + 1/4 = 1/2.
Answer: C.
Answer: (C) 1/2
Question: The top of a 15 m. high tower makes an angle of elevation of 60 degree with the bottom of an electric pole and an angle of 30 degree with the top of the pole. What is the height of the pole?
(A) 12 m.
(B) 10 m.
(C) 11 m.
(D) 5 m.
(E) 15 m.
Rationale: let distance between tower and pole be x & height of pole be y.
x=15/tan60 & (15-y)/x = tan 30
thus solving two equation gives y= 10m
ANSWER:B
Answer: (B) 10 m.
Question: A farm used two harvesting machines, H and K, to harvest 100 acres of wheat. Harvesting machine H, working alone at its constant rate, harvested 40 acres of wheat in 8 hours. Then harvesting machine K was brought in, and harvesting machines H and K, working together at their respective constant rates, harvested the remaining acres of wheat in 4 hours. Harvesting machine K harvested how many acres of wheat per hour?
(A)  7
(B)  8
(C)  11
(D)  13
(E)  15
Rationale: Rate of H = 4 acres/hr
Remaining land to be harvested = 100 - 40 = 60
Rate of H and K = 60/4 = 15 acres/hr
Rate of K = 15- 4 = 11
Answer: C
Answer: (C)  11
Question: In the new budget the price of wheat rose by 8%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase?
(A) 7.5%
(B) 7.41%
(C) 10.9%
(D) 12.6%
(E) 15%
Rationale: Reduce in consumption = R/(100+R) *100% = 8/108 *100 = 7.41%
Answer is B
Answer: (B) 7.41%
Question: Of the books standing in a row on a shelf, an atlas is the 30th book from the left and the 33rd book from the right. If 2 books to the left of the atlas and 7 books to the right of the atlas are removed from the shelf, how many books will be left on the shelf?
(A) 53
(B) 57
(C) 58
(D) 61
(E) 63
Rationale: 100%. There are total of 30+33-1=62 books and 2+7=9 books are removed, thus 62-9=53 books are left.
Answer: A.
Answer: (A) 53
Question: For which of the following functions is f(e+b)=f(e)+f(b) for all positive numbers e and b?
(A) a) f(x)=x^2
(B) b) f(x)=x+1
(C) c) f(x)=root x
(D) d) f(x)=2/x
(E) e) f(x)= -3x
Rationale: f(e+b)=f(e)+f(b) Its E
Answer: (E) e) f(x)= -3x
Question: Evaluate:55- 12*3*2 =?
(A) 42
(B) 47
(C) 62
(D) 72
(E) 82
Rationale: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right
12**2 = 4* 2 = 8
Hence
55 - 12*3*2 = 55- 8 = 47
correct answer B
Answer: (B) 47
Question: You forgot the three digit code of your safe. But you have written some hints to calculate the code if you forgot the code.
Below are the hints that you have written
Hint-1 : One of the numbers is correct and is placed in its correct position
5 4 7
Hint-2: Nothing is correct
5 3 0
Hint-3: Two numbers are correct but not placed at its correct position.
2 5 9
Hint-4: One number is correct but not placed at its correct position.
7 0 6
Hint-5: One number is correct but not placed at its correct position.
6 4 9
What's is the code.
(A) 827
(B) 728
(C) 923
(D) 323
(E) 927
Rationale: E
927
1) 5 4 7 : 7 is placed correctly
2) 5 3 0 : None of the numbers is in the code
3) 2 5 9 : 2 & 9 are correct number of code but placed at wrong position
4) 7 0 6: Number 7 is there but placed at wrong position
5) 6 4 9: Number 9 is there but placed at wrong position
Answer: (E) 927
Question: If x/y=4 and y is not '0' what % of x is 2x-y
(A) 150%
(B) 175%
(C) 200%
(D) 250%
(E) 350%
Rationale: let z be the percentt
x*z/100=2x-y
zx=7y*100
z=700y/4y
z=350/2
z=175%
ANSWER:B
Answer: (B) 175%
Question: If x/y=4 and y is not '0' what % of x is 2x-y
(A) 150%
(B) 175percent
(C) 200%
(D) 250%
(E) 350%
Rationale: let z be the percent
x*z/100= 2x-y
zx=7y* 100
z=700y/4y
z=350/2
z=175%
ANSWER:B
Answer: (B) 175percent
Question: Find the middle one when The sum of three consecutive even numbers is 21?
(A) 7
(B) 10
(C) 8
(D) 6
(E) 11
Rationale: 3 consecutive numbers can be a - 1, a, a + 1
So sum of numbers = 3a = 21.
Hence a = 7.
A
Answer: (A) 7
Question: In a class, there are 21 boys who are over 160 cm tall. If these constitute three–fourth of the boys and the total number of boys is one–fourth of the total number of students in the class. What is the total number of girls in the class
(A) 22
(B) 78
(C) 267
(D) 997
(E) 722
Rationale: Answer:A
Answer: (A) 22
Question: Two stations P and Q are 245 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?
(A) 10 am
(B) 12 am
(C) 10.30 am
(D) 12.30 am
(E) 1 pm
Rationale: Assume both trains meet after x hours after 7 am
Distance covered by train starting from P in x hours = 20x km
Distance covered by train starting from Q in (x-1) hours = 25(x-1)
Total distance = 245
=> 20x + 25(x-1) = 245
=> 45x = 270
=> x= 6
Means, they meet after 6 hours after 7 am, ie, they meet at 1pm
Answer is E.
Answer: (E) 1 pm
Question: A cricketer has a certain average for 10 innings. In the eleventh inning, he scored 108 runs, thereby increasing his average by 6 runs. His new average is
(A) 42 runs
(B) 45 runs
(C) 48 runs
(D) 52 runs
(E) None
Rationale: Sol.
Let the average for 10 innings be x. Then,
10x + 108 / 11 = x+6 ⇔ 11x + 66 = 10x + 108 ⇔ x = 42.
∴ New average = (x+6) = 48 runs.
Answer C
Answer: (C) 48 runs
Question: A radio station has to choose three days of the seven in a week to broadcast a certain program, and that set will repeat each week. The program can be broadcast equally on any of the seven weekdays —- weekdays vs. weekends don’t matter at all —- nor does it matter whether the days the program airs are adjacent or not. Absolutely any three of the seven weekdays can be chosen. How many different three-day combinations of the seven weekdays can be constructed?
(A) 9
(B) 15
(C) 21
(D) 35
(E) 56
Rationale: Behind the story, we are really being asked to evaluate 7C3. We could use the factorial formula, but above we conveniently happen to have Pascal’s Triangle written out to the seventh row. We see that 7C3, the third entry of the seventh row, is 35. Answer = D.
Answer: (D) 35
Question: At coffee factory, each employee working the second shift produced 2/3 as many widgets as each employee working the first shift. If the first shift has 3/4 as many employees, what fraction of the total widgets did the second shift produce?
(A) 8/17
(B) 1/2
(C) 8/9
(D) 9/8
(E) 17/8
Rationale: At coffee factory, Let the first shift have 3 employee and each produce 3 widgets, so the total number of widgets produced by the first shift is 3*3=9;
Then the second shift would have 4 employees and each second shift employee would produce 3*2/3=2 widgets, so the total number of widgets produced by the second shift employees would be 4*2=8;
The ratio of the second shift production to the total is 8/(9+8)=8/17.
Answer: A.
Answer: (A) 8/17
Question: Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 55% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?
(A)  5%
(B)  10%
(C)  15%
(D)  45%
(E)  30%
Rationale: Total = n(A) + n(B) - n(Exactly 2 products) -2 (AnBnC) + Neither.
Neither is zero.
Hence 100 = 60 + 50 + 55 - n (Exactly 2 products) - 2*10
100 = 145 - n (Exactly 2 products) => n (Exactly 2 products) = 45.
Answer: D
Answer: (D)  45%
Question: In a rectangular coordinate system, what is the area of a rectangle whose vertices have the coordinates (-9, 1), (1, 1), (1, -8) and (-9, -8)?
(A) 72
(B) 180
(C) 70
(D) 90
(E) 140
Rationale: Length of side 1= 9+1=10
Length of side 2= 8+1= 9
Area of rectangle= 10*9= 90
D is the answer
Answer: (D) 90
Question: If g and y are integers, then gy(g + y) is
(A) Always positive
(B) Always negative
(C) Positive when g is positive
(D) Negative when g is negative
(E) It cannot be determined by the information given
Rationale: Given g and y are integers, then gy(g + y)
Let's take even as 2 / -2 and odd as 3 / -3..we get the following.. and IMO option D is correct answer..
I presume its Option E if am not missing anything.
g=-3 and y=1
gy(g + y) is positive = 6
Answer: (E) It cannot be determined by the information given
Question: What will come in place of the x in the following Number series? 73205, 6655, 605, 55, x
(A) 64535
(B) 73205
(C) 79345
(D) 85463
(E) 84543
Rationale: (B)
5 x 11 = 55, 55 x 11 = 605, 605 x 11 = 6655, 6655 x 11 = 73205
Answer: (B) 73205
Question: 10% of the inhabitants of a village having died of cholera, a panic set in, during which 25% of the remaining inhabitants left the village. The population is then reduced to 4050. Find the number of original inhabitants?
(A) 4500
(B) 5000
(C) 3000
(D) 6000
(E) 5700
Rationale: Let the total number of original inhabitants be x
Then, (100-25)% of (100-10)% of x = 4050
75/100 * 90/100 * x = 4050
x = 6000
Answer is D
Answer: (D) 6000
Question: A watch passes through three hands and each gains 25%. If the 3rd sells it for Rs250, what did the 1st pay for it?
(A) 110
(B) 120
(C) 128
(D) 143
(E) 145
Rationale: First Purchased = 250 Wes= 128
C
Answer: (C) 128
Question: On her annual road trip to visit her family in Seal Beach, California, Traci stopped to rest after she traveled 1⁄3 of the total distance and again after she traveled 1⁄4 of the distance remaining between her first stop and her destination. She then drove the remaining 300 miles and arrived safely at her destination. What was the total distance, in miles, from Traci’s starting point to Seal Beach?
(A)  600
(B)  300
(C)  350
(D)  400
(E)  550
Rationale: Let D = total distance
Traci traveled 1/3 = D/3
i.e. remaining distance = 2D/3
She traveled 1/4 th of 2D/3 = D/6
Thus:
D = (D/3) + (D/6) + 300
D = 600
ANSWER: A
Answer: (A)  600
Question: Nancy works 3 days per week at a rate of x dollars per day. If Nancy works more than 3 days per week, any extra days are paid at double her normal rate. Nancy worked 4 weeks with no overtime, and then worked 4 more weeks, each with y days of overtime. Which of the following represents Nancy’s total earnings over this period?
(A) a) 3y(7x+2xy)
(B) b) 3x+12y
(C) c) 3xy(7x+2)
(D) d) 8x(y+3)
(E) e) 4x(y+8)
Rationale: Payment of a week for 3 days a week = $3x
Payment of 4 weeks for 3 days a week = $3x*4 = $12x
Payment of a week for y days overtime a week = $3x+$2xy
Payment of 4 weeks for y days overtime a week = ($3x+$2xy)*4
Total Earnings = $12x + ($3x+$2xy)*4 = 24x+8xy =8x(y+3)
Answer: option D
Answer: (D) d) 8x(y+3)
Question: One-third less than 40% of 180 is equal to:
(A) 15
(B) 30
(C) 35
(D) 40
(E) 48
Rationale: Lots of ways to tackle this.
40% of 180 =72
1/3 of 72= 24
So, 1/3 less than 72 is equal to 72- 24 = 48
Answer: E
Answer: (E) 48
Question: The average of 5 consecutive odd numbers is 61. What is the difference between the highest and lowest numbers?
(A) 8
(B) 10
(C) 12
(D) 15
(E) 20
Rationale: Let the numbers be x, x+2, x+4, x+6, x+8
Then, (x+ x+2+ x+4+ x+6+ x+8)/5 = 61
x = 57
Required answer is = 57+8-57 = 8
Answer is A
Answer: (A) 8
Question: Arrange the following in a meaningful sequence :
1. Letter
2. Sentence
3. Word
4. Phrase
(A) 1, 2, 4, 3
(B) 2, 1, 3, 4
(C) 2, 4, 1, 3
(D) 1, 3, 4, 2
(E) None of these
Rationale: Explanation:
A group of letters makes a word. A group of words makes a phrase. A group of phrases makes a sentence.
Thus, correct order is 1, 3, 4, 2.
ANSWER D
Answer: (D) 1, 3, 4, 2
Question: Brittany's income is 12 percent more than Tina's income, and Tina's income is 15 percent less than Jean's income. What percent of Jean's income is Brittany's income?
(A) 95.2%
(B) 91.2%
(C) 96.2%
(D) 94.2%
(E) 92.2%
Rationale: Jean's income = 100 (assume);
Tina's income = 85 (15 percent less than Jean's income);
Brittany's income = 95.2 (12 percent more than Tina's income).
Thus, Brittany's income (95.2) is 95.2% of Jean's income (100).
Answer: A
Answer: (A) 95.2%
Question: Find the probability that the sum of dots appearing in two successive throws of two dice is every time 7
(A) 1/6
(B) 2/6
(C) 3/6
(D) 4/6
(E) 5/6
Rationale: No of sample space are n(s)=(6*6)=36
no of even aren n(E)={(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)}=6
then Probability=n(e)/n(s)=6/36 =1/6
Ans is 1/6.
ANSWER:A
Answer: (A) 1/6
Question: P is a set containing 8 different positive odd numbers. Q is a set containing 7 different numbers, all of which are members of P. Which of the following statements CANNOT be true?
(A) The range of Q is even.
(B) The mean of P is even.
(C) The mean of Q is even.
(D) The range of P is equal to the range of Q.
(E) The median of Q is equal to the mean of Q.
Rationale: Given: P is a set containing 8 different positive odd numbers
Easily inferred: Q is a set containing 7 differentoddnumbers
(A) The range of Q is even. - Always even, since it is a difference of two odd numbers
(B) The mean of P is even. - can be. suppose 8 numbers consist of 4 pairs of (16n-1,16n+1) for different values of n. Adding these will give a multiple of 16, which when divided by 8 (to arrive at mean), will give an even number
(C) The mean of Q is even. - Cannot be. Mean = (sum of 7 odd numbers)/7 = Odd number/odd number thus cannot be even.
(D) The range of P is equal to the range of Q.
(E) The median of Q is equal to the mean of Q
Option C.
Answer: (C) The mean of Q is even.
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?
(A) 54
(B) 62
(C) 48
(D) 62
(E) 62
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.9 = 2 km = 2000 m.
Required time = 2000 * 3/125 = 48 sec.
Answer:C
Answer: (C) 48
Question: In five football games thus far this season, Barry has run for 98, 107, 85, 89, and 91 yards. At a minimum, how many yards F will he need to gain this Sunday if he wants to keep his season average above 100 yards?
(A) 101
(B) 116
(C) 130
(D) F=131
(E) F=141
Rationale: Sorry the answer F=131 is D.
Answer: (D) F=131
Question: What percent of a day in 6 hours?
(A) 10%
(B) 15%
(C) 20%
(D) 25%
(E) 50%
Rationale: Required percentage = 6/24 * 100 = 100/4 = 25%
Answer is D
Answer: (D) 25%
Question: The average (arithmetic mean) of all scores on a certain algebra test was 90. If the average of the 8 male students’ grades was 84, and the average of the female students’ grades was 92, how many female students took the test?
(A) 8
(B) 9
(C) 10
(D) 21
(E) 24
Rationale: Total Marks of male = M
Total Marks of female = F
Number of males = 8
Number of females = f
Given: (M+F)/(8+f) = 90 -------------1
Also given, M/8 = 84 Thus M = 672 ---------2
Also, F/f = 92 thus F = 92 F - --------3
Put 2 and 3 in 1: we get
(672+92f)/(8+f) = 90
solving this we get f = 24
Ans: E
Answer: (E) 24